How many MCQ questions are available for Continuity and Differentiability?

There are 64 MCQ questions available for Continuity and Differentiability (Class 12 Mathematics) — 24 easy, 26 medium, and 14 hard.

Continuity and Differentiability

Q: What topics are covered in Continuity and Differentiability?

Key concepts covered: Algebra of continuous functions, Chain rule, Continuity at a point, Continuity on an interval, Derivatives of inverse trigonometric functions, Differentiability, Exponential and logarithmic functions, Logarithmic differentiation, Mean value theorem and Rolle's theorem, Parametric differentiation, Second order derivatives.

Class 12 · Mathematics

64 questions24 easy26 medium14 hard

Sample Questions

Q1.The function f(x) = |x| is:

AContinuous and differentiable everywhere
BContinuous everywhere but not differentiable at x = 0
CDiscontinuous at x = 0
DNot continuous for x < 0

Q2.Every differentiable function is:

ADiscontinuous
BNot necessarily continuous
CContinuous
DA polynomial

Q3.If y = xˣ, the derivative dy/dx equals:

Ax^x
Bx^x (1 + log x)
Cx · x^(x-1)
Dx^x · log x

Q4.The derivative of log(x) (natural logarithm) is:

A1/log(x)
Blog(x)/x
C1/x
Dx

Q5.The derivative of cos⁻¹(x) is:

A1/√(1–x²)
B–1/√(1–x²)
C1/√(1+x²)
D1/(1–x²)

Q6.This is a sample question to preview what you'll get in the full practice test...

A. Option one
B. Option two
C. Option three
D. Option four

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Concepts Covered

Algebra of continuous functionsChain ruleContinuity at a pointContinuity on an intervalDerivatives of inverse trigonometric functionsDifferentiabilityExponential and logarithmic functionsLogarithmic differentiationMean value theorem and Rolle's theoremParametric differentiationSecond order derivatives

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