1. A
   $\sin^{-1}x+c$
2. B
   $\tan^{-1}x+c$
3. C
   $\sec^{-1}x+c$
4. D
   $\cos^{-1}x+c$

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1. A
   100
2. B
   96
3. C
   84
4. D
   50

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1. A
   $\frac{\cos1-\sin1}{e}$
2. B
   $\frac{\sin1-\cos1}{e}$
3. C
   $\frac{\cos1+\sin1}{e}$
4. D
   0

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1. A
   0
2. B
   1
3. C
   $2e$
4. D
   -1

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

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1. A
   $\frac{xe^x}{ex^e}$
2. B
   $\frac{e^x}{x^e}$
3. C
   $\frac{xe^x}{x^e}$
4. D
   $\frac{e^x}{ex^e}$

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

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1. A
   5
2. B
   10
3. C
   15
4. D
   20

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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
   $(-\infty,\infty)$
2. B
   $(0,\infty)$
3. C
   $[0,\infty)$
4. D
   $(-\infty,\infty)-\{0\}$

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

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1. A
   1
2. B
   2
3. C
   3
4. D
   Degree is not defined

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1. A
   $\frac{d^2y}{dx^2}+y=0$
2. B
   $\frac{d^2y}{dx^2}-y=0$
3. C
   $\frac{d^2y}{dx^2}+y=1$
4. D
   $\frac{dy}{dx}-y=0$

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1. A
   $e^x+e^y=c$
2. B
   $e^{x+y}=c$
3. C
   $e^x-e^y=c$
4. D
   $e^{x-y}=c$

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1. A
   $\frac{x^4}{4}+c$
2. B
   $\frac{x^3}{3}+c$
3. C
   $\frac{2x^5}{5}+c$
4. D
   $\frac{x^5}{5}+c$

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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
   36°
2. B
   72°
3. C
   120°
4. D
   168°

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1. A
   the height of the rectangle
2. B
   the area of the rectangle
3. C
   the width of the rectangle
4. D
   the perimeter of the rectangle

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1. A
   change of scale only
2. B
   change of origin only
3. C
   both change of scale and change of origin
4. D
   neither change of scale nor change of origin

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1. A
   3
2. B
   4
3. C
   5
4. D
   6

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1. A
   $M$
2. B
   $M+k$
3. C
   $M-k$
4. D
   $kM$

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

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1. A
   $5m=4n$
2. B
   $2m=n$
3. C
   $4m=5n$
4. D
   $m=4n$

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1. A
   2025
2. B
   450
3. C
   45
4. D
   4.5

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1. A
   $P(A|B) < \frac{L+M-1}{M}$
2. B
   $P(A|B) > \frac{L+M-1}{M}$
3. C
   $P(A|B) \geq \frac{L+M-1}{M}$
4. D
   $P(A|B) = \frac{L+M-1}{M}$

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