1. A
   $(M - m)(R + r)^2$
2. B
   $(m - M)(R + r)^2$
3. C
   $(m - M)(R - r)^2$
4. D
   0

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1. A
   $k = \dfrac{1}{m}$
2. B
   $k = m$
3. C
   $k = m^2$
4. D
   $k = \sqrt{m}$

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1. A
   20 cm to the left of the concave lens
2. B
   60 cm to the left of the concave lens
3. C
   30 cm to the right of the concave lens
4. D
   60 cm to the right of the concave lens

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1. A
   2.2 A
2. B
   5.5 A
3. C
   11.0 A
4. D
   22.0 A

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1. A
   $\dfrac{1}{4}$
2. B
   $\dfrac{1}{2}$
3. C
   1
4. D
   2

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1. A
   Series of positive humps that touch zero periodically (like $|\cos t|$ squared humps, both humps same height)
2. B
   Curve starting high, dipping to zero once (single cusp), then rising
3. C
   Constant (horizontal line)
4. D
   Increasing curve starting from zero

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1. A
   $E_A = 0, E_B = E_C$
2. B
   $E_A \neq 0, E_B = E_C$
3. C
   $E_A = 0, E_B > E_C$
4. D
   $E_A \neq 0, E_B < E_C$

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1. A
   $\sqrt{\dfrac{3Qq}{4\pi\epsilon_0 mR}}$
2. B
   $\sqrt{\dfrac{2Qq}{3\pi\epsilon_0 mR}}$
3. C
   $\sqrt{\dfrac{Qq}{3\pi\epsilon_0 mR}}$
4. D
   $\sqrt{\dfrac{Qq}{4\pi\epsilon_0 mR}}$

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1. A
   $N(\theta)$ increasing (rising straight line on log scale) from 0 to 180 degrees
2. B
   $N(\theta)$ nearly flat then falling off sharply toward 180 degrees
3. C
   $N(\theta)$ starting very high near small $\theta$ and decreasing sharply, levelling off toward 180 degrees
4. D
   $N(\theta)$ low at ends, plateau high in the middle (trapezoidal)

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1. A
   $I_A$ remains constant while $I_B$ increases
2. B
   $I_A$ decreases while $I_B$ increases
3. C
   $I_A$ increases while $I_B$ decreases
4. D
   both $I_A$ and $I_B$ remain constant

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1. A
   $[L^{-1}T^{-1}K^{-2}]$
2. B
   $[L^{-1}K^{-2}]$
3. C
   $[L^{-1}T^{-1}K^{-3}]$
4. D
   $[L^{-1}T^{-1}K^{-4}]$

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1. A
   The speed of the electromagnetic wave inside the medium is $10^8\ \text{ms}^{-1}$
2. B
   The wavelength of the electromagnetic wave inside the medium is 300 m
3. C
   The magnetic field is given by the relation $B_y = \dfrac{B_0}{v}\sin(kz - 2\pi\times 10^6 t)$ where v is the speed of the electromagnetic wave inside the medium
4. D
   The direction of propagation of the electromagnetic wave is along $+z$

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1. A
   400 J
2. B
   500 J
3. C
   600 J
4. D
   800 J

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1. A
   4
2. B
   3
3. C
   2
4. D
   1

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1. A
   $\tan^{-1}\left(\dfrac{1}{5}\right)$
2. B
   $\tan^{-1}\left(\dfrac{2}{5}\right)$
3. C
   $\tan^{-1}\left(\sqrt{3}/2\right)$
4. D
   $\tan^{-1}\left(2\sqrt{3}\right)$

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1. A
   $W_1 > W_2 > W_3$
2. B
   $W_3 = W_1 > W_2$
3. C
   $W_3 > W_2 > W_1$
4. D
   $W_2 > W_1 = W_3$

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1. A
   P-I, Q-II, R-III, S-IV
2. B
   P-I, Q-IV, R-II, S-III
3. C
   P-II, Q-I, R-IV, S-III
4. D
   P-II, Q-IV, R-III, S-I

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1. A
   8
2. B
   7
3. C
   5
4. D
   2.5

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1. A
   4
2. B
   3
3. C
   3
4. D
   1

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1. A
   If P is the sodium salt of a carboxylic acid, Q is a primary alcohol.
2. B
   P and Q are aromatic compounds.
3. C
   If P gives a carboxylic acid on acidification, Q gives a poisonous gas on exposure to air and light.
4. D
   Both P and Q are carbonyl compounds.

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1. A
   Both Statement-I and Statement-II are correct.
2. B
   Both Statement-I and Statement-II are incorrect.
3. C
   Statement-I is correct but Statement-II is incorrect
4. D
   Statement-I is incorrect but Statement-II is correct.

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1. A
   filled $\sigma$ and filled $\pi$ orbitals
2. B
   empty $\sigma$ and empty $\pi^{*}$ orbitals
3. C
   empty $\sigma^{*}$ and filled $\pi$ orbitals
4. D
   empty $\sigma^{*}$ and empty $\pi^{*}$ orbitals

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1. A
   1 : 2
2. B
   2 : 1
3. C
   2 : 3
4. D
   3 : 2

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1. A
   Tertiary structure of proteins has two or more polypeptide subunits
2. B
   Only the proteins having a quaternary structure are biologically active.
3. C
   In $\beta$-pleated sheet structures, peptide chains are held together by intermolecular hydrogen bonds.
4. D
   In $\alpha$-helices, the polypeptide chain is twisted into a left-handed screw (helix) through intramolecular hydrogen bonds.

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1. A
   17.014 and 21.023
2. B
   17.015 and 21.023
3. C
   17.014 and 21.024
4. D
   17.015 and 21.024

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