**JEE MAIN 2019 Online CBT Mode DT. 10.01.2019 Evening**

**PHYSICS**

1. The modulation frequency of an AM radio station is 250 kHz, which is 10% of the carrier wave. If another AM station approaches you for license what broadcast frequency will you allot?

(1) 2750 kHz

(2) 2900 kHz

(3) 2000 kHz

(4) 2250 kHz

2. At some location on earth the horizontal component of earth’s magnetic field is 18 × 10^{–6} At this location, magnetic needle of length 0.12 m and pole strength 1.8 Am is suspended from its mid-point using a thread, it makes 45° angle with horizontal in equilibrium. To keep this needle horizontal, the vertical force that should be applied at one of its ends is:

(1) 1.3 × 10^{–5} N

(2) 1.8 × 10^{–5} N

(3) 6.5 × 10^{–5} N

(4) 3.6 × 10^{–5} N

3. The Wheatstone bridge shown in Fig. here, gets balanced when the carbon resistor used as R_{1} has the colour code (Orange, Red, Brown). The resistors R_{2} and R_{4} are 80 Ω and 40 Ω

(1) Brown, Blue, Black

(2) Red, Green, Brown

(3) Grey, Black, Brown

(4) Brown, Blue, Brown

4. Four equal point charges Q each are placed in the xy plane at (0, 2), (4, 2), (4, –2) and (0, –2). The work required to put a fifth charge Q at the origin of the coordinate system will be:

(1)

(2)

(3)

(4)

5. The electric field of a plane polarized electromagnetic wave in free space at time t = 0 is given by an expression

The magnetic field is given by : (c is the velocity of light)

(1)

(2)

(3)

(4)

6. Charges –q and +q located at A and B, respectively, constitute an electric dipole. Distance AB = 2a, O is the mid point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where OP = y and y >> 2a. The charge Q experiences an electrostatic force F. If Q is now moved along the equatorial line to Pʹ such that OPʹ = (y/3), the force on Q will be close to : (y/3 >> 2a)

(1) F/3

(2) 9F

(3) 27F

(4) 3F

7. A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency ω. If the radius of the bottle is 2.5 cm then ω is close to: (density of water = 10^{3} kg/m^{3})

(1) 2.50 rad s^{−}^{1}

(2) 3.75 rad s^{−}^{1}

(3) 5.00 rad s^{−}^{1}

(4) 1.25 rad s^{−}^{1}

8. Half mole of an ideal monoatomic gas is heated at constant pressure of 1 atm from 20°C to 90°C. Work done by gas is close to :

(Gas constant R = 8.31 J/mol K)

(1) 291 J

(2) 581 J

(3) 146 J

(4) 73 J

9. A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their magnetic moment parallel to their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are T_{h} and T_{c} respectively, then

(1) T_{h} = 0.5T_{c}

(2) T_{h} = T_{c}

(3) T_{h} = 2T_{c}

(4) T_{h} = 1.5T_{c}

10. For the circuit shown below, the current through the Zener diode is:

(1) Zero

(2) 9 mA

(3) 14 mA

(4) 5 mA

11. An unknown metal of mass 192 g heated to a temperature of 100°C was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of 8.4°C. Calculate the specific heat of the unknown metal if water temperature stabilizes at 21.5°C. (Specific heat of brass is 394 J kg^{–1}K^{–1})

(1) 916 J kg^{–1}K^{–1}

(2) 1232 J kg^{–1}K^{–1}

(3) 654 J kg^{–1}K^{–1}

(4) 458 J kg^{–1}K^{–1}

12. The actual value of resistance R, shown in the figure is 30 Ω. This is measured in an experiment as shown using the standard formula R = V/ I, where V and I are the readings of the voltmeter and ammeter, respectively. If the measured value of R is 5% less, then the internal resistance of the voltmeter is:

(1) 570 Ω

(2) 600 Ω

(3) 350 Ω

(4) 35 Ω

13. The self induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10 A to 25 A in 1 s, the change in the energy of the inductance is:

(1) 437.5 J

(2) 740 J

(3) 637.5 J

(4) 540 J

14. A particle which is experiencing a force, given by undergoes a displacement of If the particle had a kinetic energy of 3 J at the beginning of the displacement, what is its kinetic energy at the end of the displacement?x

(1) 15 J

(2) 9 J

(3) 12 J

(4) 10 J

15. A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is :

(1) 560 pJ

(2) 692 pJ

(3) 508 pJ

(4) 600 pJ

16. Two vectors have equal magnitudes. The magnitude of is ‘n’ times the magnitude of

(1)

(2)

(3)

(4)

