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If y = *f*
(x^{2} + 2) and *f* '(3) = 5,
then dy/dx at x = 1 is

**A. ** 5

**B. ** 25

**C. ** 15

**D. ** 10

**Answer : ****Option D**

**Explaination / Solution: **

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If y = 1/4 u^{4} , u = 2/3 x^{3} + 5, then d*y*/d*x* is

**A. ** 1/ 27 x^{2} (2x^{3} +15)^{3}

**B. ** 2/27 x (2x^{3} + 5)^{3}

**C. ** 2/ 27 x^{2} (2x^{3} +15)^{3}

**D. ** 2/27 x
(2x^{3} + 5)^{3}

**Answer : ****Option C**

**Explaination / Solution: **

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If *f* (*x*) = x^{2} − 3x , then the
points at which *f* (*x*) = *f* '(*x*)
are

**A. ** both positive integers

**B. ** both negative integers

**C. ** both irrational

**D. ** one rational and another irrational

**Answer : ****Option C**

**Explaination / Solution: **

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If y = 1/ a − z , then dz/ dy is

**A. ** (a − z)^{2}

**B. ** −( z − a)^{2}

**C. ** (z + a)^{2}

**D. ** − ( z + a)^{2}

**Answer : ****Option A**

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If y = cos(sin x^{2}), then *dy/dx* at x = √[π/2] is

**A. ** - 2

**B. ** 2

**C. ** −2 √[π/2]

**D. ** 0

**Answer : ****Option D**

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If *y* = *mx* + c and *f* (0) = *f* '(0) = 1, then *f* (2) is

**A. ** 1

**B. ** 2

**C. ** 3

**D. ** - 3

**Answer : ****Option C**

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If *f* (*x*) = *x*
tan^{−1}*x* , then *f* '(1) is

**A. ** 1+ π/4

**B. ** 1/2 + π/4

**C. ** 1/2 – π/4

**D. ** 2

**Answer : ****Option B**

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If the derivative of (ax − 5)e^{3x} at x
= 0 is -13, then the value of *a*
is

**A. ** 8

**B. ** - 2

**C. ** 5

**D. ** 2

**Answer : ****Option D**

**Explaination / Solution: **

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