**JEE MAIN-2019 Online CBT Mode Dt. 11.01.2019 Evening**

**PHYSICS**

1. A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of 20 × 10^{–6} J/T when a magnetic intensity of 60 × 10^{3} A/m is applied. Its magnetic susceptibility is

(1) 3.3 × 10^{−}^{2}

(2) 2.3 × 10^{−}^{2}

(3) 3.3 × 10^{−}^{4}

(4) 4.3 × 10^{−}^{2}

2. An electric field of 1000 V/m is applied to an electric dipole at angle of 45°. The value of electric dipole moment is 10–29 Cm. What is the potential energy of the electric dipole?

(1) –9 × 10^{–20} J

(2) –10 × 10^{–29} J

(3) –7 × 10^{–27} J

(4) –20 × 10^{–18} J

3. A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0, a force F = kt acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here k is a constant. The value of T is

(1)

(2)

(3)

(4)

4. A metal ball of mass 0.1 kg is heated upto 500°C and dropped into a vessel of heat capacity 800 JK^{–1 }and containing 0.5 kg water. The initial temperature of water and vessel is 30°C. What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, 4200 Jkg^{–1}K^{–1} and 400 Jkg^{–1}K^{–1}]

(1) 25%

(2) 20%

(3) 30%

(4) 15%

5. The region between y = 0 and y = d contains a magnetic field A particle of mass m and charge q enters the region with a velocity if the acceleration of the charged particle at the point of its emergence at the other side is

(1)

(2)

(3)

(4)

6. A string is wound around a hollow cylinder of mass 5 kg and radius 0.5 m. If the string is now pulled with a horizontal force of 40 N, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string) :

(1) 16 rad/s^{2}

(2) 20 rad/s^{2}

(3) 12 rad/s^{2}

(4) 10 rad/s^{2}

7. A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad/s. The support of the pendulum starts oscillating up and down with a small angular frequency of 1 rad/s and an amplitude of 10^{–2} The relative change in the angular frequency of the pendulum is best given by

(1) 10^{−}^{3} rad/s

(2) 10^{−1} rad/s

(3) 10^{−5} rad/s

(4) 1 rad/s

8. If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young’s modulus will be

(1) V^{−}^{2}A^{2}F^{−}^{2}

(2) V^{−}^{2}A^{2}F^{2}

(3) V^{−}^{4}A^{2}F

(4) V^{−}^{4}A^{−}^{2}F

9. When 100 g of a liquid A at 100°C is added to 50 g of a liquid B at temperature 75°C, the temperature of the mixture becomes 90°C. The temperature of the mixture, if 100 g of liquid A at 100°C is added to 50 g of liquid B at 50°C, will be

(1) 85°C

(2) 80°C

(3) 70°C

(4) 60°C

10. A 27 mW laser beam has a cross-sectional area of 10 mm^{2}. The magnitude of the maximum electric field in this electromagnetic wave is given by:

[Given permittivity of space ∈_{0} = 9 × 10^{−}^{12} SI units, Speed of light c = 3 × 10^{8} m/s]

(1) 1.4 kV/m

(2) 1 kV/m

(3) 2 kV/m

(4) 0.7 kV/m

11. The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is 2 s. The period of oscillation of the same pendulum on the planet would be:

(1)

(2)

(3)

(4)

12. In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is λ. If an electron jumps from N-shell to the L-shell, the wavelength of emitted radiation will be:

(1)

(2)

(3)

(4)

13. In a photoelectric experiment, the wavelength of the light incident on a metal is changed from 300 nm to 400 nm. The decrease in the stopping potential is close to :

(1) 1.0 V

(2) 2.0 V

(3) 1.5 V

(4) 0.5 V

14. Two rods A and B of identical dimensions are at temperature 30°C. If A is heated upto 180°C and B upto T°C, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4 : 3, then the value f T is:

(1) 270°C

(2) 230°C

(3) 250°C

(4) 200°C

15. In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT = K, where K is a constant. In this process, the temperature of the gas is increased by ∆ The amount of heat absorbed by gas is (R is gas constant):

(1)

(2)

(3)

(4)

16. A galvanometer having a resistance of 20 Ω and 30 divisions on both sides has figure of merit 0.005 ampere/division. The resistance that should be connected in series such that it can be used as a voltmeter upto 15 volt, is:

(1) 100 Ω

(2) 125 Ω

(3) 80 Ω

(4) 120 Ω

17. A thermometer graduated according to a linear scale reads a value x_{0} when in contact with boiling water, and x_{0} /3 when in contact with ice. What is the temperature of an object in °C, if this thermometer in the contact with the object reads x_{0} /2?

