1. A
   $\frac{\pi}{12},\frac{\pi}{6}$
2. B
   $\frac{\pi}{6},\frac{5\pi}{6}$
3. C
   $\frac{5\pi}{12},\frac{7\pi}{12}$
4. D
   $\frac{7\pi}{12},\frac{11\pi}{12}$

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1. A
   circles have same centre
2. B
   circles have no meeting point
3. C
   circles have only one meeting point
4. D
   circles have two meeting points

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1. A
   5
2. B
   3
3. C
   1
4. D
   0

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1. A
   $\frac{1}{2}\sin\sqrt{(2x - 1)^{2} + 5} + c$
2. B
   $\frac{1}{2}\cos\sqrt{(2x + 1)^{2} + 5} + c$
3. C
   $\frac{1}{2}\cos\sqrt{(2x - 1)^{2} + 5} + c$
4. D
   $\frac{1}{2}\sin\sqrt{(2x + 1)^{2} + 5} + c$

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1. A
   $4\sqrt{2}x + 5y - (15 + 4\sqrt{2}) = 0$
2. B
   $5\sqrt{2}x + 4y - (15 + 4\sqrt{2}) = 0$
3. C
   $4\sqrt{2}x + 5y - 4\sqrt{2} = 0$
4. D
   $4\sqrt{2}x - 5y - (5 + 4\sqrt{2}) = 0$

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

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

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1. A
   $|\alpha|^{2} - ad \neq 0$
2. B
   $|\alpha|^{2} - ad > 0$ and $a \in R - \{ 0\}$
3. C
   $|\alpha|^{2} - ad \geq 0$ and $a \in R$
4. D
   $\alpha = 0$, a,d $\in R^{+}$

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1. A
   Rhombus
2. B
   Square
3. C
   Rectangle
4. D
   Parallelogram

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1. A
   540
2. B
   550
3. C
   530
4. D
   510

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1. A
   all reals except integers
2. B
   all non-integers except the interval $\lbrack - 1,1\rbrack$
3. C
   all integers except $0, - 1,1$
4. D
   all reals except the Interval $\lbrack - 1,1\rbrack$

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1. A
   $\frac{101}{404}$
2. B
   $\frac{25}{101}$
3. C
   $\frac{101}{408}$
4. D
   $\frac{99}{400}$

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1. A
   $0 \leq x \leq 1$
2. B
   $0 \leq x < 1$
3. C
   $0 < x < 1$
4. D
   $0 < x \leq 1$

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

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1. A
   1
2. B
   2
3. C
   0
4. D
   3

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1. A
   26664
2. B
   122664
3. C
   122234
4. D
   22264

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1. A
   $1.5 + \sqrt{3}$
2. B
   $2 + \sqrt{3}$
3. C
   $3 + 2\sqrt{3}$
4. D
   $4 + \sqrt{3}$

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1. A
   $3.0{\text{ }ms}^{- 1}$
2. B
   $3.50{\text{ }ms}^{- 1}$
3. C
   $2.0{\text{ }ms}^{- 1}$
4. D
   $2.50{\text{ }ms}^{- 1}$

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1. A
   1.02
2. B
   1.2
3. C
   1.25
4. D
   1.35

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1. A
   $0.69 \times 10^{2}\text{ }kg{\text{ }s}^{- 1}$
2. B
   $3.3 \times 10^{2}\text{ }kg{\text{ }s}^{- 1}$
3. C
   $1.16 \times 10^{2}\text{ }kg{\text{ }s}^{- 1}$
4. D
   None of these

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1. A
   NOR Gate
2. B
   NAND Gate
3. C
   AND Gate
4. D
   XOR Gate

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1. A
   $1.96 \times 10^{7}{Nm}^{- 2}$
2. B
   $1.44 \times 10^{7}{Nm}^{- 2}$
3. C
   $2.26 \times 10^{9}{Nm}^{- 2}$
4. D
   $1.44 \times 10^{9}{Nm}^{- 2}$

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

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1. A
   $Y(x,t) = 0.03\left\lbrack \sin5.1x - \left( 0.2 \times 10^{3} \right)t \right\rbrack$
2. B
   $Y(x,t) = 0.06\left\lbrack \sin5.1x - \left( 1.5 \times 10^{3} \right)t \right\rbrack$
3. C
   $Y(x,t) = 0.06\left\lbrack \sin0.8x - \left( 0.5 \times 10^{3} \right)t \right\rbrack$
4. D
   $Y(x,t) = 0.03\left\lbrack \sin5.1x - \left( 1.5 \times 10^{3} \right)t \right\rbrack$

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1. A
   (C) and (A)
2. B
   (C) and (D)
3. C
   (A) only
4. D
   (B) and (C)

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