Continuity and Differentiability
Class 12 · Mathematics
64 questions24 easy26 medium14 hard
Sample Questions
Q1.The derivative of (log x)² is:
- A2 log x
- B2(log x)/x
- C2/(x log x)
- D(log x)²/x
Q2.If y = sin⁻¹(x/a), then (a²–x²)y'' + xy' equals:
- A0
- B1
- Ca
- D–1
Q3.If x = sin t and y = sin(pt), then (1–x²)y'' – xy' + p²y equals:
- Ap²y
- B0
- Cp·y'
- D–p²y
Q4.Using MVT on f(x) = x³ on [0,1], the value of c is:
- A1/√3
- B1/3
- C1/2
- D√3/2
Q5.If y = sin⁻¹((1–x²)/(1+x²)), then dy/dx equals:
- A–2/(1+x²)
- B2/(1+x²)
- C–1/(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
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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