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: **

No Explaination.

No Explaination.

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If *f* (*x*) = *x*
+ 2, then *f* '( *f* (*x*)) at *x* = 4 is

**A. ** 8

**B. ** 1

**C. ** 4

**D. ** 5

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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If *f (x)*
= is differentiable at *x* = 1, then

**A. ** a = 1/2 , b = −3/2

**B. ** a = −1/2 , b = 3/2

**C. ** a = − 1/2 , b = − 3/2

**D. ** a = 1/2 , b = 3/2

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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A matrix is chosen at random from a set of all matrices of order 2, with elements 0 or 1 only. The probability that the determinant of the matrix chosen is non zero will be

**A. ** 3/16

**B. ** 3/8

**C. ** 1/4

**D. ** 5/8

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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There are three events A, B and C of which one and only one can happen. If the odds are 7 to 4 against A and 5 to 3 against B, then odds against C is

**A. ** 23: 65

**B. ** 65: 23

**C. ** 23: 88

**D. ** 88: 23

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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The gradient (slope) of a curve at any point (*x, y*) is [x^{2} – 4]/ x^{2}
. If the curve passes through the point (2, 7), then the equation of the curve
is

**A. ** *y* = *x* + 4/*x* + 3

**B. ** *y* = *x* + 4/*x* + 4

**C. ** *y* = *x*^{2} + 3*x* + 4

**D. ** *y* = *x*^{2} − 3*x* + 6

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

**Explaination / Solution: **

No Explaination.

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is

**A. ** cot *x*
+ sin^{−1} *x* + c

**B. ** − cot x + tan^{−1} *x* + c

**C. ** − tan *x*
+ cot^{−1} *x* + c

**D. ** − cot *x*
− tan^{−1} *x* + c

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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∫sin √*xdx* is

**A. ** 2(− √*x* cos√*x* + sin √*x*) + c

**B. ** 2(− √*x*
cos√*x* - sin √*x*) + c

**C. ** 2(− √*x*
sin√*x* - cos √*x*) + c

**D. ** 2(− √*x*
sin√*x* + cos √*x*) + c

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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If , then the value of lim_{x}_{→0} f (x) is equal to

**A. ** -1

**B. ** 0

**C. ** 2

**D. ** 4

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

**Explaination / Solution: **

No Explaination.

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The value of is

**A. ** 1

**B. ** - 1

**C. ** 0

**D. ** ∞

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

**Explaination / Solution: **

No Explaination.

No Explaination.

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