Build a question paper in 60 seconds.

1. A
   The work is finished in time and the payment is not made.
2. B
   The payment is made and the work is not finished in time.
3. C
   The work is finished in time and the payment is not made, or the payment is made and the work is finished in time.
4. D
   Either the work is finished in time and the payment is not made, or the payment is made and the work is not finished in time.

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1. A
   no real root
2. B
   exactly two real roots
3. C
   exactly one real root
4. D
   all three real roots

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

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1. A
   $(-\infty,-6) \cup (2,\infty)$
2. B
   $(-6,2)$
3. C
   $(-\infty,-2) \cup (6,\infty)$
4. D
   $(-6,2]$

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1. A
   122
2. B
   132
3. C
   112
4. D
   222

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1. A
   equivalent to $p \leftrightarrow q$
2. B
   contingency
3. C
   tautology
4. D
   contradiction

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

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1. A
   $x^2 + y^2 + 2x + 3y + 9 = 0$
2. B
   $x^2 + y^2 - 2x + 3y + 9 = 0$
3. C
   $x^2 + y^2 + 2x - 3y - 9 = 0$
4. D
   $x^2 + y^2 - 2x - 3y - 9 = 0$

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1. A
   $\frac{5}{3}\hat{i}+\frac{2}{3}\hat{j}+\frac{2}{3}\hat{k}$
2. B
   $-\frac{5}{3}\hat{i}+\frac{2}{3}\hat{j}+\frac{2}{3}\hat{k}$
3. C
   $\frac{5}{3}\hat{i}-\frac{2}{3}\hat{j}+\frac{2}{3}\hat{k}$
4. D
   $-\frac{5}{3}\hat{i}+\frac{2}{3}\hat{j}+\frac{1}{3}\hat{k}$

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1. A
   $\sqrt{\frac{2}{6}}$
2. B
   $\sqrt{\frac{1}{6}}$
3. C
   $\sqrt{\frac{5}{6}}$
4. D
   $\sqrt{\frac{7}{6}}$

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1. A
   $\frac{1}{\sqrt{14}}$ units
2. B
   $\frac{1}{\sqrt{5}}$ units
3. C
   $\frac{1}{\sqrt{11}}$ units
4. D
   $\frac{1}{\sqrt{6}}$ units

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1. A
   $[\vec{a}\;\vec{b}\;\vec{c}]$
2. B
   $2[\vec{a}\;\vec{b}\;\vec{c}]$
3. C
   $3[\vec{a}\;\vec{b}\;\vec{c}]$
4. D
   $4[\vec{a}\;\vec{b}\;\vec{c}]$

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1. A
   $a_1 + b_1 = c_1$
2. B
   $b_1 + c_1 = a_1$
3. C
   $a_1 + c_1 = b_1$
4. D
   $b_1 = c_1$

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

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

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

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1. A
   Geometric Progression
2. B
   Arithmetic Progression
3. C
   Harmonic Progression
4. D
   Arithmetico-Geometric Progression

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1. A
   1
2. B
   $\frac{1}{2}$
3. C
   $\frac{1}{3}$
4. D
   $\frac{1}{8}$

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1. A
   $n\pi,\;n\in\mathbb{Z}$
2. B
   $(2n+1)\frac{\pi}{2},\;n\in\mathbb{Z}$
3. C
   $(2n+1)\frac{\pi}{4},\;n\in\mathbb{Z}$
4. D
   $\frac{2n\pi}{3},\;n\in\mathbb{Z}$

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1. A
   $ae^{by} + be^{ax} = c_1$
2. B
   $ae^{-by} + be^{-ax} = c_1$
3. C
   $ae^{-by} + be^{ax} = c_1$
4. D
   $ae^{by} + be^{-ax} = c_1$

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

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1. A
   1
2. B
   −1
3. C
   $-\frac{32}{5}$
4. D
   $-\frac{9}{25}$

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1. A
   $x+\alpha$ and $\log|\sin(x+\alpha)|$
2. B
   $x-\alpha$ and $\log|\sin(x-\alpha)|$
3. C
   $x-\alpha$ and $\log|\cos(x+\alpha)|$
4. D
   $x+\alpha$ and $\log|\sin(x-\alpha)|$

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1. A
   $\frac{3}{\sqrt{77}}\hat{i} - \frac{6}{\sqrt{77}}\hat{j} + \frac{2}{\sqrt{77}}\hat{k}$
2. B
   $\frac{2}{\sqrt{77}}\hat{i} - \frac{6}{\sqrt{77}}\hat{j} + \frac{3}{\sqrt{77}}\hat{k}$
3. C
   $\frac{6}{\sqrt{77}}\hat{i} - \frac{2}{\sqrt{77}}\hat{j} + \frac{3}{\sqrt{77}}\hat{k}$
4. D
   $\frac{1}{\sqrt{77}}\hat{i} + \frac{1}{\sqrt{77}}\hat{j} - \frac{3}{\sqrt{77}}\hat{k}$

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1. A
   $\frac{1}{5\pi}$
2. B
   $\frac{1}{15\pi}$
3. C
   $\frac{2}{\pi}$
4. D
   $\frac{1}{10\pi}$

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