Build a question paper in 60 seconds.

1. A
   parallel to x-axis
2. B
   parallel to y-axis
3. C
   parallel to z-axis
4. D
   equally inclined to all the axes

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1. A
   $\left(\dfrac{a+b+c}{3}, \dfrac{a+b+c}{3}, \dfrac{a+b+c}{3}\right)$
2. B
   $(a, b, c)$
3. C
   $\left(\dfrac{a}{2}, \dfrac{b}{2}, \dfrac{c}{2}\right)$
4. D
   $\left(\dfrac{a}{3}, \dfrac{b}{3}, \dfrac{c}{3}\right)$

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1. A
   vertices of a rhombus which is not a square
2. B
   non-coplanar
3. C
   collinear
4. D
   coplanar but not collinear

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1. A
   $\left(0, -\dfrac{7}{2}, \dfrac{5}{2}\right)$
2. B
   $\left(0, \dfrac{7}{2}, \dfrac{1}{2}\right)$
3. C
   $\left(0, -\dfrac{7}{2}, -\dfrac{5}{2}\right)$
4. D
   $\left(0, \dfrac{7}{2}, -\dfrac{5}{2}\right)$

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1. A
   $ae+cg-1=0$
2. B
   $ae+bf-1=0$
3. C
   $ae+cg+1=0$
4. D
   $ag+ce+1=0$

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1. A
   $m=2$ and $n=\pm1$
2. B
   $m=\pm2$ and $n=-1$
3. C
   $m=2$ and $n=-1$
4. D
   $m=\pm2$ and $n=1$

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1. A
   $2\overrightarrow{OP}$
2. B
   $4\overrightarrow{OP}$
3. C
   $6\overrightarrow{OP}$
4. D
   $8\overrightarrow{OP}$

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1. A
   $\overrightarrow{BA}+\overrightarrow{CD}=\overrightarrow{AC}+\overrightarrow{DB}$
2. B
   $\overrightarrow{BA}+\overrightarrow{CD}-\overrightarrow{BD}+\overrightarrow{CA}$
3. C
   $\overrightarrow{BA}+\overrightarrow{CD}=\overrightarrow{AC}+\overrightarrow{BD}$
4. D
   $\overrightarrow{BA}+\overrightarrow{CD}=\overrightarrow{BC}+\overrightarrow{AD}$

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1. A
   $\vec{a}, \vec{b}, \vec{c}$ are orthogonal in pairs and $|\vec{a}|=|\vec{c}|$ and $|\vec{b}|=1$
2. B
   $\vec{a}, \vec{b}, \vec{c}$ are non-orthogonal to each other
3. C
   $\vec{a}, \vec{b}, \vec{c}$ are orthogonal in pairs but $|\vec{a}|\neq|\vec{c}|$
4. D
   $\vec{a}, \vec{b}, \vec{c}$ are orthogonal in pairs but $|\vec{b}|\neq1$

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

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1. A
   $0$
2. B
   $\dfrac{1}{2}$
3. C
   $1$
4. D
   $2$

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1. A
   $\dfrac{1}{2}$
2. B
   $1$
3. C
   $\sqrt{3}$
4. D
   None of the above

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1. A
   $\dfrac{1}{2}\ln\left|\dfrac{x^7-1}{x^7+1}\right|+c$
2. B
   $\dfrac{1}{7}\ln\left|\dfrac{x^7+1}{x^7}\right|+c$
3. C
   $\ln\left|\dfrac{x^7-1}{7x}\right|+c$
4. D
   $\dfrac{1}{7}\ln\left|\dfrac{x^7}{x^7+1}\right|+c$

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1. A
   $[0, \pi]$ and $[-1, 1]$
2. B
   $\left[-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right]$ and $[-1, 1]$
3. C
   $[0, \pi]$ and $(-1, 1)$
4. D
   $[0, \pi]$ and $[0, 1]$

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1. A
   $f\!\left(-\dfrac{a}{a+1}\right)$
2. B
   $f(a^2)$
3. C
   $f\!\left(\dfrac{1}{a}\right)$
4. D
   $f(-a)$

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1. A
   $\dfrac{x^2}{2}+c$
2. B
   $\ln(x+e)+c$
3. C
   $\ln(x^e+e^x)+c$
4. D
   $\dfrac{1}{e}\ln(x^e+e^x)+c$

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1. A
   1 only
2. B
   2 only
3. C
   Both 1 and 2
4. D
   Neither 1 nor 2

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1. A
   $f(p)=g(m)$
2. B
   $f(q)=g(n)$
3. C
   $f(n)=g(q)$
4. D
   $f(m)=g(p)$

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

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1. A
   $-\left(\dfrac{d^2y}{dx^2}\right)^{-1}\!\!\left(\dfrac{dy}{dx}\right)^{-3}$
2. B
   $\left(\dfrac{d^2y}{dx^2}\right)^{-1}\!\!\left(\dfrac{dy}{dx}\right)^{-2}$
3. C
   $-\left(\dfrac{d^2y}{dx^2}\right)\!\!\left(\dfrac{dy}{dx}\right)^{-3}$
4. D
   $\left(\dfrac{d^2y}{dx^2}\right)^{-1}$

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1. A
   one-one and into
2. B
   neither one-one nor onto
3. C
   many-one and onto
4. D
   one-one and onto

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

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

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

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1. A
   Both the statements are true and Statement 2 is the correct explanation of Statement 1
2. B
   Both the statements are true but Statement 2 is not the correct explanation of Statement 1
3. C
   Statement 1 is true but Statement 2 is false
4. D
   Statement 1 is false but Statement 2 is true

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