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

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1. A
   25
2. B
   21
3. C
   20
4. D
   10

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1. A
   $3x^2+2xy+5y^2+14x+26y+5=0$
2. B
   $3x^2+2xy-5y^2-14x-26y-5=0$
3. C
   $3x^2-2xy-5y^2-14x-26y+5=0$
4. D
   $3x^2-2xy+5y^2+14x+26y-5=0$

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1. A
   $2x+y+3=0$
2. B
   $2x+y+3\sqrt{3}=0$
3. C
   $2x-y-3\sqrt{3}=0$
4. D
   $2x+y-3\sqrt{3}=0$

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1. A
   1
2. B
   $-1$
3. C
   2
4. D
   non-existent.

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1. A
   $\frac{-14\hat{i}+4\hat{j}+10\hat{k}}{\sqrt{312}}$
2. B
   $\frac{14\hat{i}-4\hat{j}+10\hat{k}}{\sqrt{312}}$
3. C
   $\frac{14\hat{i}+4\hat{j}+10\hat{k}}{\sqrt{312}}$
4. D
   $\frac{-14\hat{i}-4\hat{j}+10\hat{k}}{\sqrt{312}}$

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

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1. A
   0.4
2. B
   0.5
3. C
   0.8
4. D
   0.9

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1. A
   $\frac{1}{2} \cdot \frac{T_2}{T_1^4}$
2. B
   $\frac{1}{2} \cdot \frac{T_2}{T_1^2}$
3. C
   $2 \cdot \frac{T_1^4}{T_2^4}$
4. D
   $2 \cdot \frac{T_1}{T_2^2}$

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

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1. A
   $K_1 = \frac{K_2}{3}$
2. B
   $K_1 < \frac{K_2}{3}$
3. C
   $K_1 = 3K_2$
4. D
   $3K_1 = 2K_2$

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1. A
   Its resultant acceleration is towards the centre.
2. B
   It moves in a spiral path with decreasing radius.
3. C
   The direction of angular momentum remains constant.
4. D
   Its angular momentum remains constant.

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1. A
   (A), (B)
   
2. B
   (B), (C)
   
3. C
   (A), (C)
   
4. D
   (B), (D)
   

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1. A
   First decreases, becomes minimum and then increases.
2. B
   Increases
3. C
   Decreases.
4. D
   Remains constant.

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1. A
   Very low and partially filled.
2. B
   Very high and completely filled.
3. C
   Very high and empty.
4. D
   Very low and empty.

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

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1. A
   0.2 Hz
2. B
   10 Hz
3. C
   20 Hz
4. D
   40 Hz

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1. A
   $\sqrt{\frac{T}{lm}}$
2. B
   $\sqrt{\frac{T}{ml}}$
3. C
   $\sqrt{\frac{ml}{T}}$
4. D
   $\sqrt{\frac{T}{ml}}$

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

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1. A
   40
2. B
   25
3. C
   4
4. D
   2.5

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1. A
   $2\pi R^2 S$
2. B
   $3\pi R^2 S$
3. C
   $4\pi R^2 S$
4. D
   $2\pi R S^2$

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1. A
   0.025
2. B
   0.25
3. C
   2.5
4. D
   40

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1. A
   $-\frac{q^2}{8\pi\varepsilon_0 r}$
2. B
   $-\frac{3q^2}{8\pi\varepsilon_0 r}$
3. C
   $-\frac{5q^2}{8\pi\varepsilon_0 r}$
4. D
   $-\frac{7q^2}{8\pi\varepsilon_0 r}$

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1. A
   $F(m-1)$
2. B
   $(m-1)F$
3. C
   $F(m+1)$
4. D
   $\frac{F}{(m-1)}$

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1. A
   $4.9 \times 10^{-4}$ m
2. B
   $5.8 \times 10^{-4}$ m
3. C
   $6.3 \times 10^{-4}$ m
4. D
   $8.6 \times 10^{-4}$ m

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