(1) 40

(2) 60

(3) 35

(4) 25

18. In the circuit shown, the potential difference between A and B is:

(1) 6 V

(2) 3 V

(3) 2 V

(4) 1 V

19. An amplitude modulated signal is plotted below:

Which one of the following best describes the above signal?

(1) (9 + sin(2π × 10^{4}t))sin(2.5π × 10^{5}t) V

(2) (9 + sin(4π × 10^{4}t))sin(5π × 10^{5}t) V

(3) (1 + 9sin(2π × 10^{4}t))sin(2.5π × 10^{5}t) V

(4) (9 + sin(2.5π × 10^{5}t))sin(2π × 10^{4}t) V

20. In the experimental set up of metre bridge shown in the figure, the null point is obtained at a distance of 40 cm from A. If a 10 Ω resistor is connected in series with R_{1}, the null point shifts by 10 cm. The resistance that should be connected in parallel with (R_{1} + 10) Ω such that the null point shifts back to its initial position is:

(1) 60 Ω

(2) 30 Ω

(3) 40 Ω

(4) 20 Ω

21. A particle of mass m and charge q is in an electric and magnetic field given by

The charged particle is shifted from the origin to the point P(x = 1 ; y = 1) along a straight path. The magnitude of the total work done is:

(1) (0.15)q

(2) (5q)

(3) (0.35)q

(4) (2.5)q

22. Seven capacitors, each of capacitance 2 μF, are to be connected in a configuration to obtain an effective capacitance of (6/13) μ Which of the combinations, shown in figures below, will achieve the desired value?

(1)

(2)

(3)

(4)

23. A pendulum is executing simple harmonic motion and its maximum kinetic energy is K_{1}. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is K_{2}. Then

(1) K_{2} = 2K_{1}

(2) K_{2} = K_{1}/4

(3) K_{2} = K_{1}

(4) K_{2} = K_{1}/2

24. A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is √3, then the angle of incidence is:

(1) 90°

(2) 30°

(3) 45°

(4) 60°

25. In a double-slit experiment, green light (5303 Å) falls on a double slit having a separation of 19.44 μm and a width of 4.05 μ The number of bright fringes between the first and the second diffraction minima is

(1) 05

(2) 09

(3) 10

(4) 04

26. A particle moves from the point at t = 0, with an initial velocity It is acted upon by a constant force which produces a constant acceleration What is the distance of the particle form the origin at time 2 s

(1) 20√2 m

(2) 15 m

(3) 10√2 m

(4) 5 m

27. The magnitude of torque on a particle of mass 1 kg is 2.5 Nm about the origin. If the force acting on it is 1 N, and the distance of the particle from the origin is 5 m, the angle between the force and the position vector is (in radians):

(1) π/8

(2) π/6

(3) π/3

(4) π/4

28. A circular disc D_{1} of mass M and radius R has two identical discs D_{2} and D_{3} of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis OOʹ, passing through the centre of D_{1} as shown in the figure, will be:

(1) 3MR^{2}

(2)

(3) MR^{2}

(4)

29. The circuit shown below contains two ideal diodes, each with a forward resistance of 50Ω. If the battery voltage is 6 V, the current through the 100 Ω resistance (in amperes) is:

(1) 0.036

(2) 0.020

(3) 0.030

(4) 0.027

30. A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3, keeping the number of turns of the coil per unit length of the frame the same, then the self inductance of the coil:

(1) Increases by a factor of 3

(2) Decreases by a factor of 9√3

(3) Decreases by a factor of 9

(4) Increases by a factor of 27

**CHEMISTRY**

1. Given the equilibrium constant :

K_{C} of the reaction :

Cu(s) + 2Ag^{+} (aq) → Cu^{2+} (aq) + 2Ag(s) is 10 × 10^{15}, calculate the E^{0} _{cell} of this reaction at 298 K

(1) 0.4736 mV

(2) 0.4736 V

(3) 0.04736 V

(4) 0.04736 mV

2. Among the colloids cheese (C), milk (M) and smoke (S), the correct combination of the dispersed phase and dispersion medium, respectively is :

