JEE Main September 3 2020 Shift 1 Question Paper with Answer Key

Physics

1. A block of mass m = 1 kg slides with velocity v = 6 m/s on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about O and swings as a result of the collision making angle θ before momentarily coming to rest. If the rod has mass M = 2 kg, and length l = 1m, the value θ of is approximately: (take g = 10 m/s2)

(1)  49°

(2)  63°

(3)  69°

(4)  55°

Answer: (2)

2. A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block of mass 2 kg is attached to its free end. A transverse short wave train of wavelength 6 cm is produced at the lower end of the rope. What is the wavelength of the wave train (in cm) when it reaches the top of the rope?

(1)  12

(2)  3

(3)  9

(4)  6

Answer: (1)

3. When a diode is forward biased, it has a voltage drop of 0.5 V. The safe limit of current through the diode is 10 mA. If a battery of emf 1.5 V is used in the circuit, the value of minimum resistance to be connected in series with the diode so that the current does not exceed the safe limit is:

(1)  300 Ω

(2)  200 Ω

(3)  50 Ω

(4)  100 Ω

Answer: (4)

4. Using screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as:

(1)  2.125 cm

(2)  2.124 cm

(3)  2.123 cm

(4)  2.121 cm

Answer: (2)

5. Model a torch battery of length l to be made up of a thin cylindrical bar of radius ‘a’ and a concentric thin cylindrical shell of radius ‘b’ filled in between with an electrolyte of resistivity ρ (see figure). If the battery is connected to a resistance of value R, the maximum joule heating in R will take place for:

(1) 

(2) 

(3) 

(4) 

Answer: (4)

6. Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature T is:

(1) 

(2)  3RT

(3) 

(4) 

Answer: (2)

7. An elliptical loop having resistance R, of semi major axis a, and semi minor axis b is placed in magnetic field as shown in the figure. If the loop is rotated about the x-axis with angular frequency ω, the average power loss in the loop due to Joule heating is:

(1) 

(2) 

(3) 

(4)  Zero

Answer: (3)

8. A balloon filled with helium (32° C and 1.7 atm.) bursts. Immediately afterwards the expansion of helium can be considered as:

(1)  reversible isothermal

(2)  irreversible isothermal

(3)  reversible adiabatic

(4)  irreversible adiabatic

Answer: (4)

9. When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to:

(1)  1.02 eV

(2)  0.61 eV

(3)  0.52 eV

(4)  0.81 eV

Answer: (2)

10. Two isolated conducting spheres S1 and S2 of radius (2/3) R and (1/3) R have 12 μC and –3μC charges, respectively, and are at a large distance from each other. They are now connected by a conducting wire. A long time after this is done the charges on S1 and S2 are respectively:

(1)  6 μC and 3 μC

(2)  4.5 μC on both

(3)  + 4.5 μC and –4.5 μC

(4)  3 μC and 6 μC

Answer: (1)

11. In a radioactive material, fraction of active material remaining after time t is 9/16. The fraction that was remaining after t/2 is:

(1)  3/4

(2)  7/8

(3)  4/5

(4)  3/5

Answer: (1)

12. Moment of inertia of a cylinder of mass M, length L and radius R about an axis passing through its centre and perpendicular to the axis of the cylinder is  If such a cylinder is to be made for a given mass of a material, the ratio L /R for it to have minimum possible I is:

(1)  2/3

(2)  3/2

(3)  √2/3

(4)  √3/2

Answer: (4)

13. A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth’s radius Re. By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become √3/2 times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is R. Value of R is:

(1)  2Re

(2)  3Re

(3)  4Re

(4)  2.5 Re

Answer: (2)

14. Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is:

(1)  4 : 1

(2)  2 : 1

(3)  0.8 : 1

(4)  8 : 1

Answer: (4)

15. In a Young’s double slit experiment, light of 500 nm is used to produce an interference pattern. When the distance between the slits is 0.05 mm, the angular width (in degree) of the fringes formed on the distance screen is close to:

(1)  0.17°

(2)  0.07°

(3)  0.57°

(4)  1.7°

Answer: (3)

16. A 750 Hz, 20 V (rms) source is connected to a resistance of 100 Ω, an inductance of 0.1803 H and a capacitance of 10 μ F all in series. The time in which the resistance (heat capacity 2 J/°C) will get heated by 10°C. (assume no loss of heat to the surroundings) is close to:

(1)  245 s

(2)  365 s

(3)  418 s

(4)  348 s

Answer: (4)

17. Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side 10 cm, 50 turns and carrying current I (Ampere) in units of μ0I/π is:

(1)  250√3

(2)  50√3

(3)  500√3

(4)  5√3

Answer: (3)

18. The magnetic field of a plane electromagnetic wave is  where c = 3 × 108 ms1 is the speed of light.

The corresponding electric field is:

(1) 

(2) 

(3) 

(4) 

Answer: (1)

19. A charged particle carrying charge 1 μC is moving with velocity  If an external magnetic field of  exists in the region where the particle is moving then the force on the particle is  The vector  is:

(1) 

(2) 

(3) 

(4) 

Answer: (3)

20. In the circuit shown in the figure, the total charge is 750 μC and the voltage across capacitor C2 is 20 V. Then the charge on capacitor C2 is:

(1)  650 μC

(2)  450 μC

(3)  590 μC

(4)  160 μC

Answer: (3)

21. A person of 80 kg mass is standing on the rim of a circular platform of mass 200 kg rotating about its axis at 5 revolutions per minute (rpm). The person now starts moving towards the centre of the platform. What will be the rotational speed (in rpm) of the platform when the person reaches its centre _____?

Answer: (9)

22. An observer can see through a small hole on the side of a jar (radius 15 cm) at a point at height of 15 cm from the bottom (see figure). The hole is at a height of 45 cm. When the jar is filled with a liquid up to a height of 30 cm the same observer can see the edge at the bottom of the jar. If the refractive index of the liquid is N/100, where N is an integer, the value of N is _____.

Answer: (158)

23. A cricket ball of mass 0.15 kg is thrown vertically up by a bowling machine so that it rises to a maximum height of 20 m after leaving the machine. If the part pushing the ball applies a constant force F on the ball and moves horizontally a distance of 0.2 m while launching the ball, the value of F(in N) is (g = 10 ms–2)_____.

Answer: (150 N)

24. When a long glass capillary tube of radius 0.015 cm is dipped in a liquid, the liquid rises to a height of 15 cm within it. If the contact angle between the liquid and glass to close to 0°, the surface tension of the liquid, in milli Newton m–1 is [ρ(liquid) =900 kgm–3 , g = 10 ms–2] (Give answer in closes integer)____.

Answer: (101)

25. A bakelite beaker has volume capacity of 500 cc at 30°C. When it is partially filled with Vm volume (at 30°C) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If γ(beaker) = 6 × 10–6 °C–1 and γ(mercury)= 1.5 × 10–4 °C–1, where γ is the coefficient of volume expansion, then Vm (in cc) is close to ____.

Answer: (20)

Chemistry

1. It is true that:

(a)  A second order reaction is always a multistep reaction

(b)  A first order reaction is always a single step reaction

(c)  A zero order reaction is a multistep reaction

(d) A zero order reaction is a single step reaction

Answer: (c)

2. An acidic buffer is obtained on mixing:

(a)  100 mL of 0.1 M HCl and 200 mL of 0.1 M CH3COONa

(b)  100 mL of 0.1 M HCl and 200 mL of 0.1 M NaCl

(c)  100 mL of 0.1 M CH3 COOH and 100 mL of 0.1 M NaOH

(d) 100 mL of 0.1 M CH3COOH and 200 mL of 0.1 M NaOH

Answer: (1)

3. The Kjeldahl method of Nitrogen estimation fails for which of the following reaction products?

(a)  (a), (c) and (d)

(b)  (b) and (c)

(c)  (c) and (d)

(d) (a) and (d)

Answer: (c)

4. If the boiling point of H2O is 373 K, the boiling point of H2S will be :

(a)  greater than 300 K but less than 373 K

(b)  equal to 373 K

(c)  more than 373 K

(d) less than 300 K

Answer: (d)

5. The complex that can show optical activity is :

(a)  cis– [CrCl2 (ox)2]3− (ox – oxalate)

(b)  trans – [Fe (NH3)2 (CN)4]

(c)  trans – [Cr (Cl2) (ox)2]3−

(d) cis– [Fe (NH3)2 (CN)4]−

Answer: (a)

6. Which one of the following compounds possesses the most acidic hydrogen?

Answer: (c)

7. Aqua regia is used for dissolving noble metals (Au, Pt, etc.). The gas evolved in this process is :

(a)  N2O3

(b)  N2

(c)  N2O5

(d) NO

Answer: (d)

8. The antifertility drug “Novestrol” can react with:

(a)  Br2 / water; ZnCl2 / HCl; FeCl3

(b)  Br2 / water; ZnCl2 / HCl; NaOCl

(c)  Alcoholic HCN; NaOCl; ZnCl2 / HCl

(d) ZnCl2 / HCl; FeCl3; Alcoholic HCN

Answer: (a)

9. Which of the following compounds produces an optically inactive compound on hydrogenation?

Answer: (c)

10. Of the species, NO, NO+, NO2+ and NO, the one with minimum bond strength is:

(a)  NO

(b)  NO+

(c)  NO2+

(d) NO

Answer: (a)

11. Glycerol is separated in soap industries by:

(a)  Fractional distillation

(b)  Distillation under reduced pressure

(c)  Differential extraction

(d) Steam distillation

Answer: (b)

12. Thermal power plants can lead to:

(a)  Ozone layer depletion

(b)  Blue baby syndrome

(c)  Eutrophication

(d) Acid rain

Answer: (d)

13. Henry’s constant (in kbar) for four gases ɑ, β, 𝛾, δ and δ in water at 298 K is given below:

α β γ δ
KH 50 2 2 × 10−5 0.5

(density of water = 103 kg m3 at 298 K)

This stable implies that :

(a)  solubility of γ at 308 K is lower than at 298 K

(b)  The pressure of a 55.5 molal solution of δ is 250 bar

(c)  α has the highest solubility in water at a given pressure

(d) The pressure of a 55.5 molal solution of γ is 1 bar

Answer: (a)

14. The electronic spectrum of [Ti(H2O)6]3+ shows a single broad peak with a maximum at 20,300 cm-1. The crystal field stabilization energy (CFSE) of the complex ion, in kJ mol−1, is:

(1 kJ mol−1 = 83.7 cm−1)

(a)  83.7

(b)  242.5

(c)  145.5

(d) 97

Answer: (d)

15. The atomic number of the element unnilennium is:

(a)  109

(b)  102

(c)  119

(d) 108

Answer: (1)

16. An organic compound [A], molecular formula C10H20O2 was hydrolyzed with dilute sulphuric acid to give a carboxylic acid [B] and an alcohol [C]. Oxidation of [C] with CrO3−H2SO4 produced [B]. Which of the following structures are not possible for [A]?

Answer: (b)

17. The mechanism of SN1 reaction is given as:

A student writes general characteristics based on the given mechanism as:

(1) The reaction is favoured by weak nucleophiles.

(2) RΘ would be easily formed if the substituents are bulky.

(3) The reaction is accompanied by racemization.

(4) The reaction is favoured by non-polar solvents. Which observations are correct?

(a)  (1) and (2)

(b)  (1), (2) and (3)

(c)  (1) and (3)

(d) (2) and (4)

Answer: (b)

18. Tyndall effect is observed when:

(a)  The diameter of dispersed particles is much smaller than the wavelength of light used.

(b)  The diameter of dispersed particles is much larger than the wavelength of light used.

(c)  The refractive index of the dispersed phase is greater than that of the dispersion medium.

(d) The diameter of dispersed particles is similar to the wavelength of light used.

Answer: (d)

19. Let CNaCl and CBaSO4 be the conductances (in S) measured for saturated aqueous solutions of NaCl and BaSO4, respectively, at a temperature T. Which of the following is false?

(a)  CNaCl (T2) > CBaSo4 (T1) for T2 > T1

(b)  CBaSo4 (T2) > CNaCl (T1) for T2 > T1

(c)  Ionic mobilities of ions from both salts increase with T.

(d) CNaCl >> CBaSo4 at a given T

Answer: (d)

20. In a molecule of pyrophosphoric acid, the number of P−OH, P = O and P − O − P bonds / moiety(ies) respectively are:

(a)  3, 3 and 3

(b)  4, 2 and 1

(c)  2, 4 and 1

(d) 4, 2 and 0

Answer: (b)

21. The mole fraction of glucose (C6H12O6) in an aqueous binary solution is 0.1. The mass percentage of water in it, to the nearest integer, is _______.

Answer: (47%)

22. The volume strength of 8.9 M H2O2 solution calculated at 273 K and 1 atm is ______. (R = 0.0821 L atm K1 mol1) (rounded off to the nearest integer)

Answer: (100)

23. An element with molar mass 2.7 10−2 kg mol−1 forms a cubic unit cell with edge length 405 pm. If its density is 2.7 103 kg m−3, the radius of the element is approximately ______ 10−12 m (to the nearest integer).

Answer: (143)

24. The total number of monohalogenated organic products in the following (including stereoisomers) reaction is ______.

Answer: (8)

25. The photoelectric current from Na (Work function, w0 = 2.3 eV) is stopped by the output voltage of the cell Pt(s) H2 (g, 1 Bar) HCl (aq. pH =1) AgCl s Ag(s). The pH of aq. HCl required to stop the photoelectric current form K(w0 = 2.25 eV), all other conditions remaining the same, is _______ 102 (to the nearest integer). Given, 

Answer: (58)

Mathematics

1. The value of (2.1P02P1+4.3P2….. up to 51th term) +(1!-2!+3!-…… up to 51th term) is equal to:

(1)  1 – 51(51)!

(2)  1 + (52)!

(3)  1

(4)  1 5 (51)!

Answer: (2)

2. Let P be a point on the parabola, y2 = 12x and N be the foot of the perpendicular drawn from P on the axis of the parabola. A line is now drawn through the mid-point M of PN, parallel to its axis which meets the parabola at Q. If the y-intercept of the line NQ is 4/3 , then:

(1)  PN = 4

(2)  MQ = 1/3

(3)  PN = 3

(4)  MQ = 1/4

Answer: (4)

3. If = AX3 + BX2 + Cx + D, then B + C is equal to:

(1)  1

(2)  −1

(3)  −3

(4)  9

Answer: (3)

4. The foot of the perpendicular drawn from the point (4,2,3) to the line joining the points (1,2,3) and (1,1,0) lies on the plane:

(1)  x – y – 2z = 1

(2)  x – 2y + z = 1

(3)  2x + y – z = 1

(4)  x + 2y – z = 1

Answer: (3)

5. If y2 + loge(cos2x) = y, x∈(−π/2, π/2), then

(1)  |y´(0)|+|y´´(0)| = 1

(2)  |y´´(0)| = 0

(3)  |y´(0)|+|y´´(0)| = 3

(4)  |y´´(0)| = 2

Answer: (4)

6. is equal to:

(1)  5π/4

(2)  3π/2

(3)  7π/4

(4)  π/2

Answer: (2)

7. A hyperbola having the transverse axis of length √2 has the same foci as that of the ellipse 3x2 + 4y2 = 12, then this hyperbola does not pass through which of the following points ?

(1) 

(2) 

(3) 

(4) 

Answer: (1)

8. For the frequency distribution

Variant (X): x1 x2 x3…x15

Frequency (f): f1 f2 f3…f15

where 0 < x1 < x2 < x3 <… x15 ≤ 10 and  the standard deviation cannot be:

(1)  1

(2)  4

(3)  6

(4)  2

Answer: (3)

9. A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared atleast once is:

(1)  1/3

(2)  1/4

(3)  1/8

(4)  1/9

Answer: (4)

10. If the number of integral terms in the expansion of (31/2 +51/8)n is exactly 33, then the least value of n is:

(1)  128

(2)  248

(3)  256

(4)  264

Answer: (3)

11. 

(1)  π2

(2)  π2/2

(3)  √2π2

(4)  2π2

Answer: (1)

12. Consider the two sets:

A = {m ∈ R : both the roots of x2 − (m + 1) x + m + 4 = 0 are real} and B = [−3, 5).

Which of the following is not true ?

(1)  A-B = (−∞,−3) ∪ (5, ∞)

(2)  A ∩ B = {−3}

(3)  B-A = (−3, 5)

(4)  A U B = R

Answer: (1)

13. The proposition p − > ∼ (p ˄ q) is equivalent to:

(1)  (∼p) ˅(∼ q)

(2)  (∼ p) ˄q

(3)  q

(4)  (∼ p) ˅q

Answer: (4)

14. The function, f(x) = (3x − 7)x2/3, x ∈ R is increasing for all x lying in:

(1) 

(2) 

(3) 

(4) 

Answer: (3)

15. If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is:

(1)  1/6

(2)  1/5

(3)  1/4

(4)  1/7

Answer: (1)

16. The solution curve of the differential equation,  which passes through the point (0, 1), is:

(1) 

(2) 

(3) 

(4) 

Answer: (4)

17. The area (in sq. units) of the region  is

(1)  23/16

(2)  79/16

(3)  23/6

(4)  79/24

Answer: (4)

18. If α and β are the roots of the equation x2 + px + 2 = 0 and 1/α and 1/β are the roots of the equation 2x2 + 2qx + 1 = 0, then is  equal to:

(1) 

(2) 

(3) 

(4) 

Answer: (3)

19. The lines  and  

(1)  do not intersect for any values of l and m

(2)  intersect when l = 1 and m = 2

(3)  intersect when l = 2 and m = 1/2

(4)  intersect for all values of l and m

Answer: (1)

20. Let [t] denote the greatest integer ≤t. If for some λ ∈ R −{0, 1},  then L is equal to:

(1)  0

(2)  2

(3)  1/2

(4)  1

Answer: (2)

21. If  then the value of k is …….

Answer: (8)

22. The diameter of the circle, whose centre lies on the line x + y = 2 in the first quadrant and which touches both the lines x = 3 and y = 2, is ……

Answer: (3)

23. The value of  is equal to………..

Answer: (4)

24. Let  and A4[aij]. If a11 = 109, then a22 is equal to…………….

Answer: (10)

25. If  (m, n ∈ N) then the greatest common divisor of the least values of m and n is……………..

Answer: (4)

JEE Main September 2 2020 Shift 2 Question Paper with Answer Key

Physics

1. If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is:

(1)  [P1/2 AT–1]

(2)  [PA1/2 T–1]

(3)  [PA1/2 T–1]

(4)  [P2 AT–2]

Answer: (2)

2. Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0.1 kg –m2 and 10 rad s–1 respectively while those for the second one are 0.2 kg–m2 and 5 rad s–1 At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The Kinetic energy of the combined system is:

(1)  2/3 J

(2)  10/3 J

(3)  5/3 J

(4)  20/3 J

Answer: (4)

3. A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is 1.878 × 10–4. The mass of the particle is close to:

(1)  4.8 × 10–27 kg

(2)  9.1 × 10–31 kg

(3)  9.7 × 10–28 kg

(4)  1.2 × 10–28 kg

Answer: (3)

4. A potentiometer wire PQ of 1 m length is connected to a standard cell E1. Another cell E2 of emf 1.02 V is connected with a resistance ‘r’ and switch S (as shown in figure). With switch S open, the null position is obtained at a distance of 49 cm from Q. The potential gradient in the potentiometer wire is:

(1)  0.03 V/cm

(2)  0.02 V/cm

(3)  0.04 V/cm

(4)  0.01 V/cm

Answer: (2)

5. In the following digital circuit, what will be the output at ‘Z’, when the input (A,B) are (1,0), (0,0), (1,1), (0,1):

(1)  0, 1, 0, 0

(2)  1, 1, 0, 1

(3)  0, 0, 1, 0

(4)  1, 0, 1, 1

Answer: (3)

6. A wire carrying current I is bent in the shape ABCDEFA as shown, where rectangle ABCDA and ADEFA are perpendicular to each other. If the sides of the rectangles are of lengths a and b, then the magnitude and direction of magnetic moment of the loop ABCDEFA is:

(1) 

(2) 

(3) 

(4) 

Answer: (3)

7. A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of the following options then correctly describe the trajectory of the mass? (Curves are drawn schematically and are not to scale).

