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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The differential coefficient of log_{10}*x* with respect to log_{x}10 is

**A. ** 1

**B. ** −(log_{10}x)^{2}

**C. ** (log_{x}10)^{2}

**D. ** x^{2}
/100

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

**Explaination / Solution: **

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If *f (x)*
= , then which one of the following is true?

**A. ** *f(x)* is not
differentiable at *x* = *a*

**B. ** *f(x)* is discontinuous at *x* = *a*

**C. ** *f(x)* is continuous for all x in R

**D. ** *f(x)* is differentiable
for all *x* ≥ *a*

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

**Explaination / Solution: **

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A letter is taken at random from the letters of the word ‘ASSISTANT’ and another letter is taken at random from the letters of the word ‘STATISTICS’. The probability that the selected letters are the same is

**A. ** 7/45

**B. ** 17/90

**C. ** 29/90

**D. ** 19/90

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

**Explaination / Solution: **

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If A and B are two events such that P(A) = P ( B)
= and P ( B / A) = 0.6 , then P ( ∩ B) is

**A. ** 0.96

**B. ** 0.24

**C. ** 0.56

**D. ** 0.66

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

**Explaination / Solution: **

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If ∫ *f ′*(*x*)*e*^{x}^{2}*dx* = (*x* − 1)e^{x2} + c , then *f*(*x*) is

**A. ** 2x^{3} − *x*^{2}/2 + *x* + c

**B. ** *x*^{3}/2 + 3*x*^{2}
+ 4*x* + c

**C. ** *x*^{3} + 4*x*^{2}
+ 6*x* + c

**D. ** 2*x*^{3}/3
- x^{2}+ x+ c

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

**Explaination / Solution: **

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is

**A. ** e^{x}
tan^{−1} (*x* + 1) + c

**B. ** tan^{−1} (e^{x} ) + c

**C. ** e^{x}
[(tan^{−1} *x*)^{2}/2] +
c

**D. ** e^{x}
tan^{−1}*x* + c

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

**Explaination / Solution: **

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is

**A. **

**B. **

**C. **

**D. **

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

**Explaination / Solution: **

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