JEE Advanced General questions with solutions

Q1. A particle of mass m is projected form the ground with an initial speed μ 0 at an angle α with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u 0 . The angle that the composite system makes with the horizontal immediately after the collision is

1. 4 π
2. 4 π + α
3. 2 π – α
4. 2 π

Answer: 4 π

Q2. The image of an object, formed by a plano-convex lens at a distance of 8m behind the lens, is real and is one third the size of the object. The wavelength of light inside the lens is 2/3 times the wavelength in free space. The radius of the curved surface of the lens is -

1. 1m
2. 2m
3. 3m
4. 6m

Answer: 3m

Q3. The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24 th division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is

1. 5.112 cm
2. 5.124 cm
3. 5.136 cm
4. 5.148 cm

Answer: 5.124 cm

Q4. The work done on a particle of mass m by a force , K ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + + + j ˆ ) y x ( y i ˆ ) y x ( x 2 / 3 2 2 2 / 3 2 2 (K being a constant of appropriate dimensions), when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the x-y plane is

1. a K 2 π
2. a K π
3. a 2 K π
4. 0

Answer: 0

Q5. One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is

1. 0.25
2. 0.50
3. 2.00
4. 4.00

Answer: 0.50

Q6. A ray of light travelling in the direction ( ) j ˆ 3 i ˆ 2 1 + is incident on a plane mirror. After reflection, it travels along the direction ( ) j ˆ 3 i ˆ 2 1 − . The angle of incidence is

1. 30º
2. 45º
3. 60º
4. 75º

Answer: 30º

Q7. Two rectangular blocks , having identical dimensions, can be arranged either in configuration I or in configuration II as show in the figure. One of the blocks has thermal conductivity K and the other 2K. The temperature difference between the ends along the x-axis is the same in both the configurations. It takes 9s to transport a certain amount of heat from the hot end to the cold end in the configuration I. The time to transport the same amount of heat in the configuration II is K 2K 2K K Configuration-I Configuration-II

1. 2.0 s
2. 3.0 s
3. 4.5 s
4. 6.0 s

Answer: 2.0 s

Q8. A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3 × 10 8 ms –1 . The final momentum of object is

1. 0.3 × 10 –17 kg ms –1
2. 1.0 × 10 –17 kg ms –1
3. 3.0 × 10 –17 kg ms –1
4. 9.0 × 10 –17 kg ms –1

Answer: 1.0 × 10 –17 kg ms –1

Q9. In the Young's double slit experiment using a monochromatic light of wavelength λ , the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is

1. (2n + 1) 2 λ
2. (2n + 1) 4 λ
3. (2n + 1) 8 λ
4. (2n + 1) 16 λ

Answer: (2n + 1) 4 λ

Q10. Two non-reactive monatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is

1. 1 : 4
2. 1 : 2
3. 6 : 9
4. 8 : 9

Answer: 8 : 9

Q11. The standard enthalpies of formation of CO 2 (g), H 2 O

1. and glucose (s) at 25ºC are –400 kJ/mol, –300 kJ/mol and –1300 kJ/mol, respectively. The standard enthalpy of combustion per gram of glucose at 25ºC is - (A) + 2900 kJ
2. –2900 kJ
3. –16.11 kJ
4. +16.11 J

Answer: –16.11 kJ

Q12. KI in acetone, undergoes S N 2 reaction with each of P, Q, R and S. The rates of the reaction vary as H 3 C–Cl P Q Cl Cl R S O Cl

1. P > Q > R > S
2. S > P > R > Q
3. P > R > Q > S
4. R > P > S > Q

Answer: S > P > R > Q

Q13. The compound that does NOT liberate CO 2 , on treatment with aqueous sodium bicarbonate solution, is -

1. Benzoic acid
2. Benzensulphonic acid
3. Salicylic acid
4. Carbolic acid (Phenol)

Answer: Carbolic acid (Phenol)

Q14. Consider the following complex ions, P, Q and R. P = [FeF 6 ] 3– Q = [V(H 2 O) 6 ] 2+ and R = [Fe(H 2 O) 6 ] 2+ The correct order of the complex ions, according to their spin-only magnetic moment values (in B.M.) is -

1. R < Q < P
2. Q < R < P
3. R < P < Q
4. Q < P < R

Answer: Q < R < P

Q15. In the reaction, P + Q ⎯→ R + S The time taken for 75 % reaction of P is twice the time taken for 50 % reaction of P. The concentration of Q varies with reaction time as shown in the figure. The overall order of the reaction is - [Q] 0 [Q] Time

1. 2
2. 3
3. 0
4. 1

Answer: 1

Q16. Concentrated nitric acid, upon long standing, turns yellow-brown due to the formation of -

1. NO
2. NO 2
3. N 2 O
4. N 2 O 4

Answer: NO 2

Q17. The arrangement of X – ions around A + ion in solid AX is given in the figure (not drawn to scale). If the radius of X – is 250 pm, the radius of A + is - X – A +

1. 104 pm
2. 125 pm
3. 183 pm
4. 57 pm

Answer: 104 pm

Q18. Upon treatment with ammoniacal H 2 S, the metal ion that precipitates as a sulfide is -

1. Fe(III)
2. A A (III)
3. Mg(II)
4. Zn(II)

Answer: Zn(II)

Q19. Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at 25ºC. For this process, the correct statement is -

1. The adsorption requires activation at 25ºC.
2. The adsorption is accompanied by a decrease in enthalpy.
3. The adsorption increases with increase of temperature.
4. The adsorption is irreversible.

