# Maths

Maths
| Chapter 10: Differential Calculus Differentiability and Methods of Differentiation | | Chapter 12: Introduction to probability theory | | Chapter 11: Integral Calculus | | Chapter 9: Differential Calculus Limits and Continuity | | Chapter 8: Vector Algebra I | | Chapter 7: Matrices and Determinants | | Chapter 6: Two Dimensional Analytical Geometry | | Chapter 5: Binomial Theorem, Sequences And Series | | Chapter 4: Combinatorics and Mathematical Induction | | Chapter 3: Trigonometry | | Chapter 2: Basic Algebra | | Chapter 1: Sets, Relations and Functions |
Q.1
If y = 1/4  u4 , u = 2/3  x3 + 5, then dy/dx is
A. 1/ 27 x2 (2x3 +15)3
B. 2/27 x (2x3 + 5)3
C.  2/ 27  x2 (2x3 +15)3
D. 2/27  x (2x3 + 5)3
Explaination / Solution:
No Explaination.

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Q.2
If f (x) = x + 2, then f '( f (x)) at x = 4 is
A. 8
B. 1
C. 4
D. 5
Explaination / Solution:
No Explaination.

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Q.3
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
Explaination / Solution:
No Explaination.

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Q.4
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
Explaination / Solution:
No Explaination.

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Q.5
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
Explaination / Solution:
No Explaination.

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Q.6
The gradient (slope) of a curve at any point (x, y) is [x2 – 4]/ x2 . 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 = x2 + 3x + 4
D. y = x2 − 3x + 6
Explaination / Solution:
No Explaination.

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Q.7
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
Explaination / Solution:
No Explaination.

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Q.8
∫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
Explaination / Solution:
No Explaination.

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Q.9
If , then the value of limx0 f (x) is equal to
A. -1
B. 0
C. 2
D. 4
Explaination / Solution:
No Explaination.

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Q.10
The value of  is
A. 1
B. - 1
C. 0
D.