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

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1. A
   $x\sqrt{x^2-16}$
2. B
   $x-\sqrt{x^2-16}$
3. C
   $\sqrt{x^2-16}$
4. D
   $4\sqrt{x^2-16}$

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1. A
   $\frac{dy}{dx}+xy(1+2\ln x)=0$
2. B
   $\frac{dy}{dx}-xy(1+2\ln x)=0$
3. C
   $\frac{dy}{dx}-2xy(1+\ln x)=0$
4. D
   $\frac{dy}{dx}+2xy(1+\ln x)=0$

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

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1. A
   $\frac{\pi}{4}$
2. B
   $\frac{\pi}{6}$
3. C
   $\frac{\pi}{8}$
4. D
   $\frac{\pi}{12}$

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1. A
   1
2. B
   2
3. C
   4
4. D
   8

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1. A
   $f(\alpha-\beta)$
2. B
   $f(\alpha+\beta)$
3. C
   $f(\alpha)f(\beta)$
4. D
   $f(\alpha\beta)$

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1. A
   $f(x)+f(-x)=0$
2. B
   $f(x)-f(-x)=0$
3. C
   $2f(x)=f(-x)$
4. D
   $f(x)=2f(-x)$

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1. A
   $\frac{1}{2\sqrt{2}}$
2. B
   $-\frac{1}{2\sqrt{2}}$
3. C
   $\sqrt{2}$
4. D
   Limit does not exist

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

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1. A
   0
2. B
   1
3. C
   2
4. D
   $\lim_{x\to0}f(x)$ does not exist

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1. A
   $\sin^2x$
2. B
   $\cos^2x$
3. C
   $\sin2x$
4. D
   $\cos2x$

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

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1. A
   $a=b$
2. B
   $a=2b$
3. C
   $a+b=0$
4. D
   $2a=b$

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1. A
   $\tan^2x = \frac{q}{p}$
2. B
   $\cot^2x = \frac{q}{p}$
3. C
   $\tan^2x = pq$
4. D
   $\cot^2x = pq$

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1. A
   $x=3.5$
2. B
   $x=4$
3. C
   $x=4.5$
4. D
   $x=5$

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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
   $-1$
2. B
   $0$
3. C
   $1$
4. D
   $\ln 2$

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1. A
   $k$
2. B
   $10k$
3. C
   $20k$
4. D
   $40k$

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

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

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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
   $x\frac{dy}{dx}+2y=0$
2. B
   $x\frac{dy}{dx}-2y=0$
3. C
   $y\frac{dx}{dy}+2x=0$
4. D
   $y\frac{dx}{dy}-2x=0$

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1. A
   $y=\tan\!\left(\frac{x}{2}\right)-x+c$
2. B
   $y=\frac{1}{2}\tan\!\left(\frac{x}{2}\right)-x+c$
3. C
   $y=2\tan\!\left(\frac{x}{2}\right)-x+c$
4. D
   $y=\tan\!\left(\frac{x}{2}\right)-2x+c$

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