Answer: The adsorption is accompanied by a decrease in enthalpy.

Q20. The initial rate of hydrolysis of methyl acetate (1M) by a weak acid (HA, 1M) is 1/100 th of that of a strong acid (HX, 1M), at 25ºC. The K a of HA is -

1. 1 × 10 –4
2. 1 × 10 –5
3. 1 × 10 –6
4. 1 × 10 –3

Answer: 1 × 10 –4

Q21. The hyperconjugative stabilities of tert-butyl cation and 2-butene, respectively, are due to -

1. σ → p (empty) and σ → π * electron delocalisations
2. σ → σ * and σ → π electron delocalisations
3. σ → p (filled) and σ → π electron delocalisations
4. p (filled) → σ → π * electron delocalisations

Answer: σ → p (empty) and σ → π * electron delocalisations

Q22. The value of cot ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ∑ ∑ = = − 23 1 n n 1 k 1 k 2 1 cot is -

1. 25 23
2. 23 25
3. 24 23
4. 23 24

Answer: 23 25

Q23. Let k ˆ 2 j ˆ i ˆ 3 PR − + = and k ˆ 4 j ˆ 3 i ˆ SQ − − = determine diagonals of a parallelogram PQRS and k ˆ 3 j ˆ 2 i ˆ PT + + = be another vector. Then the volume of the parallelepiped determined by the vectors PQ , PT and PS is -

1. 5
2. 20
3. 10
4. 30

Answer: 10

Q24. Let complex numbers α and α 1 lie on circles (x – x 0 ) 2 + (y – y 0 ) 2 = r 2 and (x – x 0 ) 2 + (y – y 0 ) 2 = 4r 2 , respectively. If z 0 = x 0 + iy 0 satisfies the equation 2 |z 0 | 2 = r 2 + 2, then | α | =

1. 2 1
2. 2 1
3. 7 1
4. 3 1

Answer: 7 1

Q25. For a > b > c > 0, the distance between (1, 1) and the point of intersection of the lines ax + by + c = 0 and bx + ay + c = 0 is less than 2 2 . Then -

1. a + b – c > 0
2. a – b + c < 0
3. a – b + c > 0
4. a + b – c < 0

Answer: a + b – c > 0

Q26. Perpendiculars are drawn from points on the line 3 z 1 1 y 2 2 x = − + = + to the plane x + y + z = 3. The feet of perpendiculars lie on the line -

1. 13 2 z 8 1 y 5 x − − = − =
2. 5 2 z 3 1 y 2 x − − = − =
3. 7 2 z 3 1 y 4 x − − = − =
4. 5 2 z 7 1 y 2 x − = − − =

Answer: 5 2 z 7 1 y 2 x − = − − =

Q27. Four persons independently solve a certain problem correctly with probabilities 8 1 , 4 1 , 4 3 , 2 1 . Then the probability that the problem is solved correctly by at least one of them is -

1. 256 235
2. 256 21
3. 256 3
4. 256 253

Answer: 256 235

Q28. The area enclosed by the curves y = sin x + cos x and y = | cos x – sin x | over the interval ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ π 2 , 0 is -

1. ) 1 2 ( 4 −
2. ) 1 2 ( 2 2 −
3. ) 1 2 ( 2 +
4. ) 1 2 ( 2 2 +

Answer: ) 1 2 ( 2 2 −

Q29. A curve passes through the point ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π 6 , 1 . Let the slope of the curve at each point (x, y) be ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + x y sec x y , x > 0. Then the equation of the curve is -

1. 2 1 x log x y sin + = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛
2. 2 x log x y ec cos + = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛
3. 2 x log x y 2 sec + = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛
4. 2 1 x log x y 2 cos + = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛

Answer: 2 1 x log x y sin + = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛

Q30. Let f : ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 1 , 2 1 → R (the set of all real numbers) be a positive, non-constant and differentiable function such that f '(x) < 2 f(x) and ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 2 1 f = 1. Then the value of ∫ 1 2 / 1 dx ) x ( f lies in the interval -

1. (2e – 1, 2e)
2. (e – 1, 2e – 1)
3. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − 1 e , 2 1 e
4. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − 2 1 e , 0

Answer: ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − 2 1 e , 0