(1) C : solid in liquid; M : liquid in liquid; S : gas in solid

(2) C : liquid in solid; M : liquid in solid; S : solid in gas

(3) C : liquid in solid; M : liquid in liquid; S : solid in gas

(4) C : solid in liquid; M : solid in liquid; S : solid in gas

3. The radius of the largest sphere which fits properly at the centre of the edge of a body centred cubic unit cell is : (Edge length is represented by ‘a’)

(1) 0.027 a

(2) 0.047 a

(3) 0.067 a

(4) 0.134 a

4. The reaction 2X → B is a zeroth order reaction. If the initial concentration of X is 0.2 M, the half-life is 6 h. When the initial concentration of X is 0.5 M, the time required to reach its final concentration of 0.2 M will be :

(1) 12.0 h

(2) 7.2 h

(3) 9.0 h

(4) 18.0 h

5. In the following compound,

the favourable site/s protonation is/are :

(1) (a)

(2) (b), (c) and (d)

(3) (a) and (d)

(4) (a) and (e)

6. The major product obtained in the following conversion is :

(1)

(2)

(3)

(4)

7. K_{2 }HgI_{4 }is 40% ionised in aqueous solution. The value of its van’t Hoff factor (i) is :

(1) 1.6

(2) 2.0

(3) 2.2

(4) 1.8

8. Match the following items in column I with the corresponding items in column II.

**Column-I Column-II**

(i) Na_{2}CO_{3}.10H_{2}O (A) Portland cement ingredient

(ii) Mg(HCO_{3})_{2 }(B) Castner-Kellner process

(iii) NaOH (C) Solvay process

(iv) Ca_{3}Al_{2}O_{6} (D) Temporary hardness

(1) (i)(B), (ii)(C), (iii)(A), (iv)(D)

(2) (i)(C), (ii)(D), (iii)(B), (iv)(A)

(3) (i)(D), (ii)(A), (iii)(B), (iv)(C)

(4) (i)(C), (ii)(B), (iii)(D), (iv)(A)

9. The de Broglie wavelength (λ) associated with a photoelectron varies with the frequency (ν) of the incident radiation as, [ν_{0}is threshold frequency]:

(1)

(2)

(3)

(4)

10. The correct option with respect to the Pauling electronegativity values of the elements is:

(1) Si < Al

(2) P > S

(3) Te > Se

(4) Ga < Ge

11. The correct match between Item I and Item II is:

**Item I Item II**

(A) Ester test (P) Tyr

(B) Carbylamine test (Q) AsP

(C) Phthalein dye test (R) Ser

(S) Lys

(1) (A) → (Q); (B) → (S); (C) → (P)

(2) (A) → (R); (B) → (Q); (C) → (P)

(3) (A) → (Q); (B) → (S); (C) → (R)

(4) (A) → (R); (B) → (S); (C) → (Q)

12. The correct match between Item I and Item II is:

**Item I **

(A) Allosteric effect

(B) Competitive

(C) Receptor

(D) Poison

**Item II**

(P) Molecule binding to the active site of enzyme

(Q) Molecule crucial for inhibitor communication in the body

(R) Molecule binding to a site other than the active site of enzyme

(S) Molecule binding to the enzyme covalently

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

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

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

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

13. Which of the following compounds will produce a precipitate with AgNO_{3} ?

(1)

(2)

(3)

(4)

14. The number of bridging CO ligand(s) and Co-Co bond(s) in Co_{2}(CO)_{8}, respectively are:

(1) 2 and 1

(2) 0 and 2

(3) 2 and 0

(4) 4 and 0

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

(1)

(2)

(3)

(4)

16.

In the above sequence of reactions, __A__ and __D__, respectively, are :

(1) KI and K_{2}MnO_{4}

(2) KIO_{3} and MnO_{2}

(3) MnO_{2} and KIO_{3}

(4) KI and KMnO_{4}

17. The major product of the following reaction is :

(1)

(2)

(3)

(4)

18. Taj Mahal is being slowly disfigured and discoloured. This is primarily due to :

(1) Acid rain

(2) Water pollution

(3) Global warming

(4) Soil pollution

19. The relative stability of +1 oxidation state of group 13 elements follows the order :

(1) Tl < In < Ga < Al

(2) Al < Ga < Tl < In

(3) Al < Ga < In < Tl

(4) Ga < Al < In < Tl

20. The homopolymer formed from 4-hydroxy-butanoic acids is :

(1)

(2)

(3)

(4)

21. The reaction that does NOT define calcination is:

22. Which of the following compounds reacts with ethylmagnesium bromide and also decolourizes bromine water solution?

(1)

