# Topic: Chapter 10: Differential Calculus Differentiability and Methods of Differentiation (Test 1)

Topic: Chapter 10: Differential Calculus Differentiability and Methods of Differentiation
Q.1
d/ dx (2/π sin x° ) is
A. π/180 . cos x°
B. 1/90 . cos x°
C. π/90 . cos x°
D. 2/ π . cos x°
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Q.2
If y = f (x2 + 2) and f '(3) = 5, then dy/dx at x = 1 is
A. 5
B. 25
C. 15
D. 10
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Q.3
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
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Q.4
If f (x) = x2 − 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
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Q.5
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
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Q.6
If y = cos(sin x2), then dy/dx at x = [π/2] is
A. - 2
B. 2
C. −2 √[π/2]
D. 0
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Q.7
If y = mx + c and f (0) = f '(0) = 1, then f (2) is
A. 1
B. 2
C. 3
D. - 3
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Q.8
If f (x) = x tan−1x , then f '(1) is
A. 1+ π/4
B. 1/2 + π/4
C. 1/2 – π/4
D. 2
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Q.9
d/ dx (ex +5logx) is
A. ex .x4 (x + 5)
B. ex .x (x + 5)
C. ex + 5/x
D. ex -  5/x
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Q.10
If the derivative of (ax − 5)e3x at x = 0 is -13, then the value of a is
A. 8
B. - 2
C. 5
D. 2