17. Consider the nuclear fission

Ne^{20} → 2He^{4} + C^{12}

Given that the binding energy/nucleon of Ne^{20}, He^{4} and C^{12} are, respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement:

(1) Energy of 12.4 MeV will be supplied

(2) 8.3 MeV energy will be released

(3) Energy of 3.6 MeV will be released

(4) Energy of 11.9 MeV has to be supplied

18. A closed organ pipe has a fundamental frequency of 1.5 kHz. The number of overtones that can be distinctly heard by a person with this organ pipe will be : (Assume that the highest frequency a person can hear is 20,000 Hz)

(1) 7

(2) 4

(3) 6

(4) 5

19. A current of 2 mA was passed through an unknown resistor which dissipated a power of 4.4 W. Dissipated power when an ideal power supply of 11 V is connected across it is

(1) 11 × 10^{−}^{5} W

(2) 11 × 10^{5} W

(3) 11 × 10^{−}^{3} W

(4) 11 × 10^{−}^{4} W

20. A metal plate of area 1 × 10^{–4} m^{2} is illuminated by a radiation of intensity 16 mW/m^{2}. The work function of the metal is 5 eV. The energy of the incident photons is 10 eV and only 10% of it produces photo electrons. The number of emitted photo electrons per second and their maximum energy, respectively, will be : [1 eV = 1.6 × 10^{–19} J]

(1) 10^{14} and 10 eV

(2) 10^{11} and 5 eV

(3) 10^{10} and 5 eV

(4) 10^{12} and 5 eV

21. Two kg of a monoatomic gas is at a pressure of 4 × 10^{4} N/m^{2}. The density of the gas is 8 kg/m^{3}. What is the order of energy of the gas due to its thermal motion ?

(1) 10^{3} J

(2) 10^{5} J

(3) 10^{4} J

(4) 10^{6} J

22. A rigid massless rod of length 3l has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be :

(1) g/2l

(2) g/3l

(3) g/13l

(4) 7g/3l

23. Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is :

(1)

(2)

(3)

(4)

24. A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is

(1) 4π/3

(2)

(3) 8π/3

(4)

25. Consider a Young’s double slit experiment as shown in figure. What should be the slit separation d in terms wavelength λ such that the first minima occurs directly in front of the slit (S_{1})?

(1)

(2)

(3)

(4)

26. A particle starts from the origin at time t = 0 and moves along the positive x-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle time t = 5 s?

(1) 9 m

(2) 6 m

(3) 10 m

(4) 3 m

27. Two stars of masses 3 × 10^{31} kg each, and at distance 2 × 10^{11} m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star’s rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is:

(Take Gravitational constant G = 6.67 × 10^{–11} Nm^{2} kg^{–2})

(1) 2.8 × 10^{5} m/s

(2) 1.4 × 10^{5} m/s

(3) 2.4 × 10^{4} m/s

(4) 3.8 × 10^{4} m/s

28. Two forces P and Q, of magnitude 2F and 3F, respectively, are at an angle θ with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle θ is:

(1) 30°

(2) 90°

(3) 60°

(4) 120°

29. The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea (7.8 mm). This surface separates two media of refractive indices 1 and 1.34, Calculate the distance from the refracting surface at which a parallel beam of light will come to focus.

(1) 4.0 cm

(2) 1 cm

(3) 3.1 cm

(4) 2 cm

30. The diameter and height of a cylinder are measured by a meter scale to be 12.6 ± 0.1 cm and 34.2 ± 0.1 cm, respectively. What will be the value of its volume in appropriate significant figures?

(1) 4264 ± 81 cm^{3}

(2) 4300 ± 80 cm^{3}

(3) 4260 ± 80 cm^{3}

(4) 4264.4 ± 81.0 cm^{3}

**CHEMISTRY**

1. The process with negative entropy change is :

(1) Sublimation of dry ice

(2) Dissociation of CaSO_{4} (s) to CaO(s) and SO_{3}(g)

(3) Synthesis of ammonia from N_{2}and H_{2}

(4) Dissolution of iodine in water

2. An aromatic compound ‘A’ having molecular formula C_{7}H_{6}O_{2} on treating with aqueous ammonia and heating forms compound ‘B’. The compound ‘B’ on reaction with molecular bromine and potassium hydroxide provides compound ‘C’ having molecular formula C_{6}H_{7} The structure ‘A’ is :

(1)

(2)

(3)

(4)