(2)

(3)

(4)

23. The hydride that is NOT electron deficient is

(1) SiH_{4}

(2) GaH_{3}

(3) B_{2}H_{6}

(4) AlH_{3}

24. For the equilibrium

2H_{2}O ⇌ H_{3}O^{+} + OH^{−}, the value of ∆G° at 298 K is approximately

(1) −80 kJ mol^{−}^{1}

(2) −100 kJ mol^{−}^{1}

(3) 80 kJ mol^{−}^{1}

(4) 100 kJ mol^{−}^{1}

25. The coordination number of Th in K_{4}[Th(C_{2}O_{4})_{4}(OH_{2})_{2}] is

(C_{2}O_{4}^{2}^{−} = Oxalato)

(1) 10

(2) 6

(3) 14

(4) 8

26. A compound ‘X’ on treatment with Br_{2}/NaOH, provided C_{3}H_{9}N, which gives positive carbylamines test. Compound ‘X’ is

(1) CH_{3}CH_{2}CH_{2}CONH_{2}

(2) CH_{3}COCH_{2}NHCH_{3}

(3) CH_{3}CH_{2}COCH_{2}NH_{2}

(4) CH_{3}CON(CH_{3})_{2}

27. The higher concentration of which gas in air can cause stiffness of flower buds?

(1) SO_{2}

(2) CO

(3) CO_{2}

(4) NO_{2}

28. The reaction

MgO(s) + C(s) → Mg(s) + CO(g), for, which ∆_{r}H° = +491.1 kJ mol^{−1} and ∆_{s}H° = 198.0 JK^{−1} mol^{−1}, is not feasible at 298 K. Temperature above which reaction will be feasible is

(1) 2040.5 K

(2) 1890.0 K

(3) 2480.3 K

(4) 2380.5 K

29. 25 ml of the given HCl solution requires 30 mL of 0.1 M sodium carbonate solution. What is the volume of this HCl solution required to titrate 30 mL of 0.2 M aqueous NaOH solution

(1) 25 mL

(2) 12.5 mL

(3) 50 mL

(4) 75 mL

30. The standard reaction Gibbs energy for a chemical reaction at an absolute temperature T is given by

∆_{r}G° A – BT

Where A and B are non-zero constants. Which of the following is true about this reaction?

(1) Exothermic if B < 0

(2) Endothermic if A > 0

(3) Endothermic if A < 0 and B > 0

(4) Exothermic if A > 0 and B < 0

**MATHEMATICS**

1. Let A and B be two invertible matrices of order 3 × 3. If det(ABA^{T}) = 8 and det(AB^{–1}) = 8, then det(BA^{–1}B^{T}) is equal to :

(1) 1

(2) 16

(3) 1/16

(4) 1/4

2. A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant 2b from the origin. Then the locus of the centre of this circle, is :

(1) A hyperbola

(2) A parabola

(3) An ellipse

(4) A straight line

3. Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression is

(1) 1/2

(2)

(3) 1

(4) 1/4

4. If (a + b + c) (x + a + b + c)^{2}, x ≠ 0 and a + b + c ≠ 0, then x is equal to :

(1) 2(a + b+ c)

(2) −(a + b +c)

(3) abc

(4) −2(a + b +c)

5. Let a function f : (0, ∞) → (0, ∞) be defined by Then f is :

(1) Injective only

(2) Both injective as well as surjective

(3) Not injective but it is surjective

(4) Neither injective nor surjective

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

(1)

(2)

(3)

(4)

7. If the area of the triangle whose one vertex is at the vertex of the parabola, y^{2} + 4(x – a^{2}) = 0 and the other two vertices are the points of intersection of the parabola and y-axis, is 250 sq. units, then a value of ‘a’ is :

(1) 5√5

(2) (10)^{2/3}

(3) 5(2^{13})

(4) 5

8. Let z be a complex number such that |z| + z = 3 + i (where i = √−1).

Then |z| is equal to :

(1) √41/4

(2) 5/4

(3) 5/3

(4) √34/3

9. Let where a, b and d are non-zero constants. Then :

(1) f is an increasing function of x

(2) f is a decreasing function of x

(3) f is neither increasing nor decreasing function of x

(4) fʹ is not a continuous function of x

10. Contrapositive of the statement

“If two numbers are not equal, then their squares are not equal.” is :