Answer: (3)

8. In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by  What is the unit vector along direction of propagation of the wave.

(1) 

(2) 

(3) 

(4) 

Answer: (1)

9. An inductance coil has a reactance of 100 Ω. When an AC signal of frequency 1000 Hz is applied to the coil, the applied voltage leads the current by 45°. The self-inductance of the coil is:

(1)  6.7 × 10–7 H

(2)  5.5 × 10–5 H

(3)  1.1 × 10–1 H

(4)  1.1 × 10–2 H

Answer: (4)

10. This displacement time graph of a particle executing S.H.M. is given in figure : (sketch is schematic and not to scale)

Which of the following statements is/are true for this motion?

(A) The force is zero at t = 3T/4

(B) The acceleration is maximum at t=T

(C) The speed is maximum at t = T/4

(D) The P.E. is equal to K.E. of the oscillation at t = T/2

(1)  (B), (C) and (D)

(2)  (A), (B) and (D)

(3)  (A) and (D)

(4)  (A), (B) and (C)

Answer: (4)

11. In a Young’s double slit experiment, 16 fringes are observed in a certain segment of the screen when light of wavelength 700 nm is used. If the wavelength of light is changed to 400 nm, the number of fringes observed in the same segment of the screen would be:

(1)  28

(2)  24

(3)  30

(4)  18

Answer: (1)

12. A heat engine is involved with exchange of heat of 1915 J, –40J, + 125J and –QJ, during one cycle achieving an efficiency of 50.0%. The value of Q is:

(1)  980 J

(2)  640 J

(3)  40 J

(4)  400 J

Answer: (1)

13. In a hydrogen atom the electron makes a transition from (n + 1)th level to the nth level. If n>>1, the frequency of radiation emitted is proportional to:

(1)  1/n2

(2)  1/n

(3)  1/n3

(4)  1/n4

Answer: (3)

14. When the temperature of a metal wire is increased from 0°C to 10°C, its length increases by 0.02%. The percentage change in its mass density will be closest to:

(1)  0.06

(2)  0.008

(3)  2.3

(4)  0.8

Answer: (1)

15. A charge Q is distributed over two concentric conducting thin spherical shells radii r and R (R > r). If the surface charge densities on the two shells are equal, the electric potential at the common centre is:

(1) 

(2) 

(3) 

(4) 

Answer: (2)

16. A 10 μF capacitor is fully charged to a potential difference of 50V. After removing the source voltage it is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes 20 V. The capacitance of the second capacitor is:

(1)  15 μF

(2)  20 μF

(3)  10 μF

(4)  30 μF

Answer: (1)

17. An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true?

(A) the mean free path of the molecules decreases.

(B) the mean collision time between the molecules decreases.

(C) the mean free path remains unchanged.

(D) the mean collision time remains unchanged.

(1)  (B) and (C)

(2)  (A) and (B)

(3)  (C) and (D)

(4)  (A) and (D)

Answer: (1)

18. A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface tension = 0.05 Nm–1, density = 667 kg m–3) which rises to height h in the tube. It is observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of 60° with one another. Then h is close to (g=10 ms–2).

(1)  0.172 m

(2)  0.049 m

(3)  0.087 m

(4)  0.137 m

Answer: (3)

19. The height ‘h’ at which the weight of a body will be the same as that at the same depth ‘h’ from the surface of the earth is (Radius of the earth is R and effect of the rotation of the earth is neglected):

(1) 

(2) 

(3) 

(4)  R/2

Answer: (3)

20. The figure shows a region of length ‘l’ with a uniform magnetic field of 0.3 T in it and a proton entering the region with velocity 4 ×105 ms–1 making an angle 60° with the field. If the proton completes 10 revolution by the time it cross the region shown, ‘l’ is close to (mass of proton = 1.67 × 10–27 kg, charge of the proton = 1.6 × 10–19 C)

(1)  0.11 m

(2)  0.22 m

(3)  0.44 m

(4)  0.88 m

Answer: (3)

21. A light ray enters a solid glass sphere of refractive index μ= √3 at an angle of incidence 60°. The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and refracted rays at this surface is ________.

Answer: (90)

22. An ideal cell of emf 10 V is connected in circuit shown in figure. Each resistance is 2Ω. The potential difference (in V) across the capacitor when it is fully charged is _______.

Answer: (8)

23. A square shaped hole of side l =a/2 is carved out at a distance d = a/2 from the centre ‘O’ of a uniform circular disk of radius a. If the distance of the centre of mass of the remaining portion from O is –a/X, value of X (to the nearest integer) is _________.

Answer: (23)

24. A particle of mass m is moving along the x-axis with initial velocity  It collides elastically with a particle of mass 10 m at rest and then moves with half its initial kinetic energy (see figure). If sinθ1 = √n sin θ2 then value of n is

Answer: (10)

25. A wire of density 9 × 10–3 kg cm–3 is stretched between two clamps 1 m apart. The resulting strain in the wire is 4.9 × 10–4. The lowest frequency of the transverse vibrations in the wire is (Young’s modulus of wire Y = 9 ×1010 Nm–2), (to the nearest integer), _______.

Answer: (35)

Chemistry

1. Cast iron is used for the manufacture of :

(1)  Wrought iron and steel

(2)  Wrought iron and pig iron

(3)  Wrought iron, pig iron and steel

(4)  Pig iron, scrap iron and steel

Answer: (1)

2. The shape/structure of [XeF5] and XeO3F2, respectively, are :

(1)  Pentagonal planar and trigonal bipyramidal

(2)  Trigonal bipyramidal and trigonal bipyramidal

(3)  Octahedral and square pyramidal

(4)  Trigonal bipyramidal and pentagonal planar

Answer: (1)

3. Simplified absorption spectra of three complexes ((i), (ii) and (iii)) of Mn+ ion are provided below; their λmax values are marked as A, B and C respectively. The correct match between the complexes and their λmax values is :

(i) [M(NCS)6](–6+n)

(ii) [MF6](–6+n)

(iii) [M(NH3)6]n+

(1)  A-(i), B-(ii), C-(iii)

(2)  A-(iii), B-(i), C-(ii)

(3)  A-(ii), B-(iii), C-(i)

(4)  A-(ii), B-(i), C-(iii)

Answer: (2)

4. The correct observation in the following reactions is:

(1)  Formation of red colour

(2)  Formation of blue colour

(3)  Formation of violet colour

(4)  Gives no colour

Answer: (1)

5. The results given in the below table were obtained during kinetic studies of the following reaction: 2A + B → C + D

Experiment [A]/

molL1

[B]/

molL1

Initial rate/

molL1 min1

I 0.1 0.1 6.00×103
II 0.1 0.2 2.40 × 102
III 0.2 0.1 1.20 × 102
IV X 0.2 7.20 × 102
V 0.3 Y 2.88 × 101

X and Y in the given table are respectively:

(1)  0.4, 0.4

(2)  0.3, 0.4

(3)  0.4,0.3

(4)  0.3, 0.3

Answer: (2)

6. Match the type of interaction in column A with the distance dependence of their interaction energy in column B:

A                                          B

(I) ion-ion                          (a) 1/r

(II) dipole-dipole              (b) 1/r2

(III) London dispersion    (c) 1/r3

                                        (d) 1/r6

(1)  (I)-(a), (II)-(b), (III)-(d)

(2)  (I)-(a), (II)-(b), (III)-(c)

(3)  (I)-(b), (II)-(d), (III)-(c)

(4)  (I)-(a), (II)-(c), (III)-(d)

Answer: (4)

7. The major product obtained from E2 – elimination of 3-bromo-2-fluoropentane is:

Answer: (1)

8. Consider the reaction sequence given below:

Which of the following statements is true:

(1)  Changing the concentration of the base will have no effect on reaction (1)

(2)  Doubling the concentration of base will double the rate of both the reactions.

(3)  Changing the base from OH to OR will have no effect on reaction (2)

(4)  Changing the concentration of the base will have no effect on reaction (2)

Answer: (1)

9. The size of a raw mango shrinks to a much smaller size when kept in a concentrated salt solution. Which one of the following processes can explain this?

(1)  Diffusion

(2)  Osmosis

(3)  Reverse osmosis

(4)  Dialysis

Answer: (2)

10. If you spill a chemical toilet cleaning liquid on your hand, your first aid would be :

(1)  Aqueous NH3

(2)  Aqueous NaHCO­3

(3)  Aqueous NaOH

(4)  Vinegar

Answer: (2)

11. Arrange the following labelled hydrogens in decreasing order of acidity:

(1)  b > a > c > d

(2)  b > c > d > a

(3)  c > b > d > a

(4)  c > b > a > d

Answer: (2)

12. An organic compound ‘A’ (C9H10O) when treated with conc. HI undergoes cleavage to yield compounds ‘B’ and ‘C’. ‘B’ gives a yellow precipitate with AgNO3 whereas ‘C’ tautomerizes to ‘D’. ‘D’ gives a positive iodoform test. ‘A’ could be:

Answer: (1)

13. Two elements A and B have similar chemical properties. They don’t form solid hydrogen carbonates but react with nitrogen to form nitrides. A and B, respectively, are :

(1)  Na and Ca

(2)  Cs and Ba

(3)  Na and Rb

(4)  Li and Mg

Answer: (4)

14. The number of subshells associated with n = 4 and m = –2 quantum numbers is :

(1)  4

(2)  8

(3)  2

(4)  16

Answer: (3)

15. The major product of the following reaction is:

Answer: (3)

16. Two compounds A and B with the same molecular formula (C3H6O) undergo Grignard’s reaction with methylmagnesium bromide to give products C and D. Products C and D show the following chemical tests.

Test C D
Ceric ammonium nitrate test Positive Positive
Lucas Test Turbidity obtained after five minutes Turbidity obtained immediately
Iodoform Test Positive Negative

C and D respectively are:

Answer: (2)

17. Three elements X, Y and Z are in the 3rd period of the periodic table. The oxides of X, Y and Z, respectively, are basic, amphoteric and acidic, The correct order of the atomic numbers of X, Y and Z is:

(1)  X < Y < Z

(2)  Y < X < Z

(3)  Z < Y < X

(4)  X < Z < Y

Answer: (1)

18. The one that is not expected to show isomerism is:

(1)  [Ni(NH3)4 (H2O)2]2+

(2)  [Ni(en)3]2+

(3)  [Pt(NH3)2Cl2]

(4)  [Ni(NH3)2Cl2]

Answer: (4)

19. Amongst the following statements regarding adsorption, those that are valid are:

(a) ΔH becomes less negative as adsorption proceeds.

(b) On a given adsorbent, ammonia is adsorbed more than nitrogen gas.

(c) On adsorption, the residual force acting along the surface of the adsorbent increases.

(d) With an increase in temperature, the equilibrium concentration of adsorbate increases.

(1)  (b) and (c)

(2)  (c) and (d)

(3)  (a) and (b)

(4)  (d) and (a)

Answer: (3)

20. The molecular geometry of SF6 is octahedral. What is the geometry of SF4 (including lone pair(s) of electrons, if any)?

(1)  Pyramidal

(2)  Trigonal bipyramidal

(3)  Tetrahedral

(4)  Square planar

Answer: (2)

21. The ratio of the mass percentages of ‘C & H’ and ‘C & O’ of a saturated acyclic organic compound ‘X’ are 4:1 and 3:4 respectively. Then, the moles of oxygen gas required for complete combustion of two moles of organic compound ‘X’ is ___________.

Answer: (5)

22. For the disproportionation reaction 2Cu+(aq) ⇌ Cu(s) + Cu2+(aq) at K, ln K (where K is the equilibrium constant) is ________ × 10–1.

Given:

Answer: (144)

23. The work function of sodium metal is 4.41 × 10–19 If photons of wavelength 300 nm are incident on the metal, the kinetic energy of the ejected electrons will be (h = 6.63 × 10–34 J s; c = 3 × 108 m/s) __________ × 10–21 J.

Answer: (222)

24. The oxidation states of transition metal atoms in K2Cr2O7, KMnO4 and K2FeO4, respectively, are x, y and z. The sum of x, y and z is ________.

Answer: (19)

25. The heat of combustion of ethanol into carbon dioxide and water is –327 kcal at constant pressure. The heat evolved (in cal) at constant volume and 27ºC (if all gases behave ideally) is (R = 2 cal mol–1K–1) __________.

Answer: (326400)

Mathematics

1. Let f : R → R be a function which satisfies f(x + y) = f(x) + f(y) ∀ x, y ∈ if f(1) = 2 and  then the value of n, for which g(n) = 20, is:

(1)  9

(2)  5

(3)  4

(4)  20

Answer: (2)

2. If the sum of first 11 terms of an A.P, a1,a2,a3… is 0 (a1 ≠ 0) then the sum of the A.P, a1, a3, a5…a23 is ka1, where k is equal to

(1)  −121/10

(2)  −72/5

(3)  72/5

(4)  121/10

Answer: (b)

3. Let EC denote the complement of an event E. Let E1, E2 and E3 be any pair wise independent events with P(E1) > 0 and P(E1 ∩ E2 ∩ E3) = 0. Then P(E2C ∩ E3C/E1) is equal to:

(1)  P(E3C) – P(E2C)

(2)  P(E3) – P(E2C)

(3)  P(E3C) – P(E2)

(4)  P(E2C) + P(E3)

Answer: (c)

4. If the equation cos4θ+sin4θ+λ = 0 has real solutions for θ, then λ lies in the interval:

(1)  (−1/2, −1/4]

(2)  [−1, −1/2]

(3)  [−3/2, −5/4]

(4)  (−5/4, −1)

Answer: (2)

5. The area (in sq. units) of an equilateral triangle inscribed in the parabola y2 = 8x, with one of its vertices on the vertex of this parabola, is:

(1)  128√3

(2)  192√3

(3)  64√3

(4)  256√3

Answer: (2)

6. The imaginary part of  can be:

(1)  √6

(2)  −2√6

(3)  6

(4)  −√6

Answer: (2)

7. A plane passing through the point (3,1,1) contains two lines whose direction ratios are (1, −2, 2) and (2, 3, -1) respectively. If this plane also passes through the point (α, −3, 5), then α is equal to:

(1)  −5

(2)  10

(3)  5

(4)  −10

Answer: (3)

8. Let A = {X = (x, y, z)T : PX = 0 and x2 + y2 + z2}, where  then the set A:

(1)  contains more than two elements

(2)  is a singleton.

(3)  contains exactly two elements

(4)  is an empty set.

Answer: (3)

9. The equation of the normal to the curve y = (1+x)2y +cos2(sin1x) at x = 0 is:

(1)  y + 4x = 2

(2)  2y + x = 4

(3)  x + 4y = 8

(4)  y = 4x + 2

Answer: (3)

10. Consider a region R = {(x, y) ∈ R2 : x2 ≤ y ≤ 2x}. If a line y = α divides the area of region R into two equal parts, then which of the following is true.?

(1)  α3 − 6α2 + 16 = 0

(2)  3α2 − 8α3/2 + 8 = 0

(3)  α3− 6α3/2 − 16 = 0

(4)  3α2 − 8α + 8 = 0

Answer: (2)

11. Let f: (−1, ∞) → R be defined by f(0) = 1 and  x ≠ 0. Then the function f:

(1)  increases in (−1, ∞)

(2)  decreases in (−1,0) and increases in (0, ∞)

(3)  increases in (−1,0) and decreases in (0, ∞)

(4)  decreases in (−1, ∞)

Answer: (d)

12. Which of the following is a tautology?

(1)  (p→q) ˄( q→p)

(2)  (~p) ˄(p ˅q)→q

(3)  (q→p) ˅~(p→q)

(4)  (~q)˅( p˄q)→q

Answer: (2)

13. Let f(x) be a quadratic polynomial such that f(−1) + f(2) = 0. If one of the roots of f(x) = 0 is 3, then its other roots lies in:

(1)  (0, 1)

(2)  (1, 3)

(3)  (−1, 0)

(4)  (−3, −1)

Answer: (3)

14. Let S be the sum of the first 9 terms of the series:

{x + ka} + {x2 + (k + 2) a} + {x3 + (k + 4) a} + {x4 + (k + 6)a} +… where a ≠ 0 and a ≠ 1.

If  then k is equal to:

(1)  3

(2)  −3

(3)  1

(4)  −5

Answer: (2)

15. The set of all possible values of θ in the interval (0, π) for which the points (1, 2) and (sin θ, cos θ ) lie on the same side of the line x + y = 1 is:

(1)  (0, π/4)

(2)  (0, π/2)

(3)  (0, 3π/4)

(4)  (π/4, 3π/4)

Answer: (2)

16. Let n > 2 be an integer. Suppose that there are n metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is 99 times the number of blue lines, then the value of n is:

(1)  201

(2)  199

(3)  101

(4)  200

Answer: (a)

17. If a curve y = f(x), passing through the point (1, 2) is the solution of the differential equation, 2x2dy = (2xy + y2)dx, then f(1/2) is equal to:

(1) 

(2)  1 + loge 2

(3) 

(4) 

Answer: (3)

18. For some θ ∈ (0, π/2) , if the eccentricity of the hyperbola, x2 − y2sec2θ = 10 is √5 times the eccentricity of the ellipse, x2sec2θ + y2 = 5, then the length of the latus rectum of the ellipse, is:

(1)  4√5/3

(2)  2√5/3

(3)  2√6

(4)  √30

Answer: ()

19. is equal to :

(1)  e

(2)  e2

(3)  2

(4)  1

Answer: (2)

20. Let a, b, c ∈ R be all non-zero and satisfy a3 + b3 + c3 = 2. If the matrix satisfies  ATA = I, then a value of abc can be:

(1)  2/3

(2)  3

(3)  −1/3

(4)  1/3

Answer: (d)

21. Let the position vectors of points ‘A’ and ‘B’ be  and   A point ‘P’ divides the line segment AB internally in the ratio λ : 1 (λ > 0). If O is the origin and then λ is equal to_______

Answer: (0.8)

22. Let [t] denote the greatest integer less than or equal to t. Then the value of  is :

Answer: (1)

23. If  then (dy/dx) at x = 0 is:

Answer: (91)

24. If the variance of the terms in an increasing A.P. b1, b2, b3, …., b11 is 90, then the common difference of this A.P. is

Answer: (3)

25. For a positive integer n, (1+1/x)n is expanded in increasing powers of x. If three consecutive coefficients in this expansion are in the ratio, 2:5:12, then n is equal to

Answer: (118)

JEE Main September 2 2020 Shift 1 Question Paper with Answer Key

Physics

1. The mass density of a spherical galaxy K varies as K/r over a large distance ‘r’ from its centre. In that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on R as:

(a)  T2 ∝ R

(b)  T2 ∝ R3

(c)  T2 ∝ (1/R3)

(d) T ∝ R

Answer: (a)

2. An amplitude modulated wave is represented by the expression vm= 5(1 + 0.6 cos 6280 t )sin (211 × 104t) volts. The minimum and maximum amplitudes of the amplitude modulated wave are, respectively :

(a) 

(b)  5V, 8V

(c)  3V, 5V

(d) 

Answer: (d)

3. A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an object is positioned in front of the mirror, what will be the nature and magnification of the image of the object ? (Figure drawn as schematic and not to scale)

(a)  Erect, virtual and unmagnified

(b)  Inverted, real and magnified

(c)  Erect, virtual and magnified

(d) Inverted, real and unmagnified

Answer: (d)

4. A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5 cm an and the angular speed of rotation is ω rad s1. The difference in the height, h (in cm) of liquid at the centre of vessel and at the side will be:

(a)  5ω2/2g

(b)  2ω2/25g

(c)  25ω2/2g

(d) 2ω2/5g

Answer: (c)

5. If speed V, area A and force F are chosen as fundamental units, then the dimension of;

Young’s modulus will be

(a)  FA2V3

(b)  FA2V2

(c)  FA1V0

(d) FA2V1

Answer: (c)

6. A bead of mass m stays at point P (a, b) on a wire bent in the shape of a parabola y = 4Cx2 and rotating with angular speed ω (see figure). The value of ω is (neglect friction):

(a) 

(b)  2√gC

(c) 

(d) 2√2gC

Answer: (d)

7. Magnetic materials used for making permanent magnets (P) and magnets in a transformer (T) have different properties of the following, which property best matches for the type of magnet required?

(a)  P : Small retentivity, large coercivity

(b)  P : Large retentivity, large coercivity

(c)  T : Large retentivity, large coercivity

(d) T : Large retentivity, small coercivity

Answer: (b)

8. Interference fringes are observed on a screen by illuminating two thin slits 1 mm apart with a light source (λ = 632.8 nm). The distance between the screen and the slits is 100cm. If a bright fringe is observed on screen at a distance of 1.27 mm from the central bright fringe, then the path difference between the waves, which are reaching this point from the slits is close to:

(a)  2.05 μm

(b)  2.87 nm

(c)  2 nm

(d) 1.27 μm

Answer: (d)

9. A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT) of the mixture is:

(a)  11

(b)  13

(c)  15

(d) 20

Answer: (c)

10. A plane electromagnetic wave, has frequency of 2.0 × 1010 Hz and its energy density is 1.02 × 10–8 J/m3 in vacuum. The amplitude of the magnetic field of the wave is close

(a)  160 nT

(b)  150 nT

(c)  180 nT

(d) 190 nT

Answer: (a)

11. Consider four conducting materials copper, tungsten, mercury and aluminium with resistivity ρc, ρm, ρT and ρA Then:

(a)  ρc > ρA > ρT

(b)  ρA> ρm > ρc

(c)  ρA> ρT > ρc

(d) ρm > ρA> ρc

Answer: (d)

12. A beam of protons with speed 4 × 105 ms–1 enters a uniform magnetic field of 0.3 T at an angle of 60° to the magnetic field. The pitch of the resulting helical path of protons is close to: (Mass of the proton =1.67 × 10–27 kg, charge of the proton =1.69 × 10–19C)

(a)  4 cm

(b)  2 cm

(c)  12 cm

(d) 5 cm

Answer: (a)

13. Two identical strings X and Z made of same material have tension Tx and Tz in them. If their fundamental frequencies are 450 Hz and 300 Hz, respectively, then the ratio Tx/Tz is:

(a)  2.25

(b)  1.25

(c)  0.44

(d) 1.5

Answer: (a)

14. A uniform cylinder of mass M and radius R is to be pulled over a step of height a(a < R) by applying a force F at its centre ‘O’ perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of F required is

(a) 

(b) 

(c) 

(d) 

Answer: (d)

15. In a reactor, 2 kg of 92U235 fuel is fully used up in 30 days. The energy released perfission is 200 MeV. Given that the Avogadro number, N = 6.023 × 1026 per kilo mole and1 eV =1.6 × 10–19 The power output of the reactor is close to

(a)  60 MW

(b)  54 MW

(c)  125 MW

(d) 35 MW

Answer: (a)

16. A charged particle (mass m and charge q) moves along X axis with velocity V0. When it passes through the origin it enters a region having uniform electric field  which extends upto x = d. Equation of path of electron in the region x > d is:

(a) 

(b) 

(c) 

(d) 

Answer: (b)

17. Train A and train B are running on parallel tracks in the opposite directions with speeds of 36 km/hour and 72 km/hour, respectively. A person is walking in train A in the direction opposite to its motion with a speed of 1.8 km/hour. Speed (in ms–1) of this person as observed from train B will be close to:

(a)  29.5 ms1

(b)  30.5 ms1

(c)  31.5 ms1

(d) 28.5 ms1

Answer: (a)

18. Shown in the figure is rigid and uniform one meter long rod AB held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass `m` and has another weight of mass 2 m hung at a distance of 75 cm from A. The tension in the string at A is:

(a)  0.75 mg

(b)  0.5 mg

(c)  1 mg

(d) 2 mg

Answer: (c)

19. The least count of the main scale of a vernier callipers is 1 mm. Its vernier scale is divided into 10 divisions and coincide with 9 divisions of the main scale. When jaws are touching each other, the 7th division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between 3.1 cm and 3.2 cm and 4th VSD coincides with a main scale division. The length of the cylinder is: (VSD is vernier scale division)

(a)  3.21 cm

(b)  3.07 cm

(c)  2.99 cm

(d) 3.2 cm

Answer: (b)

20. A particle of mass m with an initial velocity  collides perfectly elastically with a mass 3m at rest. It moves with a velocity  after collision, then v is given by:

(a) 

(b) 

(c) 

(d) 

Answer: (d)

21. A small block starts slipping down from a point B on an inclined plane AB, which is making an angle θ with the horizontal section BC is smooth and the remaining section CA is rough with a coefficient of friction. It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If BC = 2AC, the coefficient of friction is given by μ =k tan θ. The value of k is __________

Answer: (c)

22. An engine takes in 5 moles of air at 20°C and 1atm, and compresses it adiabaticaly to 1/10th of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be X kJ. The value of X to the nearest integer is ___________.

Answer: (46 kJ)

23. When radiation of wavelength λ is used to illuminate a metallic surface, the stopping potential is V. When the same surface is illuminated with radiation of wavelength 3 λ, the stopping potential is V/4. If the threshold wavelength for the metallic surface is n λ then value of n will be __________.

Answer: (9𝛌)

24. A circular coil of radius 10 cm is placed in uniform magnetic field of 3.0 × 10–5 T with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in 0.2s. The maximum value of EMF induced (in μV) in the coil will be close to the integer __________.

Answer: (15 𝛍V)

25. A 5μF capacitor is charged fully by a 220V supply. It is then disconnected from the supply and is connected in series to another uncharged 2.5μF capacitor. If the energy change during the charge redistribution is (X/100) J then value of X to the nearest integer is _________.

Answer: (d)

Chemistry

1. The increasing order of the following compounds towards HCN addition is:

(1)  (iii) < (i) < (iv) < (ii)

(2)  (iii) < (iv) < (i) < (ii)

(3)  (i) < (iii) < (iv) < (ii)

(4)  (iii) < (iv) < (ii) < (i)

Answer: (1)

2. Which of the following is used for the preparation of colloids?

(1)  Van Arkel Method

(2)  Ostwald Process

(3)  Mond Process

(4)  Bredig’s Arc Method

Answer: (4)

3. An open beaker of water in equilibrium with water vapour is in a sealed container. When a few grams of glucose are added to the beaker of water, the rate at which water molecules:

(1)  leaves the vapour increases

(2)  leaves the solution increases

(3)  leaves the vapour decreases

(4)  leaves the solution decreases

Answer: (1)

4. For octahedral Mn(II) and tetrahedral Ni(II) complexes, consider the following statements:

(I) both the complexes can be high spin.

(II) Ni(II) complexes can very rarely be low spin.

(III) with strong field ligands, Mn(II) complexes can be low spin.

(IV) the aqueous solution of Mn(II) ions is yellow in colour.

The correct statements are:

(1)  (I), (III) and (IV) only

(2)  (I), (II) and (III) only

(3)  (II), (III) and (IV) only

(4)  (I) and (II) only

Answer: (2)

5. The statement that is not true about ozone is:

(1)  in the stratosphere, it forms a protective shield against UV radiation.

(2)  in the atmosphere, it is depleted by CFCs.

(3)  in the stratosphere, CFCs release chlorine-free radicals (Cl) which reacts with O3 to give chlorine dioxide radicals.

(4)  it is a toxic gas and its reaction with NO gives NO2.

Answer: (c)

6. Consider the following reactions:

‘x’, ‘y’ and ‘z’ in these reactions are respectively.

(1)  4, 5 & 6

(2)  5, 4 & 5

(3)  5, 6 & 5

(4)  4, 6 & 5

Answer: (4)

7. The IUPAC name for the following compound is:

(1)  2,5-dimethyl-5-carboxy-hex-3-enal

(2)  2,5-dimethyl-6-oxo-hex-3-enoic acid

(3)  6-formyl-2-methyl-hex-3-enoic acid

(4)  2,5-dimethyl-6-carboxy-hex-3-enal

Answer: (2)

8. For the following Assertion and Reason, the correct option is

Assertion (A): When Cu (II) and Sulphide ions are mixed, they react together extremely quickly to give a solid.

Reason (R): The equilibrium constant of Cu2+ (aq) + S2– (aq) ⇌ CuS (s) is high because the solubility product is low.

(1)  (A) is false and (R) is true.

(2)  Both (A) and (R) are false.

(3)  Both (A) and (R) are true but (R) is not the explanation for (A).

(4)  Both (A) and (R) are true but (R) is the explanation for (A).

Answer: (4)

9. Which one of the following graphs is not correct for an ideal gas?

d = Density, P = Pressure, T = Temperature

The correct statements are:

(1)  (i)

(2)  (iv)

(3)  (iii)

(4)  (ii)

Answer: (4)

10. While titrating dilute HCl solution with aqueous NaOH, which of the following will not be required?

(1)  Bunsen burner and measuring cylinder

(2)  Burette and porcelain tile

(3)  Clamp the phenolphthalein

(4)  Pipette and distilled water

Answer: (1)

11. In Carius’ method of estimation of halogen, 0.172 g of an organic compound showed the presence of 0.08 g of bromine. Which of these is the correct structure of the compound?

Answer: (c)

12. On heating compound (A) gives a gas (B) which is a constituent of air. This gas when treated with H2 in the presence of a catalyst gives another gas (C) which is basic in nature. (A) should not be:

(1)  (NH4)2Cr2O7

(2)  NaN3

(3)  NH4NO2

(4)  Pb(NO3)2

Answer: (4)

13. The major product in the following reaction is:

Answer: (3)

14. In general, the property (magnitudes only) that shows an opposite trend in comparison to other properties across a period is:

(1)  Ionization enthalpy

(2)  Electronegativity

(3)  Atomic radius

(4)  Electron gain enthalpy

Answer: (3)

15. The figure that is not a direct manifestation of the quantum nature of atoms is:

Answer: (4)

16. The major aromatic product C in the following reaction sequence will be:

Answer: (3)

17. Consider that a d6 metal ion (M2+) forms a complex with aqua ligands, and the spin only magnetic moment of the complex is 4.90 BM. The geometry and the crystal field stabilization energy of the complex is:

(1)  tetrahedral and –0.6Δt

(2)  tetrahedral and –1.6Δt + 1P

(3)  octahedral and –1.6Δ0

(4)  octahedral and –2.4Δ0 + 2P

Answer: (1)

18. If AB4 molecule is a polar molecule, a possible geometry of AB4 is:

(1)  Square planar

(2)  Tetrahedral

(3)  Square pyramidal

(4)  Rectangular planar

Answer: (1)

19. Which of the following compounds will show retention in the configuration on nucleophilic substitution by OH ion?

Answer: (1)

20. The metal mainly used in devising photoelectric cells is:

(1)  Li

(2)  Cs

(3)  Rb

(4)  Na

Answer: (b)

21. The mass of gas adsorbed, x, per unit mass of adsorbate, m, was measured at various pressures, p. A graph between log [x / m] and log p gives a straight line with slope equal to 2 and the intercept equal to 0.4771. The value of [x / m] at a pressure of 4 atm is: (Given log 3 = 0.4771)

Answer: (48)

22. The Gibbs energy change (in J) for the given reaction at [Cu2+] = [Sn2+] = 1 M and 298 K is:

Cu(s) + Sn2+ (aq.) → Cu2+(aq.) + Sn(s)

Answer: (96500 Joules)

23. The internal energy change (in J) when 90 g of water undergoes complete evaporation at 100ºC is __________.

(Given: ΔHvap for water at 373 K = 41 kJ/mol, R = 8.314 JK–1 mol–1)

Answer: (189494.39)

24. The oxidation states of iron atoms in compounds (A), (B) and (C), respectively, are x, y and z. The sum of x, y and z is _____.

Answer: (6)

25. The number of chiral carbons present in the molecule given below is ________.

Answer: (5)

Mathematics

1. A line parallel to the straight line 2x – y = 0 is tangent to the hyperbola  at the point (x1,  y1). Then  is equal to :

(1)  6

(2)  10

(3)  8

(4)  5

Answer: (1)

2. The domain of the function  is (−∞, −a] ∪ [a, ∞). Then a is equal to :

(1) 

(2) 

(3) 

(4) 

Answer: (3)

3. If a function f(x) defined by  be continuous for some a, b, c ∈ R and f´(0) + f´(2) = e, then the value of a is:

(1) 

(2) 

(3) 

(4) 

Answer: (4)

4. The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in

(1)  (−∞,−9]∪[3, ∞)

(2)  [−3, ∞)

(3)  (−∞,−9]

(4)  (−∞,−3]∪[9, ∞)

Answer: (d)

5. If R = {(x,y) : x,y ∈ Z, x2 + 3y2 ≤ 8} is a relation on the set of integers Z, then the domain of R−1 is:

(1)  {−1, 0, 1}

(2)  {−2, −1, 1, 2}

(3)  {0,1}

(4)  {-2,-1,0,1,2}

Answer: (1)

6. The value of  is :

(1) 

(2) 

(3) 

(4) 

Answer: (3)

7. Let P(h, k) be a point on the curve y = x2 + 7x + 2, nearest to the line, y = 3x – 3. Then the equation of the normal to the curve at P is:

(1)  x + 3y – 62 = 0

(2)  x – 3y – 11 = 0

(3)  x – 3y + 22 = 0

(4)  x + 3y + 26 = 0

Answer: (4)

8. Let A be a 2×2 real matrix with entries from {0,1} and A ≠ 0. Consider the following two statements:

(P) If A ≠I2, then A = -1

(Q) If A =1, then tr(A) = 2,

where I2 denotes 2 × 2 identity matrix and tr(A) denotes the sum of the diagonal entries of A. Then:

(1)  Both (P) and (Q) are false

(2)  (P) is true and (Q) is false

(3)  Both (P) and (Q) are true

(4)  (P) is false and (Q) is true

Answer: (4)

9. Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box I is:

(1)  4/17

(2)  8/17

(3)  2/5

(4)  2/3

Answer: (2)

10. If p(x) be a polynomial of degree three that has a local maximum value 8 at x = 1 and a local minimum value 4 at x = 2; then p(0) is equal to :

(1)  12

(2)  −12

(3)  −24

(4)  6

Answer: (2)

11. The contra positive of the statement “If I reach the station in time, then I will catch the train” is:

(1)  If I will catch the train, then I reach the station in time.

(2)  If I do not reach the station in time, then I will catch the train.

(3)  If I do not reach the station in time, then I will not catch the train.

(4)  If I will not catch the train, then I do not reach the station in time.

Answer: (4)

12. Let α and β be the roots of the equation, 5x2 + 6x − 2 = 0. If Sn = αn + βn, n = 1,2,3,.. then:

(1)  5S6 + 6S5 + 2S4 = 0

(2)  6S6 + 5S5 = 2S4

(3)  6S6 + 5S5 + 2S4 = 0

(4)  5S6 + 6S5 = 2S4

Answer: (4)

13. If the tangent to the curve y = x+sin y at a point (a,b) is parallel to the line joining (0, 3/2) and (1/2, 2), then:

(1)  b = (π/2) + a

(2)  |a + b| = 1

(3)  |b – a| = 1

(4)  b = a

Answer: (3)

14. Area (in sq. units) of the region outside  and inside the ellipse  is:

(1)  3(π – 2)

(2)  6(π – 2)

(3)  6(4 – π)

(4)  3(4 – π)

Answer: (2)

15. If |x| < 1, |y| < 1 and x ≠ y, then the sum of infinity of the following series (x + y) + (x2 + + xy + y2) + (x3 + x2y + xy2 + y3)+… is:

(1) 

(2) 

(3) 

(4) 

Answer: (2)

16. Let α > 0, β > 0 be such that α3 + β2 = 4. If the maximum value of the term independent of x in the binomial expansion of (αx1/9 + βx1/6)10 is 10k, then k is equal to:

(1)  176

(2)  336

(3)  352

(4)  84

Answer: (2)

17. Let S be the set of all λ ∈ R for which the system of linear equations

2x – y + 2z = 2

x – 2y + λz = −4

x + λy + z = 4

has no solution. Then the set S

(1)  is an empty set.

(2)  is a singleton.

(3)  contains more than two elements.

(4)  contains exactly two elements.

Answer: (4)

18. Let X = {x ∈ N: 1 ≤ x ≤ 17} and Y = {ax + b : x ∈ X and a, b ∈ R, a > 0}. If mean and variance of elements of Y are 17 and 216 respectively then a + b is equal to:

(1)  −27

(2)  7

(3)  −7

(4)  9

Answer: (3)

19. Let y = y(x) be the solution of the differential equation,  If y(π) = a, and dy/dx at x = π is b, then the ordered pair (a, b) is equal to :

(1)  (2, 3/2)

(2)  (1, 1)

(3)  (2, 1)

(4)  (1, −1)

Answer: (2)

20. The plane passing through the points (1,2,1), (2,1,2) and parallel to the line, 2x = 3y, z = 1 also passes through the point:

(1)  (0, −6, 2)

(2)  (0, 6, −2)

(3)  (−2, 0, 1)

(4)  (2, 0, −1)

Answer: (c)

21. The number of integral values of k for which the line, 3x + 4y = k intersects the circle, x2 + y2 − 2x – 4y + 4 = 0 at two distinct points is…

Answer: (9)

22. Let  be three unit vectors such that  Then  is equal to:

Answer: (2)

23. If the letters of the word ’MOTHER’ be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word ’MOTHER’ is….

Answer: (309)

24. If  (n ∈ N) then the value of n is equal to:

Answer: (40)

25. The integral  is equal to:

Answer: (1.5)

JEE Main January 9 2020 Shift 2 Question Paper with Answer Key

Physics

1. An electron gun is placed inside a long solenoid of radius R on its axis. The solenoid has  and carries a current i. The electron gun shoots an electron along the radius of solenoid with speed If the electron does not hit the surface of the solenoid, maximum possible value of v is (all symbols have their standard meaning):

(a) 

(b) 

(c) 

(d) 

Answer: (b)

2. Two identical capacitors A and B, charged to the same potential 5V are connected in two different circuit as shows below at time t=0. If the charges on capacitors A and B at time t= CR is QA and QB respectively, then (Here is the base of natural logarithm)

(a)  CV, CV/e

(b)  CV/e, CV/2e

(c)  CV/e, VC/2

(d) CV/e, CV

Answer: (a)

3. For the four sets of three measured physical quantities as given below. Which of the following options is correct?

(i) A1 = 24.36, B1=0.0724, C1= 256.2

(ii) A2 = 24.44, B2=16.08, C2= 240.2

(iii) A3 = 25.2, B3 = 19.2812, C3= 236.183

(iv) A4 = 25, B4 = 236.191, C4 = 19.5

(a)  A4 + B4 + C4 < A1 + B1 + C1 < A2 + B2 + C2 = A3 + B3 +C3

(b)  A1 + B1 + C1 = A2 + B2 + C2 = A3 + B3 + C3 = A4 + B4 + C4

(c)  A1 + B1 + C1 < A3 + B3 +C3 < A2 + B2 + C2 < A4 + B4 +C4

(d) A4 + B4 +C4 < A1 + B1 +C1< A3 + B3 +C3 < A2 + B2 +C2

Answer: (a)

4. A particle starts from the origin at t = 0 with an initial velocity of from origin and moves in the x-y plane with a constant acceleration  The x-coordinate of the particle at the instant when its y-coordinated is 32 m is D meters. The value of D is:

(a)  60

(b)  50

(c)  32

(d) 40

Answer: (a)

5. A spring mass system (mass m, spring constant k and natural length l) rest in equilibrium on a horizontal disc. The free end of the spring is fixed at the center of the disc. If the disc together with spring mass system, rotates about its axis with an angular velocity (k >>> mω2), the relative change in the length of the spring is best given by the option:

(a) 

(b) 

(c) 

(d) 

Answer: (c)

6. A small circular loop of conducting wire has radius a and carries current i. It is placed in a uniform magnetic field B perpendicular to its plane such that when rotated slightly about its diameter and released, its starts performing simple harmonic motion of time period T. If the mass of the loop is m then

(a) 

(b) 

(c) 

(d) 

Answer: (b)

7. A small spherical droplet of density d is floating exactly half immersed in a liquid of density ρ and surface tension T. The radius of droplet is (take note that the surface tension applied an upward force on droplet)

(a) 

(b) 

(c) 

(d) 

Answer: (d)

8. A wire of length L and mass 6 x 103 kg/m per unit length is put under tension of 540N. Two consecutive frequencies that it resonates at are: 420 Hz and 490 Hz . Then L in meter is

(a)  8.1 m

(b)  2.1 m

(c)  1.1 m

(d) 5.1 m

Answer: (b)

9. A plane electromagnetic wave is propagating along the direction  with the polarization along the direction   The correct form of the magnetic field of the wave would be (here B0 is an appropriate constant)

(a) 

(b) 

(c) 

(d) 

Answer: (a)

10. Two gases-Argon (atomic radius 0.07 nm atomic weight 40) and Xenon (atomic radius 0.1 nm atomic weight 140) have the same number density and are at the same temperature. The ratio of their respective mean free time is closest to

(a)  4.67

(b)  2.04

(c)  1.83

(d) 3.67

Answer: (c)

11. Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1: 4, the ratio of their diameters is:

(a)  √2:1

(b)  1:√2

(c)  1:2

(d) 2:1

Answer: (a)

12. Planets A has a mass M and radius R. Planet B has the mass and half the radius of planet A. If the escape velocities from the planets A and B are vA and vB respectively, then surfaces is the value of n is:

(a)  3

(b)  2

(c)  4

(d) 5

Answer: (c)

13. A rod of length L has non-uniform linear mass density given by  where a and b are constants and 0 ≤ x ≤ The value of x for the center of mass of the rod is at:

(a) 

(b) 

(c) 

(d) 

Answer: (b)

14. A particle of mass m is projected with a speed u from the ground at angle is θ = π/3 w.r.t. horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity  The horizontal distance covered by the combined mass before reaching the ground is:

(a) 

(b) 

(c) 

(d) 

Answer: (a)

15. A uniformly thick wheel with moment of inertia I and radius R is free to rotate about its center of mass (see fig). A massless string is wrapped over its rim and two blocks of massless string is wrapped over its rim and two blocks of masses m1 and m2 (m1 > m2 ) are attached to the ends of string. The system is released from rest. The angular speed of the wheel when m1 descend by a distance h is:

(a) 

(b) 

(c) 

(d) 

Answer: (a)

16. The energy required to ionise a hydrogen like ion in its ground state is 9 Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state to the ground stare?

(a)  8.6

(b)  11.4

(c)  24.2

(d) 35.8

Answer: (b)

17. There is a small source of light at some depth below the surface of water (refractive index 4/3) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly): [Use the fact that surface area of a spherical cap of height h and radius of curvature r is 2πrh]

(a)  17%

(b)  34%

(c)  50%

(d) 21%

Answer: (a)

18. An electron of mass m and magnitude of charge |e| initially at rest gets accelerated by a constant electric field E. The of charge of de-Broglie wavelength of this electron at time t ignoring relativistic effects is

(a) 

(b) 

(c) 

(d) 

Answer: (c)

19. In LC circuit the inductance L = 40mH and C = 100 μF. If a voltage V(t) = 10sin(314t) is applied to the circuit, the current in the circuit is given as

(a)  10cos (314t)

(b)  0.52cos (314t)

(c)  0.52sin (314t)

(d) 5.2cos (314t)

Answer: (b)

20. The current (i) in the network is

(a)  0 A

(b)  0.3 A

(c)  0.2 A

(d) 0.6 A

Answer: (b)

21. Starting at temperature 300 K, one mole of an ideal diatomic gas (γ = 1.4) is first compressed adiabatically from volume to V1 to V2 = V1/16. It is then allowed to expand isobarically to volume 2V2 . If all the processes are the quasi-static then the final temperature of the gas (0K) is (to the nearest integer)

Answer: (1818 K)

22. An electric field  passes through the box shown in figure. The flux of the electric field through surface ABCD and BCGF are marked as ϕ1 and ϕ2, then difference between 

Answer: (48 Nm2/C)

23. In a Young’s double slit experiment 15 fringes are observed on a small portion of the screen when light of wavelength 500nm is used. 10 fringes are observed on the same section of the screen when another light source of wavelength λ is used. Then the value of λ is (nm)

Answer: (750 nm)

24. In a meter bridge experiment S is a standard resistance. R is a resistance wire. It is found that balancing length is l = 25 cm. If R is replaced by a wire of half length and half diameter that of R of same material, then the balancing l (in cm) will now be

Answer: (40)

25. The circuit shown below is working as a 8V dc regulated voltage source. When 12V is used as input, the power dissipated (in mW) in each diode id; (considering both zener diode are identical).

Answer: (40 mW)

Chemistry

1. 5 g of Zinc is treated separately with an excess of

(I) dilute hydrochloric acid and

(II) aqueous sodium hydroxide.

The ratio of the volumes of H2 evolved in these two reactions is:

(a)  2 : 1

(b)  1 : 2

(c)  1 : 1

(d) 1 : 4

Answer: (c)

2. The solubility product of Cr(OH)3 at 298 K is 6×1031 . The concentration of hydroxide ions in a saturated solution Cr(OH)3 will be:

(a)  (18×1031)1/4

(b)  (18×1031)1/2

(c)  (2.22×1031)1/4

(d) (4.86×1031)1/4

Answer: (a)

3. Among the statements (a)-(d), the correct ones are:

(a) Lithium has the highest hydration enthalpy among the alkali metals.

(b) Lithium chloride is insoluble in pyridine.

(c) Lithium cannot form ethynide upon its reaction with ethyne.

(d) Both lithium and magnesium react slowly with H2O.

(a)  (a), (b) and (d) only

(b)  (b) and (c) only

(c)  (a), (c) and (d) only

(d) (a) and (d) only

Answer: (a)

4. The first and second ionization enthalpies of a metal are 496 and 4560 kJ mol1 How many moles of HCl and H2SO4, respectively, will be needed to react completely with 1 mole of metal hydroxide?

(a)  1 and 2

(b)  1 and 0.5

(c)  1 and 1

(d) 2 and 0.5

Answer: (b)

5. In the figure shown below reactant A (represented by the square) is in equilibrium with product B (represented by circle). The equilibrium constant is:

(a)  1

(b)  2

(c)  8

(d) 4

Answer: (b)

6. The correct order spin-only magnetic moments of the following complexes is:

I. [Cr(H2O)6]Br2

II. Na4[FeCN6]

III. Na3[Fe(C2O4)3] (∆0 > P)

IV. (Et4N)2[CoCl4]

(a)  (III)>(I)>(II)>(IV)

(b)  (III)>(I)>(IV)>(II)

(c)  (I)>(IV)>(III)>(II)

(d) (II)≈(I)>(IV)>(III)

Answer: (c)

7. The true statement amongst the following.

(a)  S is a function of temperature but S is not a function of temperature.

(b)  Both S and S are functions of temperature.

(c)  Both S and S are not functions of temperature.

(d) S is not a function of temperature but S is a function of temperature.

Answer: (b)

8. The reaction of H3N3B3Cl3 (A) with LiBH4 in tetrahydrofuran gives inorganic benzene (B). Furthur, the reaction of (A) with (C) leads to H3N3B3(Me)3. Compounds (B) and (C) respectively, are:

(a)  Boron nitride, MeBr

(b)  Diborane, MeMgBr

(c)  Borazine, MeBr

(d) Borazine, MeMgBr

Answer: (d)

9. A mixture of gases O2, H2 and CO are taken in a closed vessel containing charcoal. The graph that represents the correct behaviour of pressure with time is:

Answer: (c)

10. The isomer(s) of [Co(NH3)4Cl2] that has/have a Cl-Co-Cl angle of 90°, is/are:

(a)  cis only

(b)  trans only

(c)  meridional and trans

(d) cis and trans

Answer: (a)

11. Amongst the following, the form of water with lowest ionic conductance at 298 K is:

(a)  distilled water

(b)  sea water

(c)  saline water used for intra venous injection

(d) water from a well

Answer: (a)

12. The number of sp2 hybrid orbitals in molecule of benzene is:

(a)  18

(b)  24

(c)  6

(d) 12

Answer: (a)

13. Which of the following reactions will not produce a racemic product?

Answer: (b)

14. Which of the following has the shortest C-Cl bond?

(a)  Cl―CH=CH2

(b)  Cl―CH=CH―CH3

(c)  Cl―CH=CH―OCH3

(d) Cl―CH=CH―NO2

Answer: (d)

15. Biochemical oxygen demand (BOD) is the amount of oxygen required (in ppm):

(a)  for the photochemical breakdown of waste present in 1m3 volume of a water body.

(b)  by anaerobic bacteria to break-down inorganic waste present in a water body.

(c)  by bacteria to break-down organic waste in a certain volume of water sample.

(d) for sustaining life in a water body.

Answer: (c)

16. Which polymer has chiral, monomer(s)?

(a)  Buna-N

(b)  Neoprene

(c)  Nylon 6,6

(d) PHBV

Answer: (d)

17. A, B and C are three biomolecules. The results of the tests performed on them are given below:

Molisch’s Test Barfoed Test Biuret Test
A Positive Negative Negative
B Positive Positive Negative
C Negative Negative Positive

A, B and C are respectively

(a)  A = Lactose B = Glucose C = Albumin

(b)  A = Lactose B = Glucose C = Alanine

(c)  A = Lactose B = Fructose C = Alanine

(d) A = Glucose B = Sucrose C = Albumin

Answer: (a)

18. The decreasing order of basicity of the following amines is:

(a)  I > II > III > IV

(b)  IV > III > I > II

(c)  II > I > III > IV

(d) IV > I > II > III

Answer: (b)

19. 

The compound [P] is

Answer: (b)

20. In the following reaction A is :

Answer: (d)

21. The sum of total number of bonds between chromium and oxygen atoms in chromate and dichromate ions is:

Answer: (12)

22. A sample of milk splits after 60 min. at 300K and after 40 min at 400K when the population of lactobacillus acidophilus in it doubles . The activation energy (in kJ/mol) for this process is closest to : (Given, R = 8.3 J mol1K1), ln(2/3) = 0.4, e3 = 4.0)

Answer: (3.98)

23. One litre of sea water (d =1.03g/cm3) contains 10.3 mg of O2 Determine the concentration of O2 in ppm:

Answer: (10.00)

24. A cylinder containing an ideal gas (0.1 mol of 1.0 dm3 ) is in thermal equilibrium with a large volume of 0.5 molal aqueous solution of ethylene glycol at it freezing point. If the stoppers S1 and S2 (as shown in the figure) suddenly withdrawn, the volume of the gas in liters after equilibrium is achieved will be: (Given, Kf (water) = 2.0 K kg mol1 ,R = 0.08 dm3 atm K1 mol1)

Answer: (2.18)

25. Consider the following reactions;

The mass percentage of carbon in A is:

Answer: (66.67)

Mathematics

1. If A = {x∈ R∶ |x| <2} and B = {x∈ R∶ |x−2| ≥3} then :

(a)  A − B = [−1,2]

(b)  B − A = R− (−2, 5)

(c)  A ⋃ B = R− (2,5)

(d) A ∩ B = (−2, −1)

Answer: (b)

2. If 10 different balls has to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is :

(a)  965/210

(b)  945/210

(c)  945/211

(d) 965/211

Answer: (b)

3. If x = 2 sin θ − sin 2 θ and y = 2 cos θ − cos 2 θ, θ ∈ [0, 2π], then d2y/dx2 at θ =π is:

(a)  −3/8

(b)  3/4

(c)  3/2

(d) −3/4

Answer: (*)

4. Let f and g be differentiable functions on R, such that fog is the identity function. If for some a, b ∈ R, g’(a) = 5 and g(a) = b, then f'(b) is equal to :

(a)  2/5

(b)  5

(c)  1

(d) 1/5

Answer: (d)

5. In the expansion of  if l1 is the least value of the term independent of x when  and l2 is the least value of the term independent of x when  then the ratio l2 : l1 is equal to:

(a)  16 : 1

(b)  8 : 1

(c)  1 : 8

(d) 1 : 16

Answer: (a)

6. Let a,b ∈R, a ≠ 0, such that the equation, ax2-2bx + 5 = 0 has a repeated root α, which is also a root of the equation x2 − 2bx − 10 = 0. If β is the root of this equation, then α2 + β2 is equal to:

(a)  24

(b)  25

(c)  26

(d) 28

Answer: (b)

7. Let a function f: [0, 5] → R, be continuous, f(1) = 3 and F be defined as:

 

Then for the function F, the point x = 1 is

(a)  a point of inflection.

(b)  a point of local maxima

(c)  a point of local minima

(d) not a critical point

Answer: (c)

8. Let [t] denotes the greatest integer ≤ t and  Then the function, f(x) = [x2] sin πx discontinuous, when x is equal to

(a) 

(b)  √A

(c) 

(d) 

Answer: (a)

9. Let a – 2b + c = 1

If   then:

(a)  f(−50) = 501

(b)  f(−50) = −1

(c)  f(50) = 1

(d) f(50) = −501

Answer: (c)

10. Given:  and  Then the area (in sq. units) of the region bounded by the curves y = f(x) and y = g(x) between the lines 2x = 1 to 2x = √3 is:

(a) 

(b) 

(c) 

(d) 

Answer: (a)

11. The following system of linear equations

7x + 6y – 2z = 0

3x + 4y + 2z = 0

x – 2y – 6z = 0, has

(a)  infinitely many solutions, (x, y, z) satisfying y = 2z

(b)  infinitely many solutions (x, y, z) satisfying x = 2z

(c)  no solution

(d) only the trivial solution

Answer: (b)

12. If p − > (p ∧~ q) is false. Then the truth values of p and q are respectively

(a)  F, T

(b)  T, F

(c)  F, F

(d) T, T

Answer: (d)

13. The length of minor axis (along y-axis) of an ellipse of the standard form is 4/√3. If this ellipse touches the line x + 6y = 8, then its eccentricity is:

(a) 

(b) 

(c) 

(d) 

Answer: (b)

14. If z be a complex number satisfying |Re(z)| + |Im(z)| = 4, then |𝑧| cannot be:

(a)  √7

(b) 

(c)  √10

(d) √8

Answer: (a)

15. If  and   where 0 < θ < π/4, then:

(a)  y(1 + x) = 1

(b)  x(1 – y) = 1

(c)  y(1 – x) = 1

(d) x(1 + y) = 1

Answer: (c)

16. If  then a value of x satisfying y(x) = e is:

(a)  √3e

(b) 

(c)  √2e

(d) e/√2

Answer: (a)

17. If one end of focal chord AB of the parabola y2 = 8x is at A(1/2, −2), then the equation of tangent to it at B is

(a)  x + 2y + 8 = 0

(b)  2x – y – 24 = 0

(c)  x – 2y + 8 = 0

(d) 2x + y – 24 = 0

Answer: (c)

18. Let an be the nth term of a G.P. of positive terms. If  then  is equal to:

(a)  300

(b)  175

(c)  225

(d) 150

Answer: (d)

19. A random variable X has the following probability distribution:

X 1 2 3 4 5
P(X) K2 2K K 2K 5K2

Then P(X > 2) is equal to:

(a)  7/12

(b)  23/36

(c)  1/36

(d) 1/6

Answer: (b)

20. If  where C is constant if integration, then the ordered pair (λ, f(θ)) is equal to:

(a)  (−1, 1 – tan θ)

(b)  (−1, 1 + tan θ)

(c)  (1, 1 + tan θ)

(d) (1, 1 – tan θ)

Answer: (b)

21. Let  be three vectors such that  and the angle between is π/3. If   is perpendicular to vector  is equal to______

Answer: (30)

22. If Cr = 25Cr and C0 + 5 ∙ C1 + 9 ∙ C2 + … + 101 ∙ C25 = 225 ∙ k is equal to ________.

Answer: (51)

23. If the curves x2 − 6x + y2 +8 = 0 and x2 − 8y + y2 + 16 − k = 0, (k > 0) touch each other at a point, then the largest value of k is

Answer: (36)

24. The number of terms common to the A.P.’s 3,7,11,…407 and 2,9,16,…709 is __________.

Answer: (14)

25. If the distance between the plane. 23x – 10y – 2z + 48 = 0 and the plane containing the lines  and  (λ ∈ R) is equal to  then k is equal to ________.

Answer: (3)

JEE Main January 9 2020 Shift 1 Question Paper with Answer Key

Physics

1. Three identical solid spheres each have mass ‘m’ and diameter ‘d’ are touching each other as shown in the figure. Calculate ratio of moment of inertia about the axis perpendicular to plane of paper and passing through point P and B as shown in the figure. Given P is centroid of the triangle.

(a)  13/23

(b)  13/15

(c)  15/13

(d) 23/13

Answer: (a)

2. A solid sphere having a radius R and uniform charge density ρ. If a sphere of radius R/2 is carved out of it as shown in the figure. Find the ratio of the magnitude of electric field at point A and B

(a)  17/54

(b)  18/54

(c)  18/34

(d) 21/34

Answer: (c)

3. Consider an infinitely long current carrying cylindrical straight wire having radius ‘a’. Then the ratio of magnetic field due to wire at distance a/3 and 2a, respectively from axis of wire is

(a)  3/2

(b)  2/3

(c)  2

(d) 1/2

Answer: (b)

4. Particle moves from point A to point B along the line shown in figure under the action of force Determine the work done on the particle by  in moving the particle from point A to point B (all quantities are in SI units)

(a)  1J

(b)  1/2 J

(c)  2 J

(d) 3/2 J

Answer: (a)

5. For the given P-V graph of an ideal gas, chose the correct V-T graph. Process BC is adiabatic. (Graphs are schematic and not to scale).

Answer: (a)

6. An electric dipole of moment  is at the origin (0, 0, 0). The electric field due to this dipole at is parallel to [Note that  ]

(a) 

(b) 

(c) 

(d) 

Answer: (c)

7. A body A of mass m is revolving around a planet in a circular orbit of radius R. At the instant the particle B has velocity  , another particle of mass m/2 moving at velocity of , collides perfectly inelastically with the first particle. Then, the combined body

(a)  Fall vertically downward towards the planet.

(b)  Continue to move in a circular orbit

(c)  Escape from the Planet’s Gravitational field

(d) Start moving in an elliptical orbit around the planet

Answer: (d)

8. Two particles of equal mass m have respective initial velocities  They collide completely inelastically. Find the loss in kinetic energy.

(a)  3mu2/4

(b)  √2mu2/√3

(c)  mu2/3

(d) mu2/8

Answer: (d)

9. Three harmonic waves of same frequency (v) and intensity (I0) having initial phase angles 0, π/4, −π/4 rad respectively. When they are superimposed, the resultant intensity is close to;

(a)  5.8I0

(b)  I0

(c)  3I0

(d) 0.2I0

Answer: (a)

10. An ideal liquid (water) flowing through a tube of non-uniform cross-sectional area, where area at A and B are 40 cm2 and 20 cm2 If pressure difference between A & B is 700 N/m2, then volume flow rate is (density of water = 1000 kgm−3)

(a)  2720 cm

(b)  2420 cm

(c)  1810 cm

(d) 3020 cm

Answer: (a)

11. A screw gauge advances by 3 mm on main scale in 6 rotations. There are 50 divisions on circular scale. Find least count of screw gauge?

(a)  0.01 cm

(b)  0.001 cm

(c)  0.001 mm

(d) 0.02 mm

Answer: (b)

12. A telescope of aperture diameter 5 m is used to observe the moon from the earth. Distance between the moon and earth is 4 × 105 The minimum distance between two points on the moon’s surface which can be resolved using this telescope is close to (Wavelength of light is 5500 Å )

(a)  60 m

(b)  20 m

(c)  600 m

(d) 200 m

Answer: (a)

13. Radiation with wavelength 6561 Å falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of 3×104 If the radius of largest circular path followed by electron is 10 mm, the work function of metal is close to;

(a)  1.8 eV

(b)  0.8 eV

(c)  1.1 eV

(d) 1.6 eV

Answer: (c)

14. Kinetic energy of the particle is 𝐸 and it’s de–Broglie wavelength is λ. On increasing its K.E by ΔE, it’s new de–Broglie wavelength becomes λ/2. Then ΔE is

(a)  3E

(b)  2E

(c)  2E

(d) 4E

Answer: (a)

15. A quantity is given by , where c is speed of light, G is universal gravitational constant and h is the Planck’s constant. Dimension of f is that of;

(a)  area

(b)  energy

(c)  volume

(d) momentum

Answer: (b)

16. A vessel of depth 2h is half filled with a liquid of refractive index √2 in upper half and with a liquid of refractive index 2√2 in lower half. The liquids are immiscible. The apparent depth of inner surface of the bottom of the vessel will be;

(a)  3h√2/4

(b)  h/√2

(c)  h/3√2

(d) h/2(√2+1)

Answer: (a)

17. In the given circuit diagram, a wire is joining point B & C. Find the current in this wire;

(a)  0.4 A

(b)  2 A

(c)  0

(d) 4 A

Answer: (b)

18. Two plane electromagnetic waves are moving in vacuum in whose electric field vectors are given by  and At t = 0 A charge q is at origin with velocity   (c is speed of light in vacuum). The instantaneous force on this charge (all data are in SI units)

(a) 

(b) 

(c) 

(d) 

Answer: (b)

19. Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an additional vibration mode and have a mass m/4 . The ratio of molar specific heat at constant volume of gas A and B is;

(a)  7/9

(b)  5/9

(c)  3/5

(d) 5/7

Answer: (d)

20. A charged particle of mass ‘m’ and charge ‘q’ is moving under the influence of uniform electric field  and a uniform magnetic field  follow a trajectory from P to Q as shown in figure. The velocities at P and Q are respectively  Then which of the following statements (A, B, C, D) are correct? (Trajectory shown is schematic and not to scale)

(A) Magnitude of electric field 

(B) Rate of work done by electric field at P is 

(C) Rate of work done by both fields at Q is zero

(D) The difference between the magnitude of angular momentum of the particle at P and Q is 2mva.

(a)  A, C and D are correct

(b)  A, B and C are correct

(c)  A, B. C and D are correct

(d) B, C and D are correct

Answer: (b)

21. In a fluorescent lamp choke (a small transformer) 100 V of reversible voltage is produced when choke changes current in from 0.25 A to 0 A in 0.025 ms. The self-inductance of choke (in mH) is estimated to be;

Answer: (10)

22. A wire of length l = 0.3 m and area of cross section 10–2 cm2 and breaking stress 4.8×107 N/m2 is attached with block of mass 10 kg. Find the maximum possible value of angular velocity (rad/s) with which block can be moved in a circle with string fixed at one end.

Answer: (4)

23. The distance x covered by a particle in one dimension motion varies as with time 𝑡 as x2 = at2 + 2bt + c, where a, b, c are constants. Acceleration of particle depend on x as x–n , the value of n is;

Answer: (3)

24. A rod of length 1 m pivoted at one end is released from rest when it makes 30° from the horizontal as shown in the figure below.

If ω of rod is √n at the moment it hits the ground, then find n.

Answer: (15)

25. In the given circuit both diodes are ideal having zero forward resistance and built-in potential of 0.7 V. Find the potential of point E in volts.

Answer: (12)

Chemistry

1. The de Broglie wavelength of an electron in the 4th Bohr orbit is:

(a)  4πa0

(b)  42πa0

(c)  8πa0

(d) 6πa0

Answer: (c)

2. If the magnetic moment of a dioxygen species is 1.73 B.M, it may be:

(a)  O2, O2, or O2+

(b)  O2 or O2+

(c)  O2 or O2

(d) O2, O2+

Answer: (b)

3. If enthalpy of atomisation for Br2(l) is x kJ/mol and bond enthalpy for Br2 is y kJ/mol, the relation between them:

(a)  is x > y

(b)  is x < y

(c)  is x = y

(d) does not exist

Answer: (a)

4. Which of the following oxides are acidic, basic and amphoteric, respectively?

(a)  MgO, Cl2O, Al2O3

(b)  N2O3, Li2O, Al2O3

(c)  SO3, Al2O3, Na2O

(d) P4O10, Cl2O, CaO

Answer: (b)

5. Complex X of composition Cr(H2O)6Cln, has a spin only magnetic moment of 3.83 BM. It reacts with AgNO3 and shows geometrical isomerism. The IUPAC nomenclature of X is :

(a)  Hexaaqua chromium(III) chloride

(b)  Tetraaquadichlorido chromium(III) chloride dihydrate

(c)  Hexaaquachromium(IV) chloride

(d) Tetraaquadichlorido chromium(IV) chloride dihydrate

Answer: (b)

6. The electronic configuration of bivalent europium and trivalent cerium, are: (Atomic Number : Xe = 54, Ce = 58, Eu = 63)

(a)  [Xe]4f7, [Xe]4f1

(b)  [Xe]4f 76s2 , [Xe]4f 26s2

(c)  [Xe]4f2, [Xe]4f7

(d) [Xe]4f4, [Xe]4f9

Answer: (a)

7. The Ksp for the following dissociation is = 1.6 × 10–5. PbCl2 (s) ⇌ Pb2 + (aq) + 2Cl(aq). Which of the following choices is correct for a mixture of 300 mL 0.134 M Pb(NO3)2 and 100mL

(a)  Q > Ksp

(b)  Q < Ksp

(c)  Q = Ksp

(d) Not enough data provided

Answer: (a)

8. The compound that cannot act both as oxidising and reducing agent is :

(a)  H2SO3

(b)  HNO2

(c)  H3PO4

(d) H2O2

Answer: (c)

9. B has a smaller first ionization enthalpy than Be. Consider the following statements:

(i) It is easier to remove 2p electron than 2s electron

(ii) 2p electron of B is more shielded from the nucleus by the inner core of electrons than the 2s electron of Be

(iii) 2s electron has more penetration power than 2p electron

Atomic radius of B is more than Be (Atomic number B=5, Be=4)

The correct statements are:

(a)  (i), (ii), and (iii)

(b)  (i), (iii), and (iv)

(c)  (ii), (ii), and (iii)

(d) (i), (ii), and (iv)

Answer: (a)

10. [Pd(F)(Cl)(Br)(I)]2−,has n number of geometrical Isomers. Then, the spin-only magnetic moment and crystal field stabilisation energy [CFSE] of [Fe(CN)6]n−6 , respectively, [Note: Ignore pairing energy].

(a)  1.73 BM and −2∆0

(b)  2.84 BM and −1.6∆0

(c)  0 BM and −2.4∆0

(d) 5.92 BM and 0

Answer: (a)

11. According to the following diagram, A reduces BO2 when the temperature is:

(a)  > 1400°C

(b)  < 1400°C

(c)  > 1200°C

(d) < 1200°C

Answer: (a)

12. For following reactions

It was found that the Ea is decreased by 30 kJ/mol in the presence of catalyst. If the rate remains unchanged, the activation energy for catalysed reaction is (Assume pre exponenetial factor is same)

(a)  75 kJ/mol

(b)  135 kJ/mol

(c)  105 kJ/mol

(d) 198 kJ/mol

Answer: (c)

13. ‘X’ melts at low temperature and is a bad conductor of electricity in both liquid and solid state. X is:

(a)  Mercuty

(b)  Silicon Carbide

(c)  Zinc Sulphide

(d) Carbon Tetrachloride

Answer: (d)

14. The major product Z obtained in the following reaction scheme is:

Answer: (c)

15. Which of these will produce the highest yield in Friedel-Craft’s reaction?

Answer: (b)

16. The major product (Y) in the following reactions is :

Answer: (a)

17. The correct order of heat of combustion for following alkadienes is:

(a)  C > B > A

(b)  B > A > C

(c)  A > B > C

(d) C > A > B

Answer: (c)

18. The increasing order of basicity for the following intermediates is (from weak to strong)

(a)  A > B > D > E > C

(b)  B > A > D > C > E

(c)  A > B > E > D > C

(d) C > E > D > B > A

Answer: (a)

19. A chemist has 4 samples of artificial sweetener A, B, C and D. To identify these samples, he performed certain experiments and noted the following observations:

(i) A and D both form blue-violet colour with ninhydrin.

(ii) Lassaigne extract of C gives positive AgNO3 test and negative Fe4[Fe(CN)6]3 test.

(iii) Lassaigne extract of B and D gives positive sodium nitroprusside test.

Based on these observations which option is correct?

(a)  A – Alitame, B – Saccharin, C – Aspartame, D – Sucralose

(b)  A –Saccharin, B – Alimate, C – Sucralose, D – Aspartame

(c)  A – Aspartame, B – Alitame, C – Saccharin, D – Sucralose

(d) A – Aspartame, B – Saccharin, C – Sucralose, D – Alitame

Answer: (d)

20. Identify (A) in the following reaction sequence:

Answer: (b)

21. The molarity of HNO3 in a sample which has density 1.4 g/mL and mass percentage of 63% is :(Molecular weight of HNO3= 63).

Answer: (14)

22. The hardness of a water sample containing 103 M MgSO4 expressed as CaCO3 equivalents (in ppm)is (molar mass of MgSO4 is 120.37 g/mol)

Answer: (100.00)

23. How much amount of NaCl should be added to 600 g of water (ρ = 1.00 g/mL) to decrease the freezing point of water to −2°C? (The freezing point depression constant for water = 2 K Kg mol1)

Answer: (1.76)

24. 108 g silver (molar mass 108 g mol-1) is deposited at cathode from AgNO3(aq) solution by a certain quantity of electricity. The volume (in L) of oxygen gas produced at 273K and 1 bar pressure from water by the same quantity of electricity is

Answer: (5.8)

25. The mass percentage of nitrogen in histamine is:

Answer: (37.84)

Mathematics

1. If C be the centroid of the triangle having vertices (3, −1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y − 1 = 0 and 3x − y + 1 = 0, then the line passing through the points C and P also passes through the point:

(a)  (−9, −7)

(b)  (−9, −6)

(c)  (7, 6)

(d) (9, 7)

Answer: (b)

2. The product 21/4×41/16×81/48×161/128… ..∞ to is equal to

(a)  21/4

(b)  2

(c)  21/2

(d) 1

Answer: (c)

3. A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness that melts at the rate of 50 cm3/min. When the thickness of ice is 5 cm, then the rate (in cm/min.) at which the thickness of ice decreases, is:

(a)  5/6π

(b)  1/54π

(c)  1/36π

(d) 1/18π

Answer: (d)

4. Let f be any function continuous on [a,b] and twice differentiable on (a,b). If for all x ∈ (a, b), f′(x) > 0 and f′′(x) < 0, then for any c ∈ (a,b),  is greater than:

(a) 

(b)  1

(c) 

(d) 

Answer: (c)

5. The value of  is:

(a)  1/4

(b)  1/2√2

(c)  1/2

(d) 1/√2

Answer: (b)

6. The number of real roots of the equation, e4x + e3x – 4e2x + ex + 1 = 0 is:

(a)  3

(b)  4

(c)  1

(d) 2

Answer: (c)

7. The value of  is equal to:

(a)  2π

(b)  4π

(c)  2π2

(d) π2

Answer: (d)

8. If for some α and β in R, the intersection of the following three planes

x + 4y − 2z = 1

x + 7y − 5z =β

x + 5y + αz = 5

is a line in R3, then α+β is equal to:

(a)  0

(b)  10

(c)  −10

(d) 2

Answer: (b)

9. If e1 and e2 are the eccentricities of the ellipse,  and the hyperbola,   respectively and (e1, e2) is a point on the ellipse, 15x2 + 3y2 = k. Then k is equal to:

(a)  14

(b)  15

(c)  17

(d) 16

Answer: (d)

10. If  is continuous at x = 0 then a + 2b is equal to:

(a)  −2

(b)  1

(c)  0

(d) −1

Answer: (c)

11. If the matrices  B = adj A and C = 3A, then   is equal to:

(a)  16

(b)  2

(c)  8

(d) 72

Answer: (c)

12. A circle touches the y-axis at the point (0,4) and passes through the point (2,0). Which of the following lines is not a tangent to the circle?

(a)  4x−3y+17 = 0

(b)  3x+4y−6 = 0

(c)  4x+3y−8 = 0

(d) 3x−4y−24 = 0

Answer: (c)

13. Let z be a complex number such that  Then the value of |z + 3i| is:

(a)  √10

(b)  7/2

(c)  15/4

(d) 2√3

Answer: (b)

14. If f′(x) = tan1(sec x + tan x),  and f(0) = 0, then f(1) is equal to:

(a)  (π+1)/4

(b)  (π+2)/4

(c)  1/4

(d) (π−1)/4

Answer: (a)

15. Negation of the statement: ′√5 is an integer or 5 is irrational′ is:

(a)  √5 is irrational or 5 is an integer.

(b)  √5 is not an integer or 5 is not irrational.

(c)  √5 is an integer and 5 is irrational.

(d) √5 is not an integer and 5 is not irrational.

Answer: (d)

16. If for all real triplets (a,b,c), f(x) = a+ bx+ cx2; then  is equal to:

(a) 

(b) 

(c) 

(d) 

Answer: (d)

17. If the number of five digit numbers with distinct digits and 2 at the 10th place is 336k, then k is equal to:

(a)  8

(b)  7

(c)  4

(d) 6

Answer: (a)

18. Let the observations xi(1 ≤ i ≤ 10) satisfy the equations,  and  If μ and λ are the mean and the variance of observations, (x1 – 3), (x2 – 3) …. (x10 – 3), then the ordered pair (μ, λ) is equal to:

(a)  (6, 3)

(b)  (3, 6)

(c)  (3, 3)

(d) (6, 6)

Answer: (c)

19. The integral  is equal to: (where C is a constant of integration)

(a) 

(b) 

(c) 

(d) 

Answer: (c)

20. In a box, there are 20 cards out of which 10 are labelled as A and remaining 10 are labelled as B. Cards are drawn at random, one after the other and with replacement, till a second A-card is obtained. The probability that the second A-card appears before the third B-card is:

(a)  15/16

(b)  9/16

(c)  13/16

(d) 11/16

Answer: (d)

21. If the vectors  and are coplanar and   then value of λ is ______.

Answer: (1)

22. The projection of the line segment joining the points (1,−1,3) and (2,−4,11) on the line joining the points (−1, 2, 3) and (3,−2,10) is _____.

Answer: (8)

23. The number of distinct solutions of the equation  in the interval [0, 2π], is _________.

Answer: (8)

24. If for x ≥ 0,y = y(x) is the solution of the differential equation (1 + x)dy = [(1 + x)2 + y − 3]dx, y(2) = 0, then y(3) is equal to:

Answer: (3)

25. The coefficient of x4 in the expansion of (1 + x + x)10 is

Answer: (615)

JEE Main January 8 2020 Shift 2 Question Paper with Answer Key

Physics

1. A very long wire ABDMNDC is shown in figure carrying current i. AB and BC parts are straight, long and at right angle. At D wire forms a circular turn DMND of radius R. AB, BC are tangential to circular turn at N and D. Magnetic field at the centre of circle is

(a) 

(b) 

(c) 

(d) 

Answer: (d)

2. A particle moves such that its position vector  where ω is a constant and t is time. Then which of the following statements is true for the velocity  and acceleration  of the particle?

(a)   both are perpendicular to 

(b)   both are parallel to 

(c)   is perpendicular to  is directed away from the origin

(d)  is perpendicular to  is directed towards the origin

Answer: (d)

3. Consider two charged metallic sphere S1 and S2 of radii r1 and r2, respectively. The electric fields E1(on S1) and E2(on S2) on their surfaces are such that  Then the ratio V1(on S1)/V2 (on S2) of the electrostatic potential on each sphere is

(a)  r1/r2

(b)  (r1/r2)2

(c)  r2/r1

(d) (r1/r2)3

Answer: (b)

4. A transverse wave travels on a taut steel wire with a velocity of V when tension in it is 2.06 × 104 N. When the tension is changed to T, the velocity changed to V/2. The value of T is close to

(a)  30.5 × 104 N

(b)  2.50 × 104 N

(c)  10.2 × 102 N

(d) 5.15 × 103 N

Answer: (d)

5. A particle of mass m is dropped from a height ℎ above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of √2gh. If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of  is

(a) 

(b) 

(c)  1/2

(d) 

Answer: (a)

6. A Carnot engine having an efficiency of 1/10 is being used as a refrigerator. If the work done on the refrigerator is 10 J, the amount of heat absorbed from the reservoir at lower temperature is

(a)  99 J

(b)  90 J

(c)  1 J

(d) 100 J

Answer: (b)

7. Two liquids of density ρ1 and ρ22 = 2ρ1) are filled up behind a square wall of side 10 𝑚 as shown in figure. Each liquid has a height of 5 𝑚. The ratio of forces due to these liquids exerted on the upper part MN to that at the lower part NO is (Assume that the liquids are not mixing)

(a)  2/3

(b)  1/2

(c)  1/4

(d) 1/3

Answer: ()

8. As shown in figure, when a spherical cavity (centered at O) of radius 1 m is cut out of a uniform sphere of radius 𝑅 (centered at C ), the center of mass of remaining (shaded) part of sphere is shown by COM, i.e. on the surface of the cavity. R can be determined by the equation

(a)  (R2 + R + 1) (2 – R) = 1

(b)  (R2 – R – 1) (2 – R) = 1

(c)  (R2 – R + 1) (2 – R) = 1

(d) (R2 + R – 1) (2 – R) = 1

Answer: (a)

9. A particle of mass m and charge q is released from rest in uniform electric field. If there is no other force on the particle, the dependence of its speed V on the distance x travelled by it is correctly given by (graphs are schematic and not drawn to scale)

Answer: (b)

10. A galvanometer having a coil resistance 100 Ω gives a full scale deflection when a current of 1 mA is passed through it. What is the value of the resistance which can convert this galvanometer into voltmeter giving full scale deflection for a potential difference of 10 V? In full scale deflection, current in galvanometer of resistance is 1 mA. Resistance required in series to convert it into voltmeter of range 10 V.

(a)  7.9 kΩ

(b)  9.9 kΩ

(c)  8.9 kΩ

(d) 10 kΩ

Answer: (b)

11. Consider a mixture of 𝑛 moles of helium gas and 2𝑛 moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its (Cp/Cv) value will be

(a)  67/45

(b)  40/27

(c)  19/13

(d) 23/15

Answer: (c)

12. A uniform sphere of mass 500 gm rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5 cm/s. Its kinetic energy is

(a)  8.75 × 104 J

(b)  6.25 × 104 J

(c)  8.75 × 103 J

(d) 1.13 × 103 J

Answer: (a)

13. A capacitor is made of two square plates each of side ‘a’ making a very small angle 𝛼 between them, as shown in figure. The capacitance will be close to

(a) 

(b) 

(c) 

(d) 

Answer: (a)

14. In a double-slit experiment, at a certain point on the screen the path difference between the two interfering waves is 1/8th of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is

(a)  0.568

(b)  0.853

(c)  0.672

(d) 0.760

Answer: (b)

15. As shown in figure, a battery of emf ε is connected to an inductor L and resistance R in series. The switch is closed at t = 0. The total charge that flows from the battery, between t = 0 and 𝑡 = tc (tc is the time constant of the circuit) is

(a)  εL/eR2

(b)  εR/eL2

(c) 

(d) εL/R2

Answer: (a)

16. A plane electromagnetic wave of frequency 25 GHz is propagating in vacuum along the z direction. At a particular point in space and time, the magnetic field is given by The corresponding electric field is given by  is (speed of light 𝑐 = 3 × 108 m/s)

(a) 

(b) 

(c) 

(d) 

Answer: (c)

17. An object is gradually moving away from the focal point of a concave mirror along the axis of the mirror. The graphical representation of the magnitude of linear magnification (m) versus distance of the object from the mirror (x) is correctly given by (Graphs are drawn schematically and are not to scale)

Answer: (b)

18. A simple pendulum is being used to determine the value of gravitational acceleration g at a certain place. The length of the pendulum is 25.0 cm and a stop watch with 1 sec resolution measures the time taken for 40 oscillations to be 50 sec. The accuracy in g

(a)  5.40%

(b)  3.40%

(c)  4.40%

(d) 2.4%

Answer: (c)

19. An electron (mass 𝑚) with initial velocity  is an electric field  If λ0 is initial de-Broglie wavelength of electron. its de-Broglie wavelength at time t is given by

(a) 

(b) 

(c) 

(d) 

Answer: (a)

20. In the given circuit, value of Y is

(a)  1

(b)  0

(c)  Will not execute

(d) Toggles between 0 and 1

Answer: (b)

21. The first member of Balmer series of hydrogen atom has a wavelength of 6561 Å. The wavelength of the second member of the Balmer series (in nm) is

Answer: (486 nm)

22. A ball is dropped from the top of a 100 m high tower on a planet. In the last 1/2 s before hitting the ground, it covers a distance of 19 𝑚. Acceleration due to gravity (in ms−2) near the surface on that planet is Solution: g = 8 m/s2

Answer: (8 m/s2)

23. Three containers C1, C2 and C3 have water at different temperatures. The table below shows the final temperature T when different amounts of water (given in liters) are taken from each container and mixed (assume no loss of heat during the process)

C1 C2 C3 T(°C)
1l 2l 60
1l 2l 30
2l 1l 60
1l 1l 1l θ

The value of θ (in °C to the nearest integer) is

Answer: (50)

24. An asteroid is moving directly towards the centre of the earth. When at a distance of 10R (R is the radius of the earth) from the earth’s centre, it has a speed of 12 km/s. Neglecting the effect of earth’s atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 12 km/s )? Give your answer to the nearest integer in km/s

Answer: (16)

25. The series combination of two batteries both of the same emf 10 V, but different internal resistance of 20 Ω and 5 Ω , is connected to the parallel combination of two resistors 30 Ω and R Ω. The voltage difference across the battery of internal resistance 20 Ω is zero, the value of R (in Ω) is

Answer: (30)

Chemistry

1. Arrange the following bonds according to their average bond energies in descending order:

C-Cl, C-Br, C-F, C-I

(a)  C-Cl > C-Br > C-I > C-F

(b)  C-Br>C-I>C-Cl>C-F

(c)  C-I>C-Br>C-Cl>C-F

(d) C-F>C-Cl>C-Br>C-I

Answer: (d)

2. The radius of second Bohr orbit, in terms of the Bohr radius, 𝑎0 , in Li2+ is:

(a)  2a0/3

(b)  4a0/9

(c)  4a0/3

(d) 2a0/9

Answer: (c)

3. A metal (A) on heating in nitrogen gas gives compound B. B on treatment with H2O gives a colourless gas which when passed through CuSO4 solution gives a dark blue-violet coloured solution. A and B respectively, are :

(a)  Na and Na­3N

(b)  Mg and Mg3N2

(c)  Mg, Mg(NO3)2

(d) Na, NaNO3

Answer: (a)

4. The correct order of the calculated spin-only magnetic moments of complexes A to D is:

(A) Ni(CO)4

(B) [Ni(H2O)6]2+

(C) Na2[Ni(CN)4]

(D) PdCl2(PPh3)2

(a)  (C) < (D) < (B) < (A)

(b)  (A) ≈ (C) ≈ (D) < (B)

(c)  (A) ≈ (C) < (B) ≈ (D)

(d) (C) ≈ (D) < (B) < (A)

Answer: (b)

5. Hydrogen has three isotopes (A), (B) and (C). If the number of neutron(s) in (A), (B) and (C) respectively, are (x), (y) and (z), the sum of (x), (y) and (z) is:

(a)  4

(b)  1

(c)  3

(d) 2

Answer: (c)

6. Consider the following plots of rate constant versus 1/T for four different reactions. Which of the following orders is correct for the activation energies of these reactions?

(a)  Ea > Ec > Ed > Eb

(b)  Ec > Ea > Ed > Eb

(c)  Eb > Ed > Ec > Ea

(d) E > Ea > Ed > Ec

Answer: (b)

7. Which of the following compounds is likely to show both Frenkel and Schottky defects in its crystalline form?

(a)  ZnS

(b)  CsCl

(c)  KBr

(d) AgBr

Answer: (d)

8. White phosphorus on reaction with concentrated NaOH solution in an inert atmosphere of CO2 gives phosphine and compound (X). (X) on acidification with HCl gives compound (Y). The basicity of compound (Y) is:

(a)  4

(b)  2

(c)  3

(d) 1

Answer: (d)

9. Among the reactions (a) – (d), the reaction(s) that does/do not occur in the blast furnace during the extraction of iron is/are:

(A) CaO + SiO2 → CaSiO3

(B) 3Fe2O3 + CO → 2Fe3O4 + CO2

(C) FeO + SiO2 → FeSiO3

(d) FeO → Fe + (1/2)O2

(a)  A

(b)  D

(c)  C and D

(d) A and D

Answer: (c)

10. The increasing order of the atomic radii of the following elements is:

(A) C

(B) O

(C) F

(D) Cl

(E) Br

(a)  B<C<D<A<E

(b)  C<B<A<D<E

(c)  A<B<C<D<E

(d) D<C<B<A<E l

Answer: (a)

11. Among (a) – (d), the complexes that can display geometrical isomerism are:

(A) [Pt(NH3)3Cl]+

(B) [Pt(NH3)Cl5]

(C) [Pt(NH3)2Cl(NO2)]

(D) [Pt(NH3)4ClBr]2+

(a)  A and B

(b)  D and A

(c)  C and D

(d) B and C

Answer: (a)

12. For the following Assertion and Reason, the correct option is:.

Assertion: The pH of water increases with increase in temperature.

Reason: The dissociation of water into H+ and OH an exothermic reaction.

(a)  Both assertion and reason are false.

(b)  Assertion is not true, but reason is true.

(c)  Both assertion and reason are true and the reason is the correct explanation for the assertion.

(d) Both assertion and reason are true, but the reason is not the correct explanation for the assertion.

Answer: (d)

13. For the following Assertion and Reason, the correct option is:

Assertion: For hydrogenation reactions, the catalytic activity increases from group-5 to group11 metals with maximum activity shown by group 7-9 elements

Reason: The reactants are most strongly adsorbed on group 7-9 elements

(a)  Both assertion and reason are false.

(b)  The assertion is true, but the reason is false.

(c)  Both assertion and reason are true, but the reason is not the correct explanation of assertion

(d) Both assertion and reason are true and the reason is the correct explanation of assertion

Answer: (a)

14. The major product of the following reactions is:

Answer: (d)

15. Find The major product [B] of the following sequence of reactions is:

Answer: (c)

16. Among the following compounds A and B with molecular formula C9H18O3, A is having higher boiling point than B. The possible structures of A and B are

Answer: (b)

17. Kjeldahl’s method cannot be used to estimate nitrogen for which of the following compounds?

(a)  CH3CH2 – C = N

(b)  C6H5NH2

(c)  C6H5NO2

(d) 

Answer: (c)

18. An unsaturated hydrocarbon absorbs two hydrogen molecules on catalytic hydrogenation, and also gives following reaction;  X will be:

Answer: (b)

19. Preparation of Bakelite proceeds via reactions:

(a)  Electrophilic substitution and dehydration.

(b)  Electrophilic addition and dehydration.

(c)  Condensation and elimination

(d) Nucleophilic addition and dehydration

Answer: (a)

20. Two monomers of maltose are:

(a)  alpha-D-Glucose and alpha-D-Galactose

(b)  alpha-D-Glucose and alpha-D-Glucose

(c)  alpha-D-Glucose and alpha-D-Fructose

(d) alpha-D-Glucose and alpha-D-Glucose

Answer: (b)

21. At constant volume, 4 mol of an ideal gas when heated from 300 K to 500 K changes its internal energy by 5000 J. The molar heat capacity at constant volume is _____.

Answer: (6.25)

22. For an electrochemical cell

Sn(s)[Sn2+(aq., 1M) ||Pb2+(aq., 1M)|Pb(s)

The ratio[Sn2+]/[Pb2+] when this cell attains equilibrium is________.

 

Answer: (2.15)

23. NaClO3 is used, even in spacecrafts, to produce O2. The daily consumption of pure O2 by a person is 492 L at 1 atm, 300 K. How much amount of NaClO3, in grams, is required to produce O2 for the daily consumption of a person at 1 atm, 300 K ?

NaClO3(s) + Fe(s) → O2(g) + FeO(s) + NaCl(s)

R = 0.082 L atm mol1 K1

Answer: (2.13)

24. Complexes [ML5] of metals Ni and Fe have ideal square pyramidal and trigonal bipyramidal and geometries, respectively. The sum of the 900, 1200 and 1800 L-M-L angles in the two complexes is ______.

Answer: (20)

25. In the following sequence of reactions, the maximum number of atoms present in molecule ‘C’ in one plane is _____

(Where A is a lowest molecular weight alkyne).

Answer: (13)

Mathematics

1. Let A and B be two events such that the probability that exactly one of them occurs is 2/5 and the probability that A or B occurs is 1/2, then the probability of both of them occur together is

(a)  0.10

(b)  0.20

(c)  0.01

(d) 0.02

Answer: (a)

2. Let 𝑆 be the set of all real roots of the equation, 3x (3x − 1) + 2 = |3x − 1| + |3x − 2|. Then S:

(a)  is a singleton.

(b)  is an empty set.

(c)  contains at least four elements

(d) contains exactly two elements.

Answer: (a)

3. The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11. Then the correct variance is:

(a)  4.01

(b)  3.99

(c)  3.98

(d) 4.02

Answer: (b)

4. Let  be two vectors. If  is a vector such that  is equal to:

(a)  1/2

(b)  −3/2

(c)  −1/2

(d) −1

Answer: (c)

5. Let f: (1,3) → 𝑅 be a function defined by f(x) = x[x]/(x2 +1) , where [x] denotes the greatest integer ≤ x. Then the range of 𝑓 is:

(a)  (2/5 , 3/5 ] ∪ ( 3/4 , 4/5 )

(b)  (2/5 , 4/5 ]

(c)  (3/5 , 4/5 )

(d) (2/5 , 1/2 ) ∪ ( 3/5 , 4/5 ]

Answer: (d)

6. If α and β be the coefficients of x4 and x2 respectively in the expansion of  then:

(a)  α + β = −30

(b)  α − β = −132

(c)  α + β = 60

(d) α − β = 60

Answer: (b)

7. If a hyperbola passes through the point (10, 16) and it has vertices at (±6, 0), then the equation of the normal at P is:

(a)  3x + 4y = 94

(b)  x + 2y = 42

(c)  2x + 5y = 100

(d) x + 3y = 58

Answer: (c)

8. is equal to:

(a)  0

(b)  1/10

(c)  −1/10

(d) −1/5

Answer: (a)

9. If a line, y = mx + c is a tangent to the circle, (x − 3)2 + y2 = 1 and it is perpendicular to a line L1, where L1 is the tangent to the circle, x2 + y2 = 1 at the point ( 1 /√2 , 1/√2 ); then:

(a)  c2 + 7c+ 6 = 0

(b)  c2 – 6c + 7 = 0

(c)  c2 – 7c + 6 = 0

(d) c2 + 6c + 7 = 0

Answer: (d)

10. Let  If  then a and b are the roots of the quadratic equation:

(a)  x2 + 101x + 100 = 0

(b)  x2 + 102x + 101 = 0

(c)  x2 – 102x + 101 = 0

(d) x2 – 101x + 100 = 0

Answer: (c)

11. The mirror image of the point (1, 2, 3) in a plane is  Which of the following points lies on  this plane?

(a)  (1, −1, 1)

(b)  (−1, −1, 1)

(c)  (1, 1, 1)

(d) (−1, −1, −1)

Answer: (a)

12. The length of the perpendicular from the origin, on the normal to the curve, x2 + 2xy – 3y2 = 0 at the point (2, 2) is:

(a)  2

(b)  2√2

(c)  4√2

(d) √2

Answer: (b)

13. Which of the following statements is a tautology?

(a)  ~(p ∧ ~q) → (p ∨ q)

(b)  (~p ∨ ~q) → (p ∧ q)

(c)  p ∨ (~q) → (p ∧ q)

(d) ~(p ∨ ~q) → (p ∨ q)

Answer: (d)

14. If  then:

(a)  1/6 < I2 < 1/2

(b)  1/8 < I2 < 1/4

(c)  1/9 < I2 < 1/8

(d) 1/16 < I2 < 1/9

Answer: (c)

15. If  then 10A1 is equal to:

(a)  6I – A

(b)  A – 6I

(c)  4I – A

(d) A – 4I

Answer: (b)

16. The area (in sq. units) of the region {(x, y) ∈ R2 : x2 ≤ y ≤ 3 – 2x}, is:

(a)  31/3

(b)  32/3

(c)  29/3

(d) 34/3

Answer: (b)

17. Let S be the set of all functions f : [0,1] →R, which are continuous on [0, 1] and differentiable on (0, 1). Then for every f in 𝑆, there exists a c ∈ (0,1), depending on f, such that:

(a) 

(b)  |f(c) + f(1)| < |f′(c)|

(c)  |f(c) + f(1)| < (1 + c)|f′(c)|

(d) |f(c) − f(1)| < (1 − c)|f′(c)|

Answer: (*)

18. The differential equation of the family of curves, x2 = 4b(y + b), b ∈ R, is:

(a)  xy′′ = y′

(b)  x(y′)2 = x + 2yy′

(c)  x(y′)2 = x – 2yy′

(d) x(y′)2 = 2yy′ − x

Answer: (b)

19. The system of linear equations

λx + 2y + 2z = 5

2λx + 3y + 5z = 8

4x + λy + 6z = 10 has:

(a)  no solution when λ = 2

(b)  infinitely many solutions when λ = 2

(c)  no solution when λ = 8

(d) a unique solution when λ = −8

Answer: (a)

20. If the 10th term of an A.P. is 1/20 and its 20𝑡ℎ term is 1/10 , then the sum of its first 200 terms is:

(a) 

(b)  100

(c)  50

(d) 

Answer: (d)

21. Let a line y = mx (m > 0) intersect the parabola, y2 = x at a point 𝑃, other than the origin. Let the tangent to it at 𝑃 meet the x−axis at the point Q. If area (ΔOPQ) = 4 sq. units, then 𝑚 is equal to __________ .

Answer: (0.5)

22. Let f(𝑥) be a polynomial of degree 3 such that f(−1) = 10, f(1) = −6, f(x) has a critical point at 𝑥 = −1 and f′(𝑥) has a critical point at x = 1. Then the local minima at x =______

Answer: (3)

23. If    then tan(α + 2β) is equal to_______.

Answer: (1)

24. The number of 4 letter words (with or without meaning) that can be made from the eleven letters of the word “EXAMINATION” is _________.

Answer: (2454)

25. The sum,  is equal to ________.

Answer: (504)

JEE Main January 8 2020 Shift 1 Question Paper with Answer Key

Physics

1. A particle of mass m is fixed to one end of a light spring having force constant k and ustreatch length l. The other end is fixed. The system is given an angular speed ω about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is

(a) 

(b) 

(c) 

(d) 

Answer: (a)

2. Three charged particles A, B and C, with charge −4q, +2q and −2q present on the circumference of a circle of radius d. The charges particles A, C and centre O of the circle formed an equilateral triangle as shown in figure. Electric field at O along x-direction is:

(a) 

(b) 

(c) 

(d) 

Answer: (c)

3. A thermodynamic cycle xyzx is shown on a V – T diagram.

The P-V diagram that best describes this cycle is : (Diagrams are schematic and not upto scale)

Answer: (c)

4. Find the co-ordinates of center of mass of the lamina shown in the figure below.

(a)  (0.75 m, 1.75 m)

(b)  (0.075 m, 0.75 m)

(c)  (1.25 m, 1.5 m)

(d) (1 m, 1.75 m)

Answer: (a)

5. The plot that depicts the behavior of the mean free time τ (time between two successive collisions) fot the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graph the schematic and not drawn to scale)

Answer: (a)

6. Effective capacitance of parallel combination of two capacitors C1 and C2 is 10 μF. When these capacitor are individually connects to a voltage source of 1 V, the energy stored in the capacitor C2 is 4 times of that in C1. If these capacitors are connected in series, their effective capacitance will be:

(a)  1.6 μF

(b)  3.2 μF

(c)  4.2 μF

(d) 8.4 μF

Answer: (a)

7. Consider a uniform rod of mass 4m and length L pivoted about its centre. A mass m is moving with a velocity ν making angle θ=π/4 to the rod’s long axis collides with one end of the rod and stick to it. The angular speed of the rod-mass system just after collision is

(a) 

(b) 

(c) 

(d) 

Answer: (a)

8. When photons of energy 4 eV strikes the surface of a metal A, the ejected photoelectrons have maximum kinetic energy TA eV and de-Broglie wavelength λA. The maximum kinetic energy of photoelectrons liberated from another metal B by photon of energy 4.50 eV is TB = (TA − 1.5) eV. If the de-Broglie wavelength of these photoelectrons λB = 2 λA, then the work function of metal B is

(a)  3 eV

(b)  1.5 eV

(c)  2 eV

(d) 4 eV

Answer: (d)

9. The length of a potentiometer wire of length 1200 𝑐𝑚 and it carries a current of 60 mA. For a cell of emf 5 V and internal resistance of 20 Ω, the null point on it is found to be at 1000 cm. The resistance of whole wire is

(a)  80 Ω

(b)  100 Ω

(c)  120 Ω

(d) 60 Ω

Answer: (b)

10. The magnifying power of a telescope with tube length 60 cm is 5. What is the focal length of its eyepiece?

(a)  10 cm

(b)  20 cm

(c)  30 cm

(d) 40 cm

Answer: (a)

11. Consider two solid spheres of radii R1 = 1 m, R2 = 2 m and masses M1 & M2, respectively. The gravitational field due to two spheres 1 and 2 are shown. The value of M1/M2 is

(a)  1/6

(b)  1/3

(c)  1/2

(d) 2/3

Answer: (a)

12. Proton with kinetic energy of 1 MeV moves from south to north. It gets an acceleration of 1012 m/s2 by an applied magnetic field (west to east). The value of magnetic field: (Rest mass of proton is 1.6 × 10−27 kg)

(a)  0.71 mT

(b)  7.1 mT

(c)  71 mT

(d) 0.071 mT

Answer: (a)

13. If finding the electric field around a surface is given by  is applicable. In the formula Ɛ0 is permittivity of free space, A is area of Gaussian and qenc is charge enclosed by the Gaussian surface. This equation can be used in which of the following equation?

(a)  Only when the Gaussian surface is an equipotential surface.

(b)  Only when  = constant on the surface.

(c)  Equipotential surface and  is constant on the surface

(d) for any choice of Gaussian surfaces.

Answer: (c)

14. The dimension of stopping potential V0 in photoelectric effect in units of Planck’s constant (h), speed of light (c), and gravitational constant (G) and Ampere (A) is

(a)  h2/3c5/3G1/3A−1

(b)  h2c1/3G3/2A−1

(c)  h1/3G2/3c1/3A−1

(d) h−2/3c−1/3G4/3A−1

Answer: (*)

15. A leak proof cylinder of length 1 m, made of metal which has very low coefficient of expansion is floating in water at 0°C such that its height above the water surface is 20 cm. When the temperature of water is increases to 4°C, the height of the cylinder above the water surface becomes 21 cm. The density of water at T = 4°C relative to the density at T = 0°C is close to

(a)  1.01

(b)  1.03

(c)  1.26

(d) 1.04

Answer: (a)

16. The graph which depicts the result of Rutherford gold foil experiment with α- particle is:

θ: Scattering angle

N : Number of scattered α – particles is detected

(Plots are schematic and not to scale)

Answer: (b)

17. At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next 5 s, then induced EMF in the loop is:

(a)  56 μV

(b)  28 μV

(c)  30 μV

(d) 48 μV

Answer: (a)

18. Choose the correct Boolean expression for the given circuit diagram:

(a)  A.B

(b) 

(c)  A + B

(d) 

Answer: (d)

19. Consider a solid sphere of density  The minimum density of a liquid in which it float is just

(a) 

(b) 

(c)  ρ0/5

(d) ρ0/3

Answer: (a)

20. The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability 4/3 for this wavelength, will be

(a)  15°

(b)  30°

(c)  45°

(d) 60°

Answer: (b)

21. A body of mass m = 10 kg has an initial velocity of  It collides elastically with another body, B of the mass which has an initial velocity of  After collision, A moves with a velocity  The energy of B after collision is written as (x/10) J, the value of x is

Answer: (1)

22. A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is 30 cm and the refractive index of lens material is 1.5, then the focal length of the lens (in cm) is

Answer: (60 cm)

23. A particle is moving along the x-axis with its coordinate with time t given by x(t) = -3t2 + 8t + 10 m. Another particle is moving along the y-axis with its coordinate as a function of time given by y = 5 – 8t3 At t = 1 s, the speed of the second particle as measured in the frame of the first particle is given as √v . Then v (m/s) is

Answer: (580 m/s)

24. A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ____Hz.

Answer: (106.05 Hz)

25. Four resistors of resistance 15 Ω, 12 Ω, 4Ω and 10Ω respectively in cyclic order to form a wheatstone’s network. The resistance that is to be connected in parallel with the resistance of 10 to balance the network is _______.

Answer: (10 Ω)

Chemistry

1. The number of bonds between sulphur and oxygen atoms in S2O82− and number of bonds between sulphur and sulphur atoms in rhombic sulphur, respectively, are:

(a)  8 and 6

(b)  4 and 6

(c)  8 and 8

(d) 4 and 8

Answer: (c)

2. The predominant intermolecular forces present in ethyl acetate, a liquid, are:

(a)  London dispersion, dipole-dipole and hydrogen bonding

(b)  hydrogen bonding and London dispersion

(c)  dipole-dipole and hydrogen bonding

(d) London dispersion and dipole-dipole

Answer: (d)

3. For the Balmer series in the spectrum of H-atom,

The correct statements among (A) to (D) are:

(A) The integer n1 = 2.

(B) The ionization energy of hydrogen can be calculated from the wave number of these lines.

(C) The lines of longest wavelength corresponds to n2= 3.

(D) As wavelength decreases, the lines of the series converge.

(a)  B, C, D

(b)  A, B, D

(c)  A, C, D

(d) A, B, C

Answer: (c)

4. The first ionization energy (in kJ/mol) of Na, Mg, Al and Si, respectively,

(a)  496, 737, 577, 786

(b)  496, 577, 737, 786

(c)  496, 577, 786, 737

(d) 786, 737, 577, 496

Answer: (a)

5. The stoichiometry and solubility product of a salt with the solubility curve given below is, respectively:

(a)  X2Y, 2 × 10−9M3

(b)  XY2, 1 × 10−9 M3

(c)  XY2, 4 × 10−9 M3

(d) XY, 2 × 10−6 M3

Answer: (c)

6. The complex that can show fac- and mer-isomers is:

(a)  [Co(NO2)3(NH3)3]

(b)  [PtCl2(NH3)2

(c)  [Co(NH3)4Cl2]

(d) [CoCl2(en)2]

Answer: (a)

7. A graph of vapour pressure and temperature for three different liquids X, Y and Z is shown below:

The following inferences are made:

(A) X has higher intermolecular interactions compared to Y

(B) X has lower intermolecular interactions compared to Y

(C) Z has lower intermolecular interactions compared to Y

The correct inference(s) is/are:

(a)  C

(b)  A

(c)  B

(d) A and C

Answer: (c)

8. As per Hardy-Schulze formulation, the flocculation values of the following for ferric hydroxide sol are in the order:

(a)  AlCl3 > K3[Fe(CN)6] > K2CrO4 > KBr = KNO3

(b)  K3 [Fe(CN)6 ] < K2CrO4 < AlCl3 < KBr < KNO3

(c)  K3 [Fe(CN)6 ] < K2CrO4 < KBr = KNO3 = AlCl3

(d) K3 [Fe(CN)6 ] > AlCl3 > K2CrO4 > KBr > KNO3

Answer: (c)

9. The rate of a certain biochemical reaction at physiological temperature (T) occurs 106 times faster with enzyme than without. The change in activation energy upon adding enzyme is:

(a)  − 6RT

(b)  – 6 × 2.303 RT

(c)  + 6RT

(d) +6 × 2.303 RT

Answer: (b)

10. When gypsum is heated to 393K, it forms:

(a) 

(b)  Dead burnt plaster

(c)  CaSO4 ∙ 5H2O

(d) Anhydrous CaSO4

Answer: (a)

11. The third ionization enthalpy is minimum for:

(a)  Mn

(b)  Co

(c)  Ni

(d) Fe

Answer: (d)

12. The strength of an aqueous NaOH solution is most accurately determined by titrating: (Note: consider that an appropriate indicator is used)

(a)  Aq. NaOH in a pipette and aqueous oxalic acid in a burette

(b)  Aq. NaOH in a volumetric flask and concentrated H2SO4 in a conical flask

(c)  Aq. NaOH in a burette and concentrated H2SO4 in a conical flask

(d) Aq. NaOH in a burette and aqueous oxalic acid in a conical flask

Answer: (d)

13. The decreasing order of reactivity towards dehydrohalogenation (E1) reaction of the following compounds is:

(a)  B > A > D > C

(b)  B > D > C > A

(c)  B > D > A > C

(d) D > B > C > A

Answer: (d)

14. Major product in the following reaction is:

Answer: (c)

15. Arrange the following compounds in increasing order of C—OH bond length: methanol, phenol, p-ethoxyphenol

(a)  Phenol < methanol < p-ethoxyphenol

(b)  methanol < p-ethoxyphenol < phenol

(c)  Phenol < p-ethoxyphenol < methanol

(d) methanol < phenol < p-ethoxypheno

Answer: (c)

16. Among the gases (i) – (v), the gases that cause greenhouse effect are:

(i) CO2

(ii) H2O

(iii) CFC

(iv) O2

(v) O3

(a)  i, ii iii and iv

(b)  i, iii iv and v

(c)  i and iv

(d) i, ii, iii and v

Answer: (d)

17. The major products A and B in the following reactions are:

Answer: (a)

18. A flask contains a mixture of isohexane and 3-methylpentane. One of the liquids boils at 63°C while the other boils at 60°C. What is the best way to separate the two liquids and which one will be distilled out first?

(a)  Fractional distillation, isohexane

(b)  Simple distillation, 3-methylpentane

(c)  Fractional distillation, 3-methylpentane

(d) Simple distillation, isohexane

Answer: (a)

19. Which of the given statement is not true for glucose?

(a)  The pentacetate glucose does not react with hydroxylamine to give oxime.

(b)  Glucose reacts with hydroxylamine to form oxime.

(c)  Glucose gives Schiff’s test for aldehyde.

(d) Glucose exists in two crystalline forms alpha and beta.

Answer: (c)

20. The reagent used for the given conversion is:

(a)  B2H6

(b)  LiAlH4

(c)  NaBH4

(d) H2, Pd

Answer: (a)

21. The volume (in mL) of 0.125 M AgNO3 required to quantitatively precipitate chloride ions in 0.3 g of [Co(NH3)6]Cl3­ is______.

Answer: (26.92)

22. What will be the electrode potential for the given half cell reaction at pH= 5?

2H2O → O2 + 4H+ + 4e; E° = −1.23 V

(R = 8.314 Jmol1K1; temp. = 298 K; oxygen under std. atm. pressure of 1 bar.)

Answer: (1.52)

23. Ferrous sulphate heptahydrate is used to fortify foods with iron. The amount (in grams) of the salt required to achieve 10 ppm of iron in 100 kg of wheat is _______. Atomic weight: Fe=55.85; S=32.00; O=16.00)

Answer: (4.96)

24. The magnitude of work done by gas that undergoes a reversible expansion along the path ABC shown in figure is

Answer: (48)

25. The number of chiral centres in Penicillin is _______.

Answer: (3)

Mathematics

1. For which of the following ordered pairs (μ, δ), the system of linear equations

x + 2y + 3z = 1

3x + 4y + 5z = μ

4x + 4y + 4z = δ

is inconsistent?

(a)  (4, 6)

(b)  (3, 4)

(c)  (1, 0)

(d) (4, 3)

Answer: (d)

2. Let y = (x) be a solution of the differential equation,  |x| < 1. If  is equal to:

(a)  −1/√2

(b)  −√3/2

(c)  1/√2

(d) √3/2

Answer: (c)

3. If a, b and c are the greatest values of 19Cp, 20Cq, 21Cr respectively, then:

(a) 

(b) 

(c) 

(d) 

Answer: (a)

4. Which of the following is a tautology?

(a)  (P ∧ (P → Q)) → Q

(b)  P ∧ (P ∨ Q)

(c)  (Q → (P ∧ (P → Q))

(d) P ∨ (P ∧ Q)

Answer: (a)

5. Let f: R → R be such that for all x ∈ R, (21+x + 21 – x), f(x) and (3x + 3x) are in A.P., then the minimum value of f(x) is:

(a)  0

(b)  4

(c)  3

(d) 2

Answer: (c)

6. The locus of a point which divides the line segment joining the point (0, −1) and a point on the parabola, x2 = 4y, internally in the ratio 1: 2, is:

(a)  9x2 – 12y = 8

(b)  4x2 – 3y = 2

(c)  x2 – 3y = 2

(d) 9x2 – 3y = 2

Answer: (a)

7. For 𝑎 > 0, let the curves C1: y2 = ax and C2 ∶ x2 = ay intersect at origin O and a point 𝑃. Let the line x = b (0 < b < a) intersect the chord OP and the x-axis at points Q and R, respectively. If the line x = b bisects the area bounded by the curves, C1 and C2, and the area of ΔOQR = 1/2,then‘a’ satisfies the equation

(a)  x6 – 12x3 + 4 = 0

(b)  x6 – 12x3 – 4 = 0

(c)  x6 + 6x3 – 4 = 0

(d) x6 – 6x3 + 4 = 0

Answer: (a)

8. The inverse function of  is

(a) 

(b) 

(c) 

(d) 

Answer: (b)

9. 

(a)  e

(b)  1/e2

(c)  1/e

(d) e2

Answer: (b)

10. Let f(x) = (sin(tan1x) + sin(cot1 x))2 – 1, where |x| > 1. If  and y(√3) = π/6, then y(−√3) is equal to:

(a)  π/3

(b)  2π/3

(c)  −π/6

(d) 5π/6

Answer: (*)

11. If the equation, x2 + bx + 45 = 0 (b ∈ R) has conjugate complex roots and they satisfy |z + 1| = 2√10, then :

(a)  b2 + b = 12

(b)  b2 – b = 42

(c)  b2 – b = 30

(d) b2 + b = 72

Answer: (c)

12. The mean and standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p and then reduced by q, where p ≠ 0 and q ≠ If the new mean and standard deviation become half of their original values, then q is equal to:

(a)  −20

(b)  −5

(c)  10

(d) −10

Answer: (a)

13. If  where c is a constant of integration, then λf(π/3) is equal to :

(a)  −9/8

(b)  9/8

(c)  2

(d) −2

Answer: (d)

14. Let A and B be two independent events such that p(A) = 1/3 and P(B) = 1/6. Then which of the following is TRUE?

(a)  P(A/(A ∪ B)) = 1/4

(b)  P(A/B′) = 1/3

(c)  P(A/B) = 2/3

(d) P(A′/B′) = 1/3

Answer: (b)

15. If volume of parallelepiped whose coterminous edges are given by  be 1 cu. unit. If θ be the angle between the edges  then cos θ can be:

(a)  7/6√6

(b)  5/7

(c)  7/6√3

(d) 5/3√3

Answer: (c)

16. Let two points be A(1, −1) and B(0, 2). If a point P(x′, y′) be such that the area of ∆PAB = 5 sq. units and it lies on the line, 3x + y = 4λ = 0. then the value of λ is:

(a)  4

(b)  1

(c)  −3

(d) 3

Answer: (d)

17. The shortest distance between the lines

(a)  2√30

(b) 

(c)  3

(d) 3√30

Answer: (d)

18. Let the line y = mx and the ellipse 2x2 + y2 = 1 intersect a point P in the first quadrant. If the normal to this ellipse at P meets the co-ordinate axes at(−1/3√2, 0) and (0, β), then β is equal to:

(a)  2/√3

(b)  2/3

(c)  2√2/3

(d) √2/3

Answer: (d)

19. If c is a point at which Rolle’s theorem holds for the function,  in the interval [3, 4], where a ∈ R, then f′′(c) is equal to:

(a)  −1/24

(b)  −1/12

(c)  √3/7

(d) 1/12

Answer: (d)

20. Let f(x) = x cos1(sin|−|x|)), x ∈ (−π/2, π/2), then which of the following is true?

(a)  f′(0) = −π/2

(b)  f′ is decreasing in (−π/2, 0) and increasing in (0, π/2)

(c)  f is not differentiable at x = 0

(d) f′ is increasing in (−π/2, 0) and decreasing in (0, π/2)

Answer: (b)

21. An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at most three of them are red is.

Answer: (490)

22. Let the normal at a P on the curve y2 – 3x2 + y + 10 = 0 intersect the y-axis at (0,3/2). If m is the slope of the tangent at P to the curve, then |m| is equal to____________.

Answer: (4)

23. The least positive value of ‘a’ for which the equation,  has real roots is _______.

Answer: (8)

24. The sum  is _______.

Answer: (1540)

25. The number of all 3×3 matrices A, with entries from the set {−1,0,1} such that the sum of the diagonal elements of (AAT) is 3, is __________.

Answer: (672)

JEE Main January 7 2020 Shift 2 Question Paper with Answer Key

Physics

1. A box weighs 196 N on a spring balance at the North Pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take g = 10 m/s2 at the North Pole and radius of the Earth = 6400 km)

(a)  194.32 N

(b)  194.66 N

(c)  195.32 N

(d) 195.66 N

Answer: (c)

2. In a building, there are 15 bulbs of 45 w, 15 bulbs of 100 W, 15 small fans of 10 W and 2 heaters of 1 kW. The voltage of electric main is 220 V. The minimum fuse capacity (rated value) of the building will be approximately

(a)  10 A

(b)  20 A

(c)  25 A

(d) 15 A

Answer: (b)

3. Under a adiabatic process, the volume of an ideal gas gets doubled. Consequently, the mean collision time between the gas molecules changes from τ1 to τ2. If  is given by

(a)  1/2

(b) 

(c)  (1/2)γ

(d) 2

Answer: (*)

4. A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid-point of the role such that the top half of the rope makes an angle of 45° with the vertical. Then F equals (Take g = 10 m/s2 and rope to be massless)

(a)  100 N

(b)  90 N

(c)  75 N

(d) 70 N

Answer: (a)

5. Mass per unit area of a circular disc of radius a depends on the distance r from its centre as σ(r) = A + Br. The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is

(a) 

(b) 

(c) 

(d) 

Answer: (a)

6. Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures T­1 and T2. The temperature of the hot reservoir of the first engine is T1 and the temperature of the cold reservoir of the second engine is T­2. T is the temperature of the sink of first engine which is also the source for the second engine. How is T related to T1 and T2 if both the engines perform equal amount of work?

(a) 

(b) 

(c)  T = 0

(d) 

Answer: (b)

7. The acitivity of a radioactive substance falls from 700 s1 to 500 s1 in 30 minutes. Its half-life is close to

(a)  66 min

(b)  62 min

(c)  52 min

(d) 72 min

Answer: (b)

8. In a Young’s double slit experiment, the separation between the slits is 0.15 mm. In the experiment, a source of light of wavelength 589 nm is used and the interference pattern is observed on a screen kept 1.5 m away. The separation between the successive bright fringes on the screen is

(a)  5.9 mm

(b)  3.9 mm

(c)  6.9 mm

(d) 4.9 mm

Answer: (a)

9. An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of minimum and maximum velocities of fluid in this pipe is

(a) 

(b)  9/16

(c)  3/4

(d) 4/3

Answer: (b)

10. In the figure, potential difference between a and b is

(a)  0 V

(b)  15 V

(c)  10 V

(d) 5 V

Answer: (c)

11. A particle of mass m and charge q has an initial velocity  If an electric field and magnetic field   act on the particle, its speed will double after a time

(a) 

(b) 

(c) 

(d) 

Answer: (a)

12. A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one receded with the same speed (much less than the speed of sound). The observer hears 2 beats/sec. The oscillation frequency of each tuning fork is υ0 = 1400 Hz and the velocity of sound in air is 350 m/s. The speed of each tuning fork is close to

(a)  1/4 m/s

(b)  1 m/s

(c)  1/2 m/s

(d) 1/8 m/s

Answer: (a)

13. An electron (of mass m) and a photon have the same energy E in the range of few eV. The ratio of the de Broglie wavelength associated with the electron and the wavelength of the photon is. (c = speed of light in vacuum)

(a)  (E/2m)1/2

(b)  1/c(2E/m)1/2

(c)  c(2mE)1/2

(d) 1/c(E/2m)1/2

Answer: (d)

14. A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane, then the magnitude of induced emf will be maximum and minimum, respectively at

(a)  2.5 sec and 5 sec

(b)  5 sec and 7.5 sec

(c)  2.5 sec and 7.5 sec

(d) 5 sec and 10 sec

Answer: (a)

15. The electric field of a plane electromagnetic wave is given by At t = 0, a positively charged particle is at the point (x, y, z) = (0, 0, π/k). If its instantaneous velocity at t = 0 is  the force acting on it due to the wave is

(a)  zero

(b) 

(c) 

(d) 

Answer: (b)

16. A thin lens made of glass (refractive index = 1.5) of focal length f =16 cm is immersed in a liquid of refractive index 1.42. If its focal length in liquid is fl, then the ratio fl/f is closest to the integer

(a)  9

(b)  17

(c)  1

(d) 5

Answer: (a)

17. An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being 68 kg. The mass of the elevator itself is 920 kg and it moves with a constant speed of 3 m/s. The frictional force opposing the motion is 6000 N. If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator (g = 10 m/s2) must be at least

(a)  66000 W

(b)  63360 W

(c)  48000 W

(d) 56300 W

Answer: (a)

18. The figure gives experimentally measured B vs H variation in a ferromagnetic material. The retentivity, coercivity and saturation, respectively, of the material are

(a)  1.5 T, 50 A/m, 1 T

(b)  1 T, 50 A/m, 1.5 T

(c)  1.5 T, 50 A/m, 1 T

(d) 150 A/m, 1 T, 1.5 T

Answer: (b)

19. An emf of 20 V is applied at time t = 0 to a circuit containing in series 10 mH inductor and 5 Ω The ratio of the currents at time t = ∞ and t = 40 s is close to (take e2 = 7.389)

(a)  1.06

(b)  1.46

(c)  1.15

(d) 0.84

Answer: (a)

20. The dimension of B2/2μ0, where B is magnetic field and μ0 is the magnetic permeability of vacuum, is

(a)  ML1T2

(b)  ML2T2

(c)  MLT2

(d) ML2T1

Answer: (a)

21. A 60 pF capacitor is fully charged by a 20 V supply. It is then disconnected from the supply and is connected to another uncharged 60 pF capacitor in parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in nJ)______.

Answer: (6)

22. M grams of steam at 100°C is mixed with 200 g of ice at its melting point in a thermally insulated container. If it produces liquid water at 40°C [heat of vaporization of water is 540 cal/g and heat of fusion of ice is 80 cal/g], the value of M is _______.

Answer: (40)

23. Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a point b above its centre of mass (see figure). If the coefficient of friction is μ = 0.4, the maximum value of  for the box not to topple before moving is ______.

Answer: (50)

24. The sum of two forces  such that The angle θ (in degrees) that the resultant of   will make with  is_______

Answer: (90°)

25. The balancing length for a cell is 560 cm in a potentiometer experiment. When an external resistance of 10 Ω is connected in parallel to the cell, the balancing length changes by 60 cm. If the internal resistance of the cell is  the value of N is_______

Answer: (12)

Chemistry

1. Consider the following reactions:

Which of these reactions are possible?

(a)  A and D

(b)  B and D

(c)  B, C and D

(d) A and B

Answer: (b)

2. In the following reaction sequence,

The major product B is:

Answer: (a)

3. For the following reactions,

ks and ke, are, respectively, the rate constants for substitution and elimination, and  the correct option is______.

(a)  μA > μB and ke(A) > ke(B)

(b)  μB > μA and ke(A) > ke(B)

(c)  μA > μB and ke(B) > ke(A)

(d) μB > μA and ke(B) > ke(A)

Answer: (c)

4. Which of the following statements is correct?

(a)  Gluconic acid can form cyclic (acetal/hemiacteal) structure

(b)  Gluconic acid is dicarboxylic acid

(c)  Gluconic acid is obtained by oxidation of glucose with HNO3

(d) Gluconic acid is a partial oxidation product of glucose

Answer: (d)

5. The correct order of stability for the following alkoxides is:

(a)  (C) > (A) > (B)

(b)  (B) > (A) > (C)

(c)  (C) > (B) > (A)

(d) (B) > (C) > (A)

Answer: (b)

6. In the following reaction sequence, structures of A and B, respectively will be:

Answer: (a)

7. A chromatography column, packed with silica gel as stationary phase, was used to separate a mixture of compounds consisting of (A) benzanilide, (B) aniline and (C) acetophenone. When the column is eluted with a mixture of solvents, hexane : ethyl acetate (20 : 80), the sequence of obtained compound is:

(a)  (B), (A) and (C)

(b)  (C), (A) and (B)

(c)  (B), (C) and (A)

(d) (A), (B) and (C)

Answer: (b)

8. The number of possible optical isomers for the complexes [MA2B2] with sp3 or dsp2 hybridized metal atom, respectively, is:

Note: A and B are unidentate neutral and unidentate monoanionic ligands, respectively.

(a)  0 and 1

(b)  2 and 2

(c)  0 and 0

(d) 0 and 2

Answer: (b)

9. The bond order and magnetic characteristics of CN are:

(a)  3, paramagnetic

(b)  3, diamagnetic

(c)  2.5, diamagnetic

(d) 2.5, paramagnetic

Answer: (c)

10. The equation that is incorrect is:

(a) 

(b) 

(c) 

(d) 

Answer: (a)

11. In the following reactions, product (A) and (B), respectively, are:

NaOH + Cl2 → (A) + side products

(hot & conc.)

Ca(OH)2 + Cl2 → (B) + side products

(dry)

(a)  NaClO3 and Ca(ClO3)2

(b)  NaOCl and Ca(ClO3)2

(c)  NaOCl and Ca(OCl)2

(d) NaClO3 and Ca(OCl)2

Answer: (d)

12. Two open beakers one containing a solvent and the other containing a mixture of that solvent with a non-volatile solute are together sealed in a container. Over time:

(a)  the volume of the solution and the solvent does not change

(b)  the volume of the solution increases and the volume of the solvent decreases

(c)  the volume of the solution decreases and the volume of the solvent increases

(d) the volume of the solution does not change and the volume of the solvent decreases

Answer: (b)

13. The refining method used when the metal and the impurities have low and high melting temperatures, respectively, is:

(a)  vapour phase refining

(b)  distillation

(c)  liquation

(d) zone refining

Answer: (c)

14. Among statements I-IV, the correct ones are:

(I) Decomposition of hydrogen peroxide gives dioxygen

(II) Like hydrogen peroxide, compounds, such as KClO3, Pb(NO3)2 and NaNO3 when heated liberate dioxygen.

(III) 2-Ethylanthraquinone is useful for the industrial preparation of hydrogen peroxide.

(IV) Hydrogen peroxide is used for the manufacture of sodium perborate

(a)  I, II, III and IV

(b)  I, II and III only

(c)  I, III and IV only

(d) I and III only

Answer: (a)

15. The redox reaction among the following is:

(a)  formation of ozone from atmospheric oxygen in the presence of sunlight

(b)  reaction of H2SO4 with NaOH

(c)  combination of dinitrogen with dioxygen at 2000 K

(d) Reaction of [Co(H2O)6]Cl3 with AgNO3

Answer: (c)

16. Identify the correct labels of A, B and C in the following graph from the options given below:

Root mean square speed (Vrms); most probable speed (Vmp); average speed (Vav)

(a)  A = Vmp, B = Vav, C = Vrms

(b)  A = Vmp, B = Vrms, C = Vav

(c)  A = Vav, B = Vrms, C = Vmp

(d) A = Vrms, B = Vmp, C = Vav

Answer: (a)

17. For the reaction,

2H2(g) + 2NO(g) → N2(g) + 2H2O(g)

The observed rate expression is, rate = kf[NO]2[H2]. The rate expression for the reverse reaction is:

(a)  kb[N2][H2O]2

(b)  kb[N2][H2O]

(c)  kb[N2][H2O]2/[H2]

(d) kb[N2][H2O]2/[NO]

Answer: (c)

18. Within each pair of elements F & Cl, S and Se and Li & Na, respectively, the elements that release more energy upon a electron gain are:

(a)  Cl, Se and Na

(b)  Cl, S and Li

(c)  F, S and Li

(d) F, Se and Na

Answer: (b)

19. Among the following statements A-D, the incorrect ones are:

(A) Octahedral Co(III) complexes with strong field ligands have high magnetic moments

(B) When ∆o < P, the d-electron configuration of Co(III) in an octahedral complex is 

(C) Wavelength of light absorbed by [Co(en)3]3+ is lower than that of [CoF6]3−.

(D) If the ∆o for an octahedral complex of Co(III) is 18000 cm1, the ∆t for its tetrahedral complex with the same ligand will be 1600 cm1.

(a)  B and C only

(b)  A and D only

(c)  A and B only

(d) C and D only

Answer: (c)

20. The ammonia (NH3) released on quantitative reaction of 0.6 g urea (NH2CONH2) with sodium hydroxide (NaOH) can be neutralized by:

(a)  200 mL of 0.2 N HCl

(b)  100 mL of 0.1 N HCl

(c)  200 mL of 0.4 N HCl

(d) 100 mL of 0.2 N HCl

Answer: (d)

21. Number of sp2 hybrid carbon atoms present in aspartame is______.

Answer: (9)

22. 3 grams of acetic acid is added to 250 mL of 0.1 M HCl and the solution is made up to 500 mL. to 20 mL of this solution 1/2 mL of 5 M NaOH is added. The pH of this solution is_______.

(Given: log 3 = 0.4771, pKa of acetic acid = 4.74, molar mass of acetic acid = 60 g/mole).

Answer: (5.22)

23. The flocculation value of HCl for As2S3 sol is 30 mmolL1. If H2SO4 is used for the flocculation of arsenic sulphide, the amount, in grams, of H2SO4 in 250 mL required for the above purpose is _____.

Answer: (0.3675 g)

24. Consider the following reactions:

NaCl + K2Cr2O7 + H2SO4 → (A) + side products

(A) + NaOH → (B) + side products

(B) + H2SO4(dil.) + H2O2 → (C) + side products

The sum of the total number of atoms in one molecule of (A), (B) & (C) is ______.

Answer: (18)

25. The standard heat of formation (∆fH298°) of ethane (in kJ/mol), if the heat of combustion of ethane, hydrogen and graphite are −1560, −393.5 and −286 kJ/mol, respectively, is_______.

Answer: (−192.5 kJ/mol)

Mathematics

1. If 3x + 4y = 12√2 is a tangent to the ellipse  for some a ∈ R then the distance between the foci of the ellipse is:

(a)  2√5

(b)  2√7

(c)  2√2

(d) 4

Answer: (b)

2. Let A, B, C and D be four non-empty sets. The Contrapositive statement of “If A ⊆ B and B ⊆ D then A ⊆ C is :

(a)  If A ⊆ C, then B ⊂ A or D ⊂ B

(b)  If A ⊈ C, then A ⊆ B and B ⊆ D

(c)  If A ⊈ C, then A ⊈ B and B ⊆ D

(d) If A ⊈ C, then A ⊈ B or B ⊈ D

Answer: (d)

3. The coefficient of x7 in the expression (1+ x)10 + x(1 + x)9 + x2(1 + x)8 + … + x10 is :

(a)  420

(b)  330

(c)  210

(d) 120

Answer: (b)

4. In a workshop, there are five machines and the probability of any one of them to be out of service on a day is 1/4. If the probability that at most two machines will be out of service on the same day is (3/4)3k, then k is equal to :

(a)  17/2

(b)  4

(c)  17/4

(d) 17/8

Answer: (d)

5. If locus of mid points of the perpendiculars drawn from points on the line x = 2y to the line x = y is:

(a)  2x – 3y = 0

(b)  3x – 2y = 0

(c)  5x – 7y = 0

(d) 7x – 5y = 0

Answer: (c)

6. The value of α for which  is:

(a)  loge 2

(b)  loge √2

(c)  loge (4/3)

(d) loge (3/2)

Answer: (a)

7. If the sum of the first 40 terms of the series, 3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 + …. is

(a)  10

(b)  25

(c)  5

(d) 20

Answer: (d)

8. If  is a real number, then the argument of sin θ + i cos θ is:

(a)  π − tan1 (4/3)

(b)  −tan1 (3/4)

(c)  π – tan1 (4/3)

(d) tan1 (4/3)

Answer: (a)

9. Let A = [aij] and B = [bij] be two 3 × 3 real matrices such that bij = (3)(i+j2)ji, where i, j = 1, 2, 3. If the determinant of B is 81, then the determinant of A is:

(a)  1/9

(b)  1/81

(c)  1/3

(d) 3

Answer: (c)

10. Let f(x) be a polynomial of degree 5 such that x = ±1 are its critical points. If  then which one of the following is not true?

(a)  f(1) – 4f(−1) = 4

(b)  x = 1 is a point of maxima and x = −1 is a point of minimum of f.

(c)  f is an odd function.

(d) x = 1 is a point of minima and x = −1 is a point of maxima of f.

Answer: (d)

11. The number of ordered pairs (r, k) for which 6 . 35Cr = (k2 – 3) . 36Cr+1, where k is an integer, is:

(a)  4

(b)  6

(c)  2

(d) 3

Answer: (a)

12. Let a1, a2, a3,… be a G.P. such that a1 < 0, a1 + a2 = 4 and a3 + a4 = 16. If 

(a)  171

(b)  511/3

(c)  −171

(d) −513

Answer: (c)

13. Let  be three unit vectors such that   and  then the ordered pair  is equal to:

(a) 

(b) 

(c) 

(d) 

Answer: (c)

14. Let y = y(x) be the solution curve of the differential equation, satisfying y(0) = 1 This curve intersects the x-axis at a point whose abscissa is:

(a)  2 + e

(b)  2

(c)  2 – e

(d) −e

Answer: (c)

15. If θ1 and θ2 be respectively the smallest and the largest values of θ in (0, 2π) – {π} which satisfy the equation, is equal to:

(a)  2π/3

(b)  π/3

(c)  π/3 + 1/6

(d) π/9

Answer: (b)

16. Let α and β are the roots of the equation x2 – x – 1 = 0. If pk = (α)k + (β)k, k ≥ 1 then which one of the following statements is not true?

(a)  (p1 + p2 + p3 + p4 + p5) = 26

(b)  p5 = 11

(c)  p5 = p2 ∙ p3

(d) p3 = p5 – p4

Answer: (c)

17. The area (in sq. units) of the region {(x, y) ϵ R|4x2 ≤ y ≤ 8x + 12} is:

(a)  125/3

(b)  128/3

(c)  124/3

(d) 127/3

Answer: (b)

18. The value of c in Lagrange’s mean value theorem for the function f(x) = x3 – 4x2 + 8x + 11, where x ∈ [0, 1] is:

(a) 

(b)  2/3

(c) 

(d) 

Answer: (a)

19. Let y = y(x) be a function of x satisfying  where k is a constant and  is equal to:

(a)  −√5/2

(b)  √5/2

(c)  −√5/4

(d) 2/√5

Answer: (a)

20. Let the tangents drawn from the origin to the circle, x2 + y2 – 8x – 4y + 16 = 0 touch it at the points A and B. The (AB)2 is equal to:

(a)  32/5

(b)  64/5

(c)  52/5

(d) 56/5

Answer: (b)

21. If system of linear equations

x + y + z = 6

x + 2y + 3z = 10

3x + 2y + λz = μ

has more than two solutions, then μ – λ2 is equal to_______.

Answer: (13)

22. If the foot of perpendicular drawn from the point (1, 0, 3) on a line passing through (α, 7, 1) is (5/3, 7/3, 17/3), then α is equal to________.

Answer: (4)

23. If the function f defined on (−1/3, 1/3) by

is continuous, the k is equal to ______.

Answer: (5)

24. If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively then xy is equal to ________.

Answer: (54)

25. Let X = {n ∈ N: 1 ≤ n ≤ 50}. If A = {n ∈ X: n is a multiple of 2} and B = {n ∈ X : n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is _______.

Answer: (29)

JEE Main January 7 2020 Shift 1 Question Paper with Answer Key

Physics

1. A polarizer-analyzer set is adjusted such that the intensity of light coming out of the analyzer is just 10% of the original intensity. Assuming that the polarizer-analyzer set does not absorb any light, the angle by which the analyzer need to be rotated further to reduce the output intensity to be zero is

(a)  45°

(b)  71.6°

(c)  90°

(d) 18.4°

Answer: (d)

2. Which of the following gives reversible operation?

Answer: (c)

3. A 60 HP electric motor lifts an elevator with a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to (Given 1 HP = 746 W, g = 10 m/s2)

(a)  1.5 m/s

(b)  2.0 m/s

(c)  1.7 m/s

(d) 1.9 m/s

Answer: (d)

4. A long solenoid of radius R carries a time (t) dependent current I(t) = I0t(1 – t). A ring of radius 2R is placed coaxially near its middle. During the time instant 0 ≤ t ≤ 1, the included current (IR) and the induced EMF (V­R) in the ring changes as:

(a)  Direction of IR remains unchanged and VR is maximum at t = 0.5

(b)  Direction of IR remains unchanged and VR is zero at t = 0.25

(c)  At t = 0.5 direction of IR reverses and VR is zero

(d) At t = 0.25 direction of IR reverse and VR is maximum

Answer: (c)

5. Two moles of an ideal gas with  are  mixed with 3 moles of another ideal gas with The value of   for the mixture is

(a)  1.47

(b)  1.42

(c)  1.45

(d) 1.50

Answer: (b)

6. Consider a circular coil of wire carrying current I, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by ϕi. The magnetic flux through the area of the circular coil area is given by ϕ Which of the following option is correct?

(a)  ϕi = − ϕ0

(b)  ϕi > ϕ0

(c)  ϕi < ϕ0

(d) ϕi = ϕ0

Answer: (a)

7. The current (i1) (in A) flowing through 1 Ω resistor in the following circuit is

(a)  0.40 A

(b)  0.20 A

(c)  0.25 A

(d) 0.5 A

Answer: (b)

8. Two infinite planes each with uniform surface charge density +σ C/m2 are kept in such a way that the angle between them is 30°. The electric field in the region shown between them is given by:

(a) 

(b) 

(c) 

(d) 

Answer: (a)

9. If the magnetic field in a plane electromagnetic wave is given by  then what will be expression for electric filed?

(a) 

(b) 

(c) 

(d) 

Answer: ()

10. The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6 × 1016 The frequency of revolution of the electron in its first excited state (in s1) is:

(a)  6.2 × 1015

(b)  1.6 × 1014

(c)  7.8× 1014

(d) 5.6 × 1012

Answer: (c)

11. A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant ‘b’, the correct equivalence will be

(a) 

(b)  L ↔ k, C ↔ b, R ↔ m

(c)  L ↔ m, C ↔ k, R ↔ b

(d) 

Answer: (d)

12. Visible light of wavelength 6000 × 108 cm falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minima is at 60° from the central maxima. If the first minimum is produced at θ1, then θ1 is close to

(a)  20°

(b)  30°

(c)  45°

(d) 25°

Answer: (d)

13. The radius of gyration of a uniform rod of length l about an axis passing through a point l/4 away from the center of the rod, and perpendicular to it, is

(a) 

(b)

(c)  

(d)

Answer: (a)

14. A satellite of mass m is launched vertically upward with an initial speed u from the surface of the earth. After it reaches height R(R = radius of earth), it ejects a rocket of mass m/10 so that subsequently the satellite moves in a circular orbit, The kinetic energy of the rocket is (G = gravitational constant; M is the mass of earth)

(a) 

(b) 

(c) 

(d) 

Answer: (a)

15. Three point particles of mass 1 kg, 1.5 kg and 2.5 kg are placed at three corners of a right triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The centre of mass of the system is at the point:

(a)  0.9 cm right and 2.0 cm above 1 kg mass

(b)  2.0 cm right and 0.9 cm above 1 kg mass

(c)  1.5 cm right and 1.2 cm above 1 kg mass

(d) 0.6 cm right and 2.0 cm above 1 kg mass

Answer: (a)