3. The ground state energy of hydrogen atom is –13.6 eV. The energy of second excited state of He^{+} ion in eV is :

(1) −27.2

(2) −6.04

(3) −54.4

(4) −3.4

4. In the cell

Pt(s)|H_{2}(g,1bar)|HCl(aq)|AgCl(s)|Ag(s)|Pt(s) the cell potential is 0.92 V when a 10^{–6} molal HCl solution is used. The standard electrode potential of (AgCl/Ag,Cl^{–}) electrode is:

(1) 0.20 V

(2) 0.40 V

(3) 0.76 V

(4) 0.94 V

5. The correct match between item ‘I’ and item ‘II’ is :

Item ‘I’ Item ‘II’

(compound) (reagent)

(A) Lysine (P) 1-naphthol

(B) Furfural (Q) ninhydrin

(C) Benzyl alcohol (R) KMnO_{4}

(D) Styrene (S) Ceric ammonium nitrate

(1) (A) → (R); (B) → (P); (C) → (Q); (D) → (S)

(2) (A) → (Q); (B) → (P); (C) → (S); (D) → (R)

(3) (A) → (Q); (B) → (R); (C) → (S); (D) → (P)

(4) (A) → (Q); (B) → (P); (C) → (R); (D) → (S)

6. Among the following reactions of hydrogen with halogens, the one that requires a catalyst is :

(1) H_{2} + Cl_{2} → 2HCl

(2) H_{2} + I_{2} → 2HI

(3) H_{2} + Br_{2} → 2HBr

(4) H_{2} + F_{2} → 2HF

7. The electrolytes usually used in the electroplating of gold and silver, respectively, are :

(1) [Au(CN)_{2}]^{–} and [AgCl_{2}]^{–}

(2) [Au(NH_{3})_{2}]+ and [Ag(CN)_{2}]^{–}

(3) [Au(CN)_{2}]^{–} and [Ag(CN)_{2}]–

(4) [Au(OH)_{4}]^{–} and [Ag(OH)_{2}]^{–}

8. The major product of the following reaction is :

(1)

(2)

(3)

(4)

9. A reaction of cobalt (III) chloride and ethylenediamine in a 1 : 2 mole ratio generates two isomeric products A (violet coloured) and B (green coloured). A can show optical activity, but, B is optically inactive. What type of isomers does A and B represent?

(1) Ionisation isomers

(2) Coordination isomers

(3) Geometrical isomers

(4) Linkage isomers

10. Sodium metal on dissolution in liquid ammonia gives a deep blue solution due to the formation of

(1) Ammoniated electrons

(2) Sodium-ammonia complex

(3) Sodium ion-ammonia complex

(4) Sodamide

11. In the reaction of oxalate with permanganate in acidic medium, the number of electrons involved in producing one molecule of CO_{2} is

(1) 1

(2) 10

(3) 2

(4) 5

12. 5.1 g NH_{4}SH is introduced in 3.0 L evacuated flask at 327ºC. 30% of the solid NH_{4}SH decomposed to NH_{3} and H_{2}S as gases. The Kp of the reaction at 327ºC is (R = 0.082 L atm mol^{–1}K–1, Molar mass of S = 32 g mol^{–1}, molar mass of N = 14 g mol^{–1})

(1) 4.9 × 10^{−}^{3} atm^{2}

(2) 0.242 atm^{2}

(3) 1 × 10^{−}^{4} atm^{2}

(4) 0.242 × 10^{−}^{4} atm^{2}

13. What will be the major product in the following mononitration reaction?

(1)

(2)

(3)

(4)

14. The number of 2-centre-2-electron and 3-centre-2-electron bonds in B_{2}H_{6} respectively are:

(1) 4 and 2

(2) 2 and 2

(3) 2 and 4

(4) 2 and 1

15. The 71st electron of an element X with an atomic number of 71 enters into the orbital:

(1) 5 d

(2) 6 p

(3) 4 f

(4) 6 s

16. Which of the following tests cannot be used for identifying amino acids?

(1) Barfoed test

(2) Biuret test

(3) Xanthoproteic test

(4) Ninhydrin test

17. The amount of sugar (C_{12}H_{22}O_{11}) required to prepare 2L of its 0.1 M aqueous solution is:

(1) 136.8 g

(2) 17.1 g

(3) 34.2 g

(4) 68.4 g

18. The major product obtained in the following reaction is:

(1)

(2)

(3)

(4)

19. The difference in the number of unpaired electrons of a metal ion in its high spin and low-spin octahedral complexes is two. The metal ion is:

