Continuity And Differentiability Mock Tests

25 questions available

Continuity And Differentiability Mock Test 1

Questions: 25

Sample Questions

Class 12 Mathematics

If y = eˣ sin x, then dy/dx is:

A eˣ(sin x + cos x)

B eˣ(sin x − cos x)

C eˣ sin x + cos x

D eˣ cos x

Class 12 Mathematics

The function f : R → R defined by f(x) = [x], where [x] is the greatest integer ≤ x, is:

A continuous everywhere

B continuous only at integer points

C continuous only at non-integer points

D neither continuous nor differentiable at any integer point

Class 12 Mathematics

If y = sin⁻¹(2x√(1 − x²)), then dy/dx equals:

A 2/√(1 − x²)

B 2/√(1 − 4x⁴)

C 1/√(1 − x²)

D −2/√(1 − x²)

Class 12 Mathematics

The function f(x) = |x − 3| cos x is:

A differentiable everywhere on R

B not differentiable at x = 0 only

C not differentiable at x = 3 only

D differentiable everywhere except at x = 0 and x = 3

CUET Mathematics

The function f(x) = |x − 2| is not differentiable at:

A x = 2

B x = 0

C x = 1

D x = −2

Class 12 Mathematics

The function f: R → R defined by f(x) = eˣ is:

A one-one and onto

B one-one but not onto

C onto but not one-one

D neither one-one nor onto

Class 12 Mathematics

If y = sin⁻¹(2x√(1 − x²)), then dy/dx at x = 0 is:

A 2

B π/2

C −2

D 1

Class 12 Mathematics

If y = eˣ · sin(x), then dy/dx is:

A eˣ(sin x + cos x)

B eˣ(sin x − cos x)

C eˣ · sin x

D eˣ · cos x

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