JEE Questions for Maths Differentiation Quiz 2 - MCQExams.com

The derivative of a^{sec x} with respect to a^{tan x} (a >is

0%
sec x asec x – tan x
0%
sin x a tan x – sec x
0%
sin x asec x – tan x
0%
a sec x – tan x

A value of x in the interval (1,such that f '(x) = 0 where f(x) = x³ – 3x² + 2x + 10 is

0%
0%
2)
0%
0%

0%
–1
0%
1
0%
2
0%
4

The derivative of log |x| is

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

0%
0%
2)
0%
0%
None of the above

If y = 2^{log x}, then dy/dx is equal to

0%
0%
2)
0%
0%

0%
a x
0%
a2 x2
0%
x/a
0%
x/2a
0%
2a

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

The differential coefficient of f(log x), where f(x) = log x, is

0%
0%
(x log x)–1
0%
0%
None of these

Derivative of log₁₀ x with respect to x² is

0%
2x2 loge 10
0%
2)
0%
0%
x2 loge 10

0%
1
0%
–1
0%
0
0%
2

If y is a function of x and log(x + y) = 2xy, then the value of y'(is

0%
1
0%
–1
0%
2
0%
0

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

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

0%
0%
2)
0%
0%

0%
22
0%
11
0%
0
0%
20
0%
None of these

0%
16/3
0%
32/3
0%
16√2/3
0%
32√2/3
0%
32(2)1/2/3

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

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

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

0%
0%
2)
0%
0%

0%
sin x
0%
– cos x
0%
cos x
0%
– sinx

0%
0%
2)
0%
0%

If y = logⁿ x, where logⁿ means log log log...(repeated n times), then x log x log² x log³ x ...log^n–1 x logⁿ x dy/dx is equal to

0%
log x
0%
x
0%
1/logx
0%
logn x

0%
1
0%
0
0%
0%
0%

If f(x) be a polynomial function of the second degree. If f(= f(–and a₁, a₂, a₃ are in AP, then f ' (a₁), f ' (a₂), f ' (a₃) are in

0%
AP
0%
GP
0%
HP
0%
None of these

If f(x) = cos x cos 2x cos 4x cos 8x cos 16x, then f '(π/is equal to

0%
√2
0%
1/√2
0%
0
0%
√3/2

0%
0
0%
1/2
0%
1
0%
2

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

If x^m yⁿ = (x + y)^m+n, then (dy/dx)_{x = 1, y =2} is equal to

0%
1/2
0%
2
0%
2m/n
0%
m/2n

If x = a (θ – sin θ) and y = a(1 – cos θ), then dy/dx is equal to

0%
cot θ/2
0%
tan θ/2
0%
1/2 cosec2 θ/2
0%
– (1/cosec2 θ/2

0%
sec2 x
0%
2)
0%
0%

0%
0%
2)
0%
0%

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

Suppose that f(x) is a differentiable function such that f '(x) is continuous f '(= 1 and f '' (does not exist. If g(x) = x f ' (x). Then,

0%
g'(does not exist
0%
g'(= 0
0%
g'(= 1
0%
g'(= 2

0%
0%
2)
0%
0%

If f be twice differentiable function satisfying f(= 1, f(= 4, f(= 9, then

0%
f '' (x) = 2, ∀ x ϵ R
0%
f ' (x) = 5 = f ''(x), for someone x ϵ (1,3)
0%
there exists atleast one x ϵ (1,such that f '' (x) = 2
0%
None of the above

If y = cos(3 cos^–1 x), then d³y/dx³ is equal to

0%
24
0%
27
0%
3 – 12 x2
0%
–24

0%
1/2
0%
2/3
0%
1/3
0%
2/5
0%
1/5

If x = a(1 + cos θ), y = a(θ + sin θ) , then d²y/ dx² at θ = π/2 is equal to

0%
– (1/a)
0%
1/a
0%
–1
0%
–2
0%
– (2/a)

0%
2/3
0%
3/2
0%
1/2
0%
1
0%
0

The second order derivative of a sin³ t with respect to a cos³ t and t = π/4 is

0%
2
0%
1/12a
0%
4√2/3a
0%
3a/4√2

If 8 f(x) + 6f(1/x) = x + 5 and y = x² f(x), then dy/dx at x = – 1 is equal to

0%
0
0%
1/14
0%
– (1/14)
0%
1

If f be a twice differentiable function such that f ' (x) = – f (x) and f ' (x) = g(x) .
If h ' (x) [f(x)² + g(x)²], h(= 8 and h(= 2, then h(is equal to

0%
1
0%
2
0%
3
0%
None of these

0%
0%
2)
0%
0%

0%
0
0%
2 ab
0%
ab (a + b)
0%
ab

0:0:1

Answered

Not Answered

Not Visited

Correct : 0

Incorrect : 0

Practice Maths Quiz Questions and Answers