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

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1. A
   $(x^2-2y^2)p^2-4pxy-x^2=0$
2. B
   $(x^2-2y^2)p^2+4pxy-x^2=0$
3. C
   $(x^2+2y^2)p^2-4pxy-x^2=0$
4. D
   $(x^2+2y^2)p^2-4pxy+x^2=0$

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1. A
   $x=y^2+cy$
2. B
   $x=2cy^2$
3. C
   $x=2y^2+cy$
4. D
   None of the above

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1. A
   $f(5)f'(0)$
2. B
   $f(5)-f'(0)$
3. C
   $f(5)f(0)$
4. D
   $f(5)+f'(0)$

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1. A
   $\int_0^a g(x)\,dx$
2. B
   $\int_0^a f(x)\,dx$
3. C
   $2\int_0^a f(x)\,dx$
4. D
   $0$

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1. A
   $y=xe^a+c$
2. B
   $x=ye^a+c$
3. C
   $y-\ln x+c$
4. D
   $x=\ln y+c$

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1. A
   It is discontinuous at $x=-2$ but continuous at every other point.
2. B
   It is continuous only in the interval $(-3,-2)$.
3. C
   It is discontinuous at $x=0$ but continuous at every other point.
4. D
   It is discontinuous at every point.

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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
   $x^2-1$
2. B
   $x+\dfrac{3}{x}$
3. C
   $|x|$
4. D
   $x^2(x-3)$

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1. A
   $\dfrac{x\log_{10}e}{5x^2+3}$
2. B
   $\dfrac{2x\log_{10}e}{5x^2+3}$
3. C
   $\dfrac{10x\log_{10}e}{5x^2+3}$
4. D
   $\dfrac{10x\log_e 10}{5x^2+3}$

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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
   $\dfrac{3a^2}{4}$
2. B
   $\dfrac{a^2}{2}$
3. C
   $\dfrac{3\sqrt{3}a^2}{4}$
4. D
   $\dfrac{\sqrt{3}a^2}{4}$

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1. A
   $f(x)$ fluctuates in the interval
2. B
   $f(x)$ increases in the interval
3. C
   $f(x)$ decreases in the interval
4. D
   None of the above

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1. A
   $[1,\infty)$
2. B
   $(0,\infty)$
3. C
   $\left(\dfrac{1}{2},\infty\right)$
4. D
   None of the above

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

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1. A
   5
2. B
   10
3. C
   15
4. D
   45

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1. A
   18
2. B
   20
3. C
   21
4. D
   22

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

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1. A
   $\dfrac{1}{24}$
2. B
   $\dfrac{1}{4}$
3. C
   $\dfrac{3}{4}$
4. D
   $\dfrac{23}{24}$

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1. A
   50
2. B
   55
3. C
   60
4. D
   100

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1. A
   $\dfrac{2}{5},\, \dfrac{3}{5}$
2. B
   $\dfrac{2}{5},\, 1$
3. C
   $1,\, \dfrac{2}{5}$
4. D
   Information is insufficient

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

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

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1. A
   $40°$
2. B
   $90°$
3. C
   $144°$
4. D
   $320°$

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

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