(1) Ni^{2+}

(2) Mn^{2+}

(3) Fe^{2+}

(4) Co^{2+}

20. Haemoglobin and gold sol are examples of :

(1) negatively charged sols

(2) positively charged sols

(3) positively and negatively charged

(4) negatively and positively charged sols, respectively

21. For an elementary chemical reaction,

the expression for

(1) k_{1}[A_{2}] + k_{–1}[A]^{2}

(2) 2k_{1}[A_{2}] – 2k_{–1}[A]^{2}

(3) 2k_{1}[A_{2}] – k_{–1}[A]^{2}

(4) k_{1}[A^{2}] – k_{–1}[A]^{2}

22. What is the IUPAC name of the following compound?

(1) 3-Bromo-1, 2-dimethylbut-1-ene

(2) 4-Bromo-3-methylpent-2-ene

(3) 3-Bromo-3-methyl-1, 2- dimethylprop-1-ene

(4) 2-Bromo-3-methylpent-3-ene

23. An ideal gas undergoes isothermal compression from 5 m^{3} to 1 m^{3} against a constant external pressure of 4 Nm^{-2}. Heat released in this process is used to increase the temperature of 1 mole of Al. If molar heat capacity of Al is 24 J mol-1K^{-1}, the temperature of Al increases by:

(1)

(2) 1 K

(3) 2 K

(4)

24. The pair that contains two P-H bond in each of the oxoacids is :

(1) H_{4}P_{2}O_{5} and H_{4}P_{2}O_{6}

(2) H_{4}P_{2}O_{5} and H_{3}PO_{3}

(3) H_{3}PO_{2} and H_{4}P_{2}O_{5}

(4) H_{3}PO_{3} and H_{3}PO_{2}

25. The major product of the following reaction

(1)

(2)

(3)

(4)

26. Elevation in the boiling point for 1 molal solution of glucose is 2 K. The depression in the freezing point for 2 molal solution of glucose in the same solvent is 2 K. The relation between K_{b} and K_{f} is :

(1) K_{b} = 0.5 K_{f}

(2) K_{b} = 2 K_{f}

(3) K_{b} = 1.5 K_{f}

(4) K_{b} = K_{f}

27. A compound of formula A_{2}B_{3} has the hcp lattice. Which atom forms the hcp lattice and what fraction of tetrahedral voids is occupied by the other atoms:

(1) hcp lattice – B, 1/3 Tetrahedral voids – A

(2) hcp lattice – A, 2/3 Tetrahedral voids – B

(3) hcp lattice – B, 2/3 Tetrahedral voids – A

(4) hcp lattice – A, 1/3 Tetrahedral voids – B

28. The reaction that is NOT involved in the ozone layer depletion mechanism in the stratosphere is :

(1)

(2)

(3)

(4)

29. Which is the most suitable reagent for the following transformation?

(1) I_{2}/NaOH

(2) Alkaline KMnO_{4}

(3) Tollen’s reagent

(4) CrO_{2}Cl_{2}/CS_{2}

30. The major product of the following reaction is :

**MATHEMATICS**

1. Let and be two given vectors where vectors are non-collinear. The value of λ for which vectors are collinear, is

(1) −3

(2) −4

(3) 3

(4) 4

2. If the area of an equilateral triangle inscribed in the circle, x^{2} + y^{2} + 10x + 12y + c = 0 is 27√3 sq. units

(1) 13

(2) 25

(3) −25

(4) 20

3. The number of values of θ ∈ (0, π) for which the system of linear equations

x + 3y + 7z = 0

– x + 4y + 7z = 0

(sin3θ)x + (cos2θ)y + 2z = 0

has a non-trivial solution, is:

(1) Four

(2) One

(3) Three

(4) Two

4. The positive value of λ for which the co-efficient of x^{2} in the expression is 720, is

(1) 3

(2) 4

(3) √5

(4) 2√2

5. The plane which bisects the line segment joining the points (–3, –3, 4) and (3, 7, 6) at right angles, passes through which one of the following points?

(1) (–2, 3, 5)

(2) (4, 1, –2)

(3) (2, 1, 3)

(4) (4, –1, 7)

6. Let If R(z) and I(z) respectively denote the real and imaginary parts of z, then

(1) I(z) = 0

(2) R(z) > 0 and I(z) > 0

(3) R(z) < 0 and I(z) > 0

(4) R(z) = – 3

7. If the probability of hitting a target by a shooter, in any shot, is 1/3, then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than 5/6, is

(1) 4

(2) 5

(3) 3

(4) 6

8. Let f :(–1, 1)→ R be a function defined by If K be the set of all points at which f is not differentiable, then K has exactly

(1) Three elements

(2) Two elements

(3) One element

(4) Five elements

9. The value of

(1) 19/21

(2) 23/22

(3) 22/23

(4) 21/19

10. Consider the following three statements:

P : 5 is a prime number.

