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: **

No Explaination.

No Explaination.

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If *y* =
(1− *x*)^{2}/* x*^{2} , then *dy/ dx* is

**A. ** 2/*x*^{2}
+ 2/*x*^{3}

**B. ** −2/*x*^{2}
+ 2/*x*^{3}

**C. ** −2/*x*^{2}
− 2/*x*^{3}

**D. ** −2/*x*^{2}
+ 2/*x*^{3}

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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The number of points in R in which the function *f (x)* =| *x* − 1| + | *x* − 3| + sin *x* is not differentiable, is

**A. ** 3

**B. ** 2

**C. ** 1

**D. ** 4

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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A bag contains 5 white and 3 black balls. Five balls are drawn successively without replacement. The probability that they are alternately of different colours is

**A. ** 3/14

**B. ** 5/14

**C. ** 1/14

**D. ** 9/14

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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If a and b are chosen randomly from the set {1,2,3,4}with
replacement, then the probability of the real
roots of the equation x^{2} + ax + b = 0 is

**A. ** 3/16

**B. ** 5/16

**C. ** 7/16

**D. ** 11/16

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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is

**A. ** cot*(xe*^{x}
) + c

**B. ** sec*(xe*^{x}
) + c

**C. ** tan*(xe*^{x}
) + c

**D. ** cos*( xe*^{x}
) + c

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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∫ *x*^{2} cos *x* *dx* is

**A. ** *x*^{2} sin *x* + 2*x* cos *x* − 2sin *x* + c

**B. ** *x*^{2} sin *x* − 2*x* cos *x* − 2sin *x* + c

**C. ** − *x*^{2}
sin *x* + 2*x* cos *x* + 2sin *x* + c

**D. ** − *x*^{2}
sin *x* − 2*x* cos *x* + 2sin *x* + c

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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∫e^{√x} *dx* is

**A. ** 2 √*x* (1− e^{√x}) + c

**B. ** 2 √*x* (e^{√x} − 1) + c

**C. ** 2e^{√x} (1− √*x *) + c

**D. ** 2e^{√x} (√*x* − 1) + c

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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No Explaination.

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The value of , where *k* is an integer is

**A. ** - 1

**B. ** 1

**C. ** 0

**D. ** 2

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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