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1. A
   $x+3y=10$
2. B
   $3x+y=6$
3. C
   $x-3y+8=0$
4. D
   $3x-2y+3=0$

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1. A
   $\frac{5\pi}{6}$
2. B
   $\frac{2\pi}{3}$
3. C
   $\frac{\pi}{6}$
4. D
   $\frac{\pi}{3}$

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1. A
   $\vec{r}=(-2\hat{i}+\frac{1}{3}\hat{j}+\frac{1}{2}\hat{k})+\lambda(3\hat{i}+2\hat{j}+\hat{k})$
2. B
   $\vec{r}=(-2\hat{i}-\frac{1}{3}\hat{j}+\frac{1}{2}\hat{k})+\lambda(3\hat{i}+2\hat{j}+\hat{k})$
3. C
   $\vec{r}=(2\hat{i}+\hat{j}+\hat{k})+\lambda(3\hat{i}+2\hat{j}+\hat{k})$
4. D
   $\vec{r}=(-2\hat{i}-\hat{j}+\hat{k})+\lambda(3\hat{i}+2\hat{j}+\hat{k})$

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1. A
   $\frac{\pi}{4}$
2. B
   $\frac{\pi}{3}$
3. C
   $\cos^{-1}\frac{1}{3}$
4. D
   $\cos^{-1}\frac{2}{7}$

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1. A
   $-(\log(\cot x))^2 + c$
2. B
   $2(\log(\cot x))^2 + c$
3. C
   $-\frac{1}{4}(\log(\sin x))^2 + c$
4. D
   $-\frac{1}{4}(\log(\cot x))^2 + c$

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

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1. A
   $1.33\times10^{-5}/{}^\circ C$
2. B
   $1.66\times10^{-5}/{}^\circ C$
3. C
   $1.33\times10^{-3}/{}^\circ C$
4. D
   $1.66\times10^{-3}/{}^\circ C$

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1. A
   $-0.1$ cm
2. B
   $-10$ cm
3. C
   $-20$ cm
4. D
   $+10$ cm

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1. A
   $\frac{\pi x}{t}$
2. B
   $\frac{\pi x}{2t}$
3. C
   $\frac{\pi^2 x}{2t}$
4. D
   $\frac{\pi^2 x}{t}$

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1. A
   $4.5\times10^6\,A\,m^{-1}$
2. B
   $6.0\times10^6\,A\,m^{-1}$
3. C
   $7.5\times10^6\,A\,m^{-1}$
4. D
   $9.0\times10^6\,A\,m^{-1}$

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1. A
   inversely with the intensity of incident radiation and is independent of its frequency.
2. B
   inversely with the frequency of incident radiation and is independent of its intensity.
3. C
   linearly with the frequency of incident radiation and depends on its intensity.
4. D
   linearly with the frequency of incident radiation and is independent of its intensity.

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

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1. A
   $\frac{1+2\pi fCR}{4\pi^2 f^2 C}$
2. B
   $\frac{1-2\pi fCR}{4\pi^2 f^2 C}$
3. C
   $\frac{4\pi^2 f^2 C}{1+2\pi fCR}$
4. D
   $\frac{4\pi^2 f^2 C}{1-2\pi fCR}$

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1. A
   The emitter-base junction is reversed biased in n-p-n transistor.
2. B
   The emitter injects minority carriers into the base region of the p-n-p transistor.
3. C
   The emitter injects holes into the base of the p-n-p transistor and electrons into the base region of n-p-n transistor.
4. D
   The emitter injects the base of n-p-n transistor.

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1. A
   $(100-l)$
2. B
   $(100-2l)$
3. C
   $(100-3l)$
4. D
   $100-\frac{l}{2}$

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1. A
   2:1
2. B
   1:1
3. C
   1:2
4. D
   $\infty:1$

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1. A
   $G\!\left(\dfrac{V}{V_g}-1\right)$
2. B
   $\dfrac{G(V+V_g)}{V}$
3. C
   $\dfrac{G(V-V_g)}{V}$
4. D
   $\dfrac{G}{V_g}$

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

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1. A
   8:1
2. B
   2:1
3. C
   4:1
4. D
   1:4

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1. A
   increases with increase of slit width.
2. B
   decreases with increase of slit width.
3. C
   decreases with decreases of slit width.
4. D
   may increase or decrease with decrease of slit width.

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1. A
   1.5 A
2. B
   0.9 A
3. C
   0.6 A
4. D
   0.3 A

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1. A
   Zero
2. B
   infinity
3. C
   unity
4. D
   same as that at any other temperature.

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1. A
   $\frac{Ma^2}{6}$
2. B
   $\frac{2Ma^2}{3}$
3. C
   $\frac{Ma^2}{3}$
4. D
   $\frac{2Ma^2}{5}$

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

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1. A
   $\sqrt{E_1}+\sqrt{E_2}$
2. B
   $\left(\sqrt{E_1}+\sqrt{E_2}\right)^2$
3. C
   $\sqrt{E_2}-\sqrt{E_1}$
4. D
   $\left(\sqrt{E_2}-\sqrt{E_1}\right)^2$

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