JEE Questions for Maths Differentiation Quiz 3 - MCQExams.com

If f (x) = sin x, g (x) = x² and h (x) = log_ex. If F (x) = (hogof) (x), then F '' (x) is equal to

0%
a cosec3 x
0%
2 cot x2 – 4x2 cosec2 x2
0%
2 cot x2
0%
– 2 cosec2 x
0%
4 cosec2 x

If x = e^t sin t, y = e^t cos t, then d²y/dx² at x = π is equal to

0%
2 eπ
0%
(1/eπ
0%
1/2eπ
0%
2/eπ

0%
0
0%
1
0%
– b2 y
0%
– by

0%
0%
2)
0%
0%

If y² = ax² + bx + c, where a, b and c are constant, then y³. d²y/dx² is

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a constant
0%
a function of x
0%
a function of y
0%
a function of x and y both

0%
0%
2)
0%
0%

0%
0%
9y
0%
–9y
0%

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

If x = sin t, y = cos pt, then

0%
(1 – xy2 + xy1 + p2y = 0
0%
(1 – x2)y2 + xy1 - p2y = 0
0%
(1 + x2)y2 - xy1 + p2y = 0
0%
(1 – x2)y2 - xy1 + p2y = 0

If y = t¹⁰ + 1 and x = t⁸ + t, then d²y/dx² is equal to

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5/2 t
0%
20 t8
0%
5/16 t6
0%
None of these

If sin (x + y) + cos (x + y) = log (x + y), then d²y/dx² is equal to

0%
–y/x
0%
0
0%
–1
0%
1

0%
0%
2)
0%
0%
None of these

0%
n2y
0%
– n2y
0%
– y
0%
2x2y

0%
0%
2)
0%
0%

nth derivative of (x + 1)ⁿ is equal to

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(n – 1)!
0%
(n + 1)!
0%
n!
0%
n[(n + 1)]n–1

0%
0%
2)
0%
0%
None of these

0%
0%
2)
0%
0%
0%

If f (x) = 10 cos x + (13 + 2x) sin x, then f '' (x) + f (x) is equal to

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cos x
0%
4 cos x
0%
sin x
0%
4 sinx

0%
– x
0%
x
0%
y
0%
– y

0%
– sin 2u
0%
sin 2u
0%
cos 2u
0%
– cos 2u

0%
cot z
0%
2 cot z
0%
2 tan z
0%
2 sec z

0%
sin u
0%
cosecu
0%
2 tan u
0%
3 tan u

0%
0%
2)
0%
0%
None of these

0%
–1
0%
0
0%
1
0%
2

0%
0
0%
1
0%
2
0%
None of the above

If g is the inverse of a function f and

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1 + x5
0%
5x4
0%
0%
1 + {g(x)}5

If x sin (a + y) + sin a cos (a + y) = 0, then dy/dx is equal to

0%
0%
2)
0%
0%

0%
P' ' ' (x) + P' (x)
0%
P' ' (x) P' ' ' (x)
0%
P(x) P' ' ' (x)
0%
a constant

If f(x) = x² + bx + 7. If f '(= 2f '(7/2), then the value of b is

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4
0%
3
0%
–4
0%
–3
0%
2

If f(x) = x/(1 + x) and g(x) = f[f(x)], then g'(x) is equal to

0%
0%
2)
0%
0%

If sin(x + y) = log(x + y), then dy/dx is equal to

0%
2
0%
–2
0%
1
0%
–1

0%
2
0%
–1
0%
a/b
0%
0
0%
None of these

0%
0%
2)
0%
0%
None of these

0%
∆1 = 3(∆2)2
0%
(d/dx)(∆= 3∆2
0%
(d/dx)(∆= 3(∆2)2
0%
∆1 = 3(∆2)3/2

If x is measured in degrees, then d/dx (cos x) is equal to

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– sin x
0%
– (180/π) sin x
0%
– (π/sin x
0%
sin x

0%
0%
2)
0%
0%

0%
√3
0%
1/√3
0%
0
0%
–√3

If x ≠ 0 and y = log_e |2x|, then dy/dx is equal to

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1/x
0%
– 1/x
0%
± 1/2x
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None of these

If f : (–1,→ R be a differentiable function with f(= – 1 and f '(= 1. Let g(x) = [f{2f(x) + 2}]². Then, g'(is equal to

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4
0%
–4
0%
0
0%
–2

0%
0%
2)
0%
0%

If f(x) = 2^{2x – 1} and ∅(x) = – 2^x + 2x log 2 . If f '(x) > ∅' (x), then

0%
0 < x < 1
0%
0 ≤ x < 1
0%
x > 0
0%
x ≥ 0

0%
0%
2)
0%
0%
None of these

If x² + y² = t + 1/t and x⁴ + y⁴ = t² + 1/t², then dy/dx is equal to

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y/x
0%
– (y/x)
0%
x/y
0%
– (x/y)

If y = log x^x, then the value of dy/dx is

0%
xx (1 + log x)
0%
log (ex)
0%
log (e/x)
0%
log (x/e)

0%
0%
2)
0%
0%
x

If y = sin[cos^–1 {sin (cos^–1 x)}], then dy/dx at x = 1/2 equal to

0%
0
0%
–1
0%
2/√3
0%
1/√3
0%
1

If x² + y² = t – 1/t and x⁴ + y⁴ = t² + 1/t², then dy/dx is equal to

0%
0%
2)
0%
0%
0%

If f(x) = (x – 7)² (x – 2)⁷, x ϵ [2, 7]. Then, the value of θ ϵ (2,such that f '(θ) = 0 is

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49/4
0%
53/9
0%
53/7
0%
49/9
0%
45/7

If 2 f(x) = f '(x) and f(= 3, then f(is equal to

0%
3 e4
0%
3 e2
0%
e4
0%
None of these

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