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1. A
   $5x + 6y - 2z - 23 = 0$
2. B
   $-5x + 6y + 2z + 23 = 0$
3. C
   $5x + 6y + 2z - 23 = 0$
4. D
   $5x - 6y + 2z - 23 = 0$

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1. A
   $\dfrac{x+1}{2} = \dfrac{y-3}{7} = \dfrac{z+2}{4}$
2. B
   $\dfrac{x+1}{-2} = \dfrac{y-3}{-7} = \dfrac{z+2}{4}$
3. C
   $\dfrac{x+1}{2} = \dfrac{y-3}{7} = \dfrac{z+2}{-4}$
4. D
   $\dfrac{x+1}{2} = \dfrac{y-3}{-7} = \dfrac{z+2}{4}$.

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1. A
   a function of x.
2. B
   a function of x and y.
3. C
   a function of y.
4. D
   a constant.

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1. A
   $-11, 6$
2. B
   $11, 6$
3. C
   $-11, -6$
4. D
   $11, -6$

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1. A
   $1 - \left(\dfrac{1}{10}\right)^{10}$
2. B
   $1 - \left(\dfrac{3}{10}\right)^{10}$
3. C
   $1 - \left(\dfrac{9}{10}\right)^{10}$
4. D
   $1 - \left(\dfrac{7}{10}\right)^{10}$

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1. A
   statement II is negation of statement I.
2. B
   statement II is converse of statement I.
3. C
   statement II and statement I are equivalent.
4. D
   statement II is an inverse of statement I.

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1. A
   $\dfrac{24}{25}$
2. B
   $-\dfrac{24}{25}$
3. C
   $\dfrac{8}{25}$
4. D
   $-\dfrac{8}{25}$

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

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1. A
   $(10, 0)$
2. B
   $(8, 4)$
3. C
   $(0, 12)$
4. D
   $(12, 0)$

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1. A
   1
2. B
   4
3. C
   2
4. D
   5

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1. A
   252500
2. B
   250500
3. C
   250000
4. D
   255000

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1. A
   $9[\sqrt{2} - \log(\sqrt{2}+1)]$ sq. units
2. B
   $4[\sqrt{2} - \log(\sqrt{2}+1)]$ sq. units
3. C
   $3[\sqrt{2} - \log(\sqrt{2}+1)]$ sq. units
4. D
   $18[\sqrt{2} - \log(\sqrt{2}+1)]$ sq. units

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

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1. A
   $\left(-\dfrac{1}{2}, -\dfrac{1}{2}\right)$
2. B
   $\left(\dfrac{1}{2}, \dfrac{1}{2}\right)$
3. C
   $\left(\dfrac{1}{2}, -\dfrac{1}{3}\right)$
4. D
   $\left(\dfrac{1}{2}, \dfrac{1}{3}\right)$

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1. A
   $(0, 1)$
2. B
   $-2, -\dfrac{4}{3}$
3. C
   $-\dfrac{4}{3}, 0$
4. D
   $0, \dfrac{4}{3}$

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1. A
   $\begin{pmatrix} 1 & -\frac{1}{2} \\ 2 & \frac{3}{2} \end{pmatrix}$
2. B
   $\begin{pmatrix} 1 & \frac{1}{2} \\ -2 & \frac{3}{2} \end{pmatrix}$
3. C
   $\begin{pmatrix} 1 & -\frac{1}{2} \\ -2 & \frac{3}{2} \end{pmatrix}$
4. D
   $\begin{pmatrix} 1 & \frac{1}{2} \\ 2 & \frac{3}{2} \end{pmatrix}$

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1. A
   ferromagnetic domains are perfectly arranged.
2. B
   ferromagnetic domains become random.
3. C
   ferromagnetic domains are not influenced.
4. D
   ferromagnetic material changes itself into diamagnetic material.

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1. A
   threshold frequency $v_0$
2. B
   intensity of light (I)
3. C
   frequency of light (v)
4. D
   work function $\phi_0$

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1. A
   0.6 W
2. B
   W
3. C
   1.25 W
4. D
   1.67 W

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1. A
   $W = \pi r^2 T$
2. B
   $W = 2\pi^2 rT$
3. C
   $W = \frac{4}{3}\pi^2 rT$
4. D
   $W = 2\pi rT$

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1. A
   $\sqrt{\frac{2R}{15}}$
2. B
   $\sqrt{\frac{2}{15}}R$
3. C
   $\sqrt{\frac{4R}{15}}$
4. D
   $\frac{R}{4}$

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1. A
   $H_2 = 4H_1$
2. B
   $H_2 = 2H_1$
3. C
   $H_2 = \frac{H_1}{2}$
4. D
   $H_2 = \frac{H_1}{4}$

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

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1. A
   0.1 H
2. B
   1 mH
3. C
   1 H
4. D
   10 mH

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1. A
   at resonance, impedance of the circuit is zero.
2. B
   at resonance, impedance of the circuit is 12 $\Omega$.
3. C
   the resonant frequency of the circuit is $\frac{1}{2\pi}$.
4. D
   the inductive reactance is less than the capacitive reactance.

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