(1) If the squares of two numbers are equal, then the numbers are equal

(2) If the squares of two numbers are not equal, then the numbers are equal

(3) If the squares of two numbers are equal, then the numbers are not equal

(4) If the squares of two numbers are not equal, then the numbers are not equal

11. If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2, 5), then the equation of the diagonal AD is :

(1) 5x + 3y – 11 = 0

(2) 3x + 5y – 13 = 0

(3) 3x – 5y + 7 = 0

(4) 5x – 3y + 1 = 0

12. is equal to :

(1) 2

(2) 4

(3) 1

(4) 0

13. Two lines and intersect at the point R. The reflection of R in the xy-plane has coordinates :

(1) (–2, 4, 7)

(2) (2, 4, 7)

(3) (2, –4, –7)

(4) (2, –4, 7)

14. Let (x + 10)^{50} + (x – 10)^{50} = a_{0} + a_{1}x + a_{2}x^{2} + … + a_{50}x^{50}. for all x ∈ R; then a_{2}/a_{0} is equal to

(1) 12.25

(2) 12.75

(3) 12.00

(4) 12.50

15. Given for ∆ABC with usual notation. If then the ordered triplet (α, β, γ) has a value :

(1) (3, 4, 5)

(2) (7, 19, 25)

(3) (19, 7, 25)

(4) (5, 12, 13)

16. If 19th term of a non-zero A.P. is zero, then its (49th term) : (29th term) is :

(1) 2 : 1

(2) 1 : 3

(3) 4 : 1

(4) 3 : 1

17. The number of function f from {1, 2, 3, …,20} onto {1, 2, 3, …, 20} such that f(k) is a multiple of 3, whenever k is a multiple of 4, is :

(1) 5^{6} × 15

(2) 6^{5} × (15)!

(3) 5! × 6!

(4) (15)! × 6!

18. The integral equals :

(1)

(2)

(3)

(4)

19. Let α and β the roots of the quadratic equation x^{2} sin θ – x(sin θ cos θ +1) + cos θ = 0 (0 < θ > 45°), and α < β. Then is equal to :

(1)

(2)

(3)

(4)

20. A bag contains 30 white ball and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then is equal to :

(1) 3√2

(2) 4√3

(3) 4√3/3

(4) 4

21. If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is :

(1) 2

(2) 13/8

(3) 13/6

(4) 13/12

22. Let S_{n} = 1 + q + q^{2} + … + q^{n} and where q is a real number and q ≠

If ^{101}C_{1} + ^{101}C_{2} ∙ S_{1} + … + ^{101}C_{101} ^{∙} S_{100} = α T_{100}.

(1) 200

(2) 202

(3) 2^{99}

(4) 2^{100}

23. Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it?

(1) (4√3, 2√3)

(2) (4√3, 2√2)

(3) (4√2, 2√2)

(4) (4√2, 2√3)

24. Let S = {1, 2, …., 20}. A subset B of S is said to be “nice”, if the sum of the elements of B is 203. Then the probability that a randomly chosen subset of S is “nice” is

(1) 7/2^{20}

(2) 6/2^{20}

(3) 4/2^{20}

(4) 5/2^{20}

25. If the point (2, α, β) lies on the plane which passes through the points (3, 4, 2) and (7, 0, 6) and is perpendicular to the plane 2x – 5y = 15, then 2α – 3β is equal to

(1) 5

(2) 12

(3) 17

(4) 7

26. All x satisfying the inequality (cot^{–1}x)^{2} – 7 (cot^{–1}x) + 10 > 0, lie in the interval

(1) (cot 2, ∞)

(2) (cot 5, cot 4)

(3) (−∞, cot 5) ∪ (cot 4, cot 2)

(4) (−∞, cot 5) ∪ (cot 2, ∞)

27. Let respectively be the position vectors of the points A, B and C with respect to the origin O. If the distance of C from the bisector of the acute angle between OA and OB is 3/√2, then the sum of all possible values of β is

(1) 3

(2) 1

(3) 4

(4) 2

28. The solution of the differential equation, when Y(1) = 1, is

(1)

(2)

(3)

(4)

29. Let K be the set of all real values of x where the function

f(x) = sin |x| – |x| + 2(x – π) is not differentiable. Then the set K is equal to

(1) {π}

(2) ϕ (an empty set)

(3) {0}

(4) {0, π}

30. The area (in sq. units) in the first quadrant bounded by the parabola, y = x^{2} + 1, the tangent to it at the point (2, 5) and the coordinate axes is

(1) 187/24

(2) 8/3

(3) 14/3

(4) 37/24

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