Chapter Quizzes

NDA Calculus Practice Questions: Limits, Derivatives & Integrals

By SenaPrep Math Faculty July 13, 2026 9 min read

Calculus is the single highest-yielding block in Mathematics, accounting for 20 to 25 questions (approx. 50 to 62.5 marks). Master limits, differentiation, and integration to secure your selection.

Below is a preview of 5 high-yield Calculus questions. Study the step-by-step methods and formulas carefully.

Core Concept Shortcuts

L'Hopital's Rule: If $\lim_{x \to c} \frac{f(x)}{g(x)} = \frac{0}{0}$ or $\frac{\infty}{\infty}$, then the limit equals $\lim_{x \to c} \frac{f'(x)}{g'(x)}$, provided the derivatives exist.
Derivative: $\frac{d}{dx}(\sin^2 x) = 2\sin x\cos x = \sin 2x$.
Definite Integral: $\int_a^b f(x) dx = -\int_b^a f(x) dx$.

Interactive Practice Quiz

Test your preparation live! Choