# 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°

2. Which of the following gives reversible operation?

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

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

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

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

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

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)

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)

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

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)

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°

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)

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)

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

16. If we need a magnification of 375 of from a compound microscope of tube length 150 mm and an objective of focal length 5 mm, the focal length of the eye-piece should be close to:

(a)  22 mm

(b)  2 mm

(c)  12 mm

(d) 33 mm

17. Speed of transverse wave of a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm2) is 90 m/s. If the Young’s modulus of wire is 16 × 1011 Nm2, the extension of wire over its natural length is

(a)  0.03 mm

(b)  0.02 mm

(c)  0.04 mm

(d) 0.01 mm

18. 1 liter of dry air at STP expands adiabatically to a volume of 3 litres. If γ = 1.4, the work done by air is (34 = 4.655) (take air to be an ideal gas)

(a)  48 J

(b)  90.5 J

(c)  100.8 J

(d) 60.7 J

19. A bob of mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from the rest, the bob starts falling vertically. When it has covered a distance h, the angular speed of the wheel will be:

(a)

(b)

(c)

(d)

20. A parallel plate capacitor has plates of area A separated by distance ‘d’ between them It is filled with a dielectric which has a dielectric constant varies as k(x) = k(1 + ax), where ‘x’ is the distance measured from one of the plates. If (αd << 1), the total capacitance of the system is best given by t he expression:

(a)

(b)

(c)

(d)

21. A non-isotropic solid metal cube has coefficient of linear expansion as 5 × 105/°C along the x-axis and 5 × 106/°C along y-axis and z-axis. If the coefficient of volumetric expansion of the solid is C × 106/°C then the value of C is___

22. A loop ABCDEFA of straight edges has six corner points A(0, 0, 0), B(5, 0, 0), C(5, 5, 0), D(0, 5, 0), E(0, 5, 5), F(0, 0, 5). The magnetic field in this region is  The quantity of flux through the loop ABCDEFA (in Wb) is______

23. A carnot engine operates between two reservoirs of temperature 900 K and 300 K. The engine performs 1200 J of work per cycle. The heat energy in (J) delivered by the engine to the low temperature reservoir, in a cycle, is _______

24. A particle of mass 1 kg slides down a frictionless track (AOC) starting from rest at a point A(height 2 m). After reaching C, the particle continues to move freely in air as a projectile. When it reaches its highest point P(height 1 m) the kinetic energy of the particle (in J) is: (Figure drawn is schematic and not to scale; take g = 10 m/s2)______

25. A beam of electromagnetic radiation of intensity 6.4 × 105 W/cm2 is comprised of wavelength. λ = 310 nm. It falls normally on a metal (work function ϕ = 2 eV) of surface area 1 cm2. If one is 103 photons ejects an electron, total number of electrons ejected in 1s is 10x(hc = 1240 eV – nm, 1 eV = 1.6 × 109 J), then x is _________

Chemistry

1. The relative strength of interionic/intermolecular forces forces in decreasing order is:

(a)  ion-dipole > dipole-dipole > ion-ion

(b)  dipole-dipole > ion-dipole > ion-ion

(c)  ion-ion > ion-dipole > dipole-dipole

(d) ion-dipole > ion-ion > dipole-dipole

2. Oxidation number of potassium in K2O, K2O2 and KO­2, respectively, is:

(a)  +2, +1 and +1/2

(b)  +1, +2 and +4

(c)  +1, +1 and +1

(d) +1, +4, and +2

3. At 35°C, the vapour pressure of CS2 is 512 mm Hg and that of acetone is 344 mm Hg. A solution of CS2 in acetone has a total vapour pressure of 600 mm Hg. The false statement amongst the following is:

(a)  CS2 and acetone are less attracted to each other than to themselves

(b)  heat must be absorbed in order to produce the solution at 35°C

(c)  Raoult’s law is not obeyed by this system

(d) a mixture of 100 mL CS2 and 100 mL acetone has a volume < 200 mL

4. The atomic radius of Ag is closest to:

(a)  Ni

(b)  Cu

(c)  Au

(d) Hg

5. The dipole moments of CCl4, CHCl3 and CH4 are in the order:

(a)  CH4 < CCl4 < CHCl3

(b)  CHCl3 < CH4 = CCl4

(c)  CH4 = CCl4 < CHCl3

(d) CCl4 < CH4 < CHCl3

6. The comparison to the zeolite process for the removal of permanent hardness, the synthetic resins method is:

(a)  less efficient as it exchanges only anions

(b)  more efficient as it can exchanges only cations

(c)  less efficient as the resins cannot be regenerated

(d) more efficient as it can exchange both cations as well as anions

7. Amongst the following statements, that which was not proposed by Dalton was:

(a)  matter consists of indivisible atoms

(b)  when gases combine or reproduced in a chemical reaction they do so in a simple ratio by volume provided all gases are at the same T & P.

(c)  Chemical reactions involve reorganization of atoms. These are neither created nor destroyed in a chemical reaction.

(d) all the atoms of given element have identical properties including identical mass. Atoms of different elements differ in mass.

8. The increasing order of pKb for the following compounds will be:

(a)  ii < iii < i

(b)  iii < i < ii

(c)  i < ii < iii

(d) ii < i < iii

9. What is the product of the following reaction?

10. The number of orbitals associated with quantum number n = 5, ms = +1/2 is:

(a)  11

(b)  15

(c)  25

(d) 50

11. The purest form of commercial iron is:

(a)  cast iron

(b)  wrought iron

(c)  scrap iron and pig iron

(d) pig iron

12. The theory that can completely/properly explain the nature of bonding is [Ni(CO)4] is:

(a)  Werner’s theory

(b)  Crystal Field Theory

(c)  Molecular Orbital Theory

(d) Valence Bond Theory

13. The IUPAC name of the complex [Pt(NH­3)2Cl(NH2CH3)]Cl is:

(a)  Diamminechlorido(methanamine) platinum(II) chloride

(b)  Bisammine (methanamine) chloridoplatinum (II) chloride

(c)  Diammine (methanamine) chloridoplatinum (II) chloride

(d) Diamminechlorido (amino methane) platinum (II) chloride

14. 1-methyl ethylene oxide when treated with an excess of HBr produces:

15. Consider the following reaction:

The product ‘X’ is used:

(a)  in protein estimation as an alternative to ninhydrin

(c)  in laboratory test for phenols

(d) in acid-base titration as an indicator

16. Match the following:

17. Given that the standard potential; (E°) of Cu2+/Cu and Cu+/Cu are 0.34 V and 0.522 V respectively, the E° of Cu2+/Cu+ is:

(a)  +0.158 V

(b)  −0.158 V

(c)  0.182 V

(d) −0.182 V

18. A solution of m-chloroaniline, m-chlorophenol and m-chlorobenzoic acid in ethyl acetate was extracted initially with a saturated solution of NaHCO3 to give fraction A. The left over organic phase was extracted with dil. NaOH solution to give fraction B. The final organic layer was labeled as fraction C. Fraction A, B and C, contain respectively.

(a)  m-chlorobenzoic acid, m-chlorophenol and m-chloroaniline

(b)  m-cholrophenol, m-chlorobenzoic acid and m-chloroaniline

(c)  m-chloroaniline, m-chlorobenzoic acid and m-chlorophenol

(d) m-chlorobenzoic acid, m-chloroaniline and m-chlorophenol

19. The electron gain enthalpy (in kJ/mol) of fluorine, chlorine, bromine, and iodine, respectively, are:

(a)  −333, −325, −349 and −296

(b)  −333, −349, −325 and −296

(c)  −296, −325, −333 and −349

(d) −349, −333, −325 and −296

20. Consider the following reactions:

Which of these reaction(s) will not produce Saytezff product?

(a)  b and d

(b)  d only

(c)  a, c and d

(d) c only

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21. Two solutions A and B each of 100 L was made by dissolving 4 g of NaOH and 9.8 g of H2SO4 in water, respectively. The pH of the resulting solution obtained from mixing 40 L of Solution A and 10 L of Solution B is :

22. During the nuclear explosion, one of the products is 90Sr with half of 6.93 years. If 1 μg of 90Sr was absorbed in the bones of a newly born baby in place of Ca, how much time, in years, is required to reduce it by 90% if it is not lost metabolically

23. Chlorine reacts with hot and concentrated NaOH and produces compounds (X) and (Y). Compound (X) gives white precipitate with silver nitrate solution. The average bond order between Cl and O atoms in (Y) is

24. The number of chiral carbons in chloramphenicol is:

25. For the reaction A(l) → 2B(g)

∆U = 2.1 kcal, ∆S = 20 calK1 at 300 K, Hence ∆G in kcal is

Mathematics

1. The area of the region, enclosed by the circle x2 + y2 = 2, which is not common to the region bounded by the parabola y2 = x and the straight line y = x, is

(a)  1/3(12π – 1)

(b)  1/6(12π – 1)

(c)  1/3(6π – 1)

(d) 1/6(24π – 1)

2. Total number of six-digit numbers in which only and all five digits 1, 3, 5, 7 and 9 appear, is

(a)  56

(b)  1/2(6!)

(c)  6!

(d) 5/2(6!)

3. An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k = 3, 4, 5, otherwise X takes the value − The expected value of X, is

(a)  1/8

(b)  3/16

(c)  −1/8

(d) −3/16

4. If  where z = x +  iy, then the point (x, y) lies on a

(a)  circle whose centre is at (−1/2, −3/2).

(b)  straight line whose slope is 3/2.

(c)  circle whose diameter is √5/2.

(d) straight line whose slope is −2/3.

5. If f(a + b + 1 – x) = f(x) ∀ x, where a and b are fixed positive real numbers, then  is equal to

(a)

(b)

(c)

(d)

6. If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is

(a)  2√3

(b)  √3

(c)  3/√2

(d) 3√2

7. The logical statement (p ⇒ q) ⋀ (q ⇒ ~ p) is equivalent to

(a)  ~ p

(b)  p

(c)  q

(d) ~ q

8. The greatest positive integer k, for which 49k + 1 is a factor of the sum 49125 + 49124 + … + 492 + 49 + 1, is

(a)  32

(b)  60

(c)  65

(d) 63

9. A vector  lies in the plane of the vectors,  If  bisects the angle between  then

(a)

(b)

(c)

(d)

10. If  where  is

(a)  −1/4

(b)  4/3

(c)  4

(d) −4

11. If y = mx + 4 is a tangent to both the parabolas, y 2 = 4x and x2 = 2by, then b is equal to

(a)  −64

(b)  128

(c)  −128

(d) −32

12. Let α be a root of the equation x2 + x + 1 = 0 and the matrix  then the matrix A31 is equal to

(a)  A

(b)  A2

(c)  A3

(d) I3

13. If g(x) = x2 + x – 1 and (gof)(x) = 4x2 – 10x + 5, then f(5/4) is equal to

(a)  −3/2

(b)  −1/2

(c)  1/2

(d) 3/2

14. Let α and β are two real roots of the equation (k + 1) tan2x – √2λ tan x = 1 – k, where (k ≠ −1) and λ are real numbers. If tan2(α + β) = 50, then value of λ is

(a)  5√2

(b)  10√2

(c)  10

(d) 5

15. Let P be a plane passing through the points (2, 1, 0), (4, 1, 1) and (5, 0, 1) and R be any point (2, 1, 6).

(a)  (6, 5, 2)

(b)  (6, 5, −2)

(c)  (4, 3, 2)

(d) (3, 4, −2)

16. Let xk + yk = ak, (a, k > 0) and  then k is

(a)  1/3

(b)  3/2

(c)  2/3

(d) 4/3

17. Let the function f:[−7, 0] → R be continuous on [−7, 0] and differentiable on (−7, 0). If f(−7) = −3 and f’(x) ≤ 2, for all x ∈ (−7, 0), then for all such functions f, f(−1) + f(0) lies in the interval:

(a)  [−6, 20]

(b)  (−∞, 20]

(c)  (−∞, 11]

(d) [−3, 11]

18. If y = y(x) is the solution of the differential equation,  such that y(0) = 0, then y(1) is equal to

(a)  loge 2

(b)  2e

(c)  2 + loge 2

(d) 1 + loge 2

19. Five numbers are in A.P., whose sum is 25 and product is 2520. If one of these five numbers is −1/2, then the greatest number amongst them is

(a)  16

(b)  27

(c)  7

(d) 21/2

20. If the system all linear equations

2x + 2ay + az = 0

2x + 3by + bz = 0

2x + 4cy + cz = 0,

where a, b, c ∈ R are non-zero and distinct; has non-zero solution, then

(a)  a + b + c = 0

(b)  a, b, c are in A.P.

(c)  1/a, 1/b, 1/c are in A.P.

(d) a, b, c are in G.P.

21.

22. If variance of first n natural numbers is 10 and variance of first m even natural numbers is 16, m + n is equal to _______.

23. If the sum of the coefficients of all even powers of x in the product (1 + x + x2 + x3 … . + x2n) (1 – x + x2 – x3 … . + x2n) is 61, then n is equal to_____