Q : 7 is a factor of 192.

R : L.C.M. of 5 and 7 is 35.

Then the truth value of which one of the following statements is true?

(1) (~P) ⋀ (~Q ⋀ R)

(2) (~P) ⋁ (Q ⋀ R)

(3) P ⋁ (~Q ⋀ R)

(4) (P ⋀ Q) ⋁ (~R)

11. The curve amongst the family of curves represented by the differential equation, (x^{2} – y^{2})dx + 2xydy = 0 which passes through (1, 1) is

(1) A hyperbola with transverse axis along the x-axis.

(2) A circle with centre on the y-axis.

(3) An ellipse with major axis along the y-axis.

(4) A circle with centre on the x-axis.

12. The length of the chord of the parabola x^{2} = 4y having equation x – √2y + 4√2 = 0 is

(1) 3√2

(2) 6√3

(3) 2√11

(4) 8√2

13. If where C is a constant of integration, then f(x) is equal to

(1) 4x^{3} + 1

(2) −4x^{3} – 1

(3) –2x^{3} + 1

(4) –2x^{3} – 1

14. On which of the following lines lies the point of intersection of the line, and the plane, x + y + z = 2?

(1)

(2)

(3)

(4)

15. Let , where r ≠ ± then S represents

(1) An ellipse whose eccentricity is when r > 1.

(2) An ellipse whose eccentricity is when r > 1.

(3) A hyperbola whose eccentricity is when 0 < r < 1.

(4) A hyperbola whose eccentricity is when 0 < r < 1.

16. Two sides of a parallelogram are along the lines, x + y = 3 and x – y + 3 = 0. If its diagonals intersect at (2, 4) then one of its vertex is :

(1) (2, 1)

(2) (3, 5)

(3) (2, 6)

(4) (3, 6)

17. Let a_{1}, a_{2}, a_{3}… , a_{10}in G.P with a_{i} > 0 for i = 1,2, … , 10 and S be the set of pairs (r, k), r, k ∈ N(the set of natural numbers for which

(1) 2

(2) 0

(3) 4

(4) Infinitely many

18. With the usual notation, in ∆ABC, if ∠A + ∠B = 120°, a = √3 + 1 and b = √3 – 1, then the ration ∠A : ∠B, is :

(1) 7 : 1

(2) 3 : 1

(3) 9 : 7

(4) 5 : 3

19. Let where b > 0. Then

(1) −√3

(2) √3

(3) 2√3

(4) −2√3

20. The value of where [t] denotes the greatest integer less than or equal to t, is :

(1)

(2)

(3)

(4)

21. Let f be a differentiable function such that and f(1) ≠ Then

(1) Exist and equals 4.

(2) Does not exist.

(3) Exists and equals 4/7.

(4) Exists and equals 0.

22. then K is equal to :

(1) 2^{25} – 1

(2) (25)^{2}

(3) 2^{25}

(4) 2^{24}

23. Two vertices of a triangle are (0, 2) and (4, 3). If its orthocentre is at the origin, then its third vertex lies in which quadrant?

(1) Fourth

(2) Third

(3) First

(4) Second

24. Let N be the set of natural numbers and two functions f and g be defined as

f, g : N → N such that

and g(n) = n – 1(−1)^{n}. Then fog is :

(1) One-one but not onto.

(2) Onto but not one-one.

(3) Neither one-one nor onto.

(4) Both one-one and onto.

25. The tangent to the curve passing through the point (I, e) also passes through the point :

(1)(2, 3e)

(2) (4/3, 2e)

(3) (3, 6e)

(4) (5/3, 2e)

26. A helicopter is flying along the curve given by y – x^{3/2} = 7, (x ≥ 0)). A soldier positioned at the point (1/2, 7) wants to shoot down the helicopter when it is nearest to him. Then this nearest distance is :

(1)

(2)

(3)

(4)

27. If then fʹ(1/2) is :

(1) 6/25

(2) 24/25

(3) 4/5

(4) 18/25

28. If mean and standard deviation of 5 observations x_{1}, x_{2}, x_{3}, x_{4}, x_{5} are 10 and 3, respectively, then the variance of 6 observations x_{1} , x_{2}, …, x_{5} and –50 is equal to :

(1) 586.5

(2) 582.5

(3) 509.5

(4) 507.5

29. The value of is:

(1) 1/512

(2) 1/256

(3) 1/2

(4) 1/1024

30. The value of λ such that sum of the squares of the roots of the quadratic equation, x^{2} + (3 – λ) x + 2 = λ has the least value is:

(1) 2

(2) 1

(3) 15/8

(4) 4/9

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