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1. A
   $-3$ V
2. B
   $3$ V
3. C
   $6$ V
4. D
   $9$ V

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1. A
   OR gate.
2. B
   AND gate.
3. C
   NOR gate.
4. D
   X-OR gate.

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

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1. A
   $\frac{V}{g}$
2. B
   $\frac{V^2}{g}$
3. C
   $\frac{V^2}{2g}$
4. D
   $\frac{V}{\sqrt{2g}}$

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1. A
   $\frac{3}{4}F$
2. B
   $\frac{4}{3}F$
3. C
   $\frac{9}{16}F$
4. D
   $\frac{16}{9}F$

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1. A
   $5440\,\text{\AA}$
2. B
   $5890\,\text{\AA}$
3. C
   $5900\,\text{\AA}$
4. D
   $6630\,\text{\AA}$

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1. A
   $R\sqrt{3}$
2. B
   $\frac{R}{\sqrt{3}}$
3. C
   $\sqrt{3} \cdot R$
4. D
   $3 \cdot R$

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1. A
   zero
2. B
   $\sqrt{\frac{e}{\varepsilon_0 r_0 m}}$
3. C
   $\frac{e}{\sqrt{4\pi\varepsilon_0 r_0 m}}$
4. D
   $\sqrt{\frac{4\pi\varepsilon_0 r_0 m}{e}}$

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1. A
   2.5 kJ
2. B
   3.0 kJ
3. C
   3.5 kJ
4. D
   4.0 kJ

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1. A
   $\frac{\mu_0 \pi r_2^2}{2r_1}$
2. B
   $\frac{\mu_0 \pi^2 r_1 r_2}{2}$
3. C
   $\frac{\mu_0 \pi r_1^2}{2r_2}$
4. D
   $\frac{\mu_0 \pi r_2^2 \pi^2}{2r_1}$

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1. A
   $\frac{9\theta}{4}$
2. B
   $\frac{2\theta}{5}$
3. C
   $\frac{5\theta}{3}$
4. D
   $\frac{7\theta}{3}$

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1. A
   45 m/s
2. B
   75 m/s
3. C
   48 m/s
4. D
   80 m/s

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1. A
   $\frac{\sqrt{5}}{2}R,\, \tan^{-1}\!\left(\frac{1}{2}\right)$
2. B
   $\frac{\sqrt{13}}{2}R,\, \tan^{-1}\!\left(\frac{3}{2}\right)$
3. C
   $\sqrt{5}R,\, \tan^{-1}(1)$
4. D
   $\sqrt{13}R,\, \tan^{-1}(2)$

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1. A
   large and large
2. B
   large and small.
3. C
   small and large.
4. D
   small and small.

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1. A
   6 cm
2. B
   8 cm
3. C
   10 cm
4. D
   12 cm

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1. A
   $\frac{E_2\lambda_2 - E_1\lambda_1}{\lambda_2 - \lambda_1}$
2. B
   $\frac{E_1\lambda_1 + E_2\lambda_2}{\lambda_2 - \lambda_1}$
3. C
   $\frac{E_1\lambda_1 - E_2\lambda_2}{\lambda_2 - \lambda_1}$
4. D
   $\frac{E_2\lambda_2 + E_1\lambda_1}{\lambda_1 - \lambda_2}$

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1. A
   $\frac{399}{400}G$
2. B
   $\frac{1}{400}G$
3. C
   $\frac{499}{500}G$
4. D
   $\frac{1}{500}G$

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1. A
   $\frac{4l}{x}$
2. B
   $4lx$
3. C
   $4l$
4. D
   $2l$

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1. A
   $\frac{1}{r}$
2. B
   $\frac{1}{r^2}$
3. C
   $r$
4. D
   $\frac{1}{r^3}$

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1. A
   $2.0 \times 10^{-9}$
2. B
   $3.0 \times 10^{-9}$
3. C
   $4.0 \times 10^{-9}$
4. D
   $5.0 \times 10^{-9}$

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1. A
   Alcohols < Amines < Carboxylic acids
2. B
   Amines < Carboxylic acids < Alcohols
3. C
   Amines < Alcohols < Carboxylic acid
4. D
   Carboxylic acids < Alcohols < Amines

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1. A
   3s
2. B
   3p
3. C
   3d
4. D
   3f

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1. A
   It is immiscible in water.
2. B
   It is pale blue coloured liquid in pure state.
3. C
   It's strength is explained in volume unit.
4. D
   It is mild oxidising as well reducing agent.

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1. A
   0.0223
2. B
   0.0422
3. C
   0.0642
4. D
   0.0821

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1. A
   $\text{C}_4\text{H}_9\text{OH} + \text{NaBr} + \text{H}_2\text{SO}_4 \rightarrow \text{C}_4\text{H}_9\text{Br} + \text{NaHSO}_4 + \text{H}_2\text{O}$
2. B
   $\text{C}_2\text{H}_4 + \text{H}_2 \xrightarrow{\text{Ni}} \text{C}_2\text{H}_6$
3. C
   $\text{C}_2\text{H}_5\text{OH} + \text{C}_2\text{H}_5\text{COOH} \rightarrow \text{C}_2\text{H}_5\text{COOC}_2\text{H}_5 + \text{H}_2\text{O}$
4. D
   $\text{C}_4\text{H}_9\text{OH} + \text{SOCl}_2 \xrightarrow{\Delta} \text{C}_4\text{H}_9\text{Cl} + \text{HCl} + \text{SO}_2$

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