JEE Questions for Maths Differentiation Quiz 4 - MCQExams.com

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2 cos (x2)
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2 cos x
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2x cos x
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2x cos (x2)

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xx (1 + log x) + a . xa - 1
0%
xx (1 + log x) + a . xa - 1 + ax log a
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xx (1 + log x) + aa (1 + log a)
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xx (1 + log x) + aa (1 + log a) + axa - 1 + aa (1 + log a)

If y = cot^–1 (cos 2x)^1/2, then the value of dy/dx at x = π/6 will be

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(2/3)1/2
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(1/3)1/2
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(3)1/2
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(6)1/2

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0%
2)
0%
0%

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0%
2)
0%
0%

If x^y = y^x, then (x – y log x) dy/dx is equal to

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y (y – x log y)
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y(y + x log y)
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x(x + y log x)
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x(y – x log y)

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0%
2)
0%
0%

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0%
2)
0%
0%

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0%
2)
0%
0%

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0%
2)
0%
0%

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–1/4
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1/4
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–1/2
0%
1/2

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0%
2)
0%
0%

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0%
2)
0%
0%

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0%
2)
0%
0%

If y = (tan^–1 x)², then (x² +y₂ + 2x(x² + 1)y₁ is equal to

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4
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0
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2
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1

If x = sin t and y = tan t, then dy/dx is equal to

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cos3 t
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1/cos3 t
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1/cos2 t
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sin2 t
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1/sin2 t

If x = a cos³ θ and y = a sin³ θ, 1 + (dy/dx)² is equal to

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tan θ
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tan2 θ
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1
0%
sec2 θ
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sec θ

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– 2a2
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a2
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2a2
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0

If y = sec (tan^–1 x), then dy/dx at x = 1 is equal to

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1/√2
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1/2
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1
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√2

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1
0%
0
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2
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None of these

If f (x) = tan^–1 x, Then, f ' (x) + f ''(x) = 0, where x is equal to

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0
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1
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i
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–i

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n(n – 1)2n – 1
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(n –1)2n – 1
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n(n – 1)2n – 2
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n(n – 1)2n

y = e^{a sin^–1 x} ⇒ (1 – x²)y_n+2 – (2n + 1)xy_n+1 is equal to

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– (n2 + a2)yn
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(n2 – a2)yn
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(n2 + a2)yn
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–(n2 – a2)yn

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0%
2)
0%
0%

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0%
2)
0%
0%

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sin (loge x)
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cos (loge x)
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y2
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– y

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2)
0%
0%

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–5y
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5y
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25y
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–25y

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0%
2)
0%
0%

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1/4
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3/2
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1
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2/3
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2/3

If x = A cos 4t + b sin 4t, then d²x/dt² is equal to

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–16 x
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16 x
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x
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– x

If f : R → R is an even function which is twice differentiable on R and f ' (π) = 1, then f '' (–π) is equal to

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–1
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0
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1
0%
2

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I is correct but II is correct ?
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Both I and II are correct
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Neither I nor II is correct
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I is correct but II is correct

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0
0%
2
0%
0%

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1
0%
2
0%
3
0%
4

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sin u
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tan u
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cos u
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cot u

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2)
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0%

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0%
2)
0%
0%

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2)
0%
0%
None of these

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0%
2)
0%
0%
None of these

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0%
2)
0%
0%

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0%
2)
0%
1
0%
0

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0%
2)
0%
0%

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0%
2)
0%
0%
None of these

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0%
2)
0%
0%
None of these

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0%
2)
0%
0%

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0%
2)
0%
0%

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2)
0%
0%
None of these

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-2
0%
2
0%
0%
0

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0%
2)
0%
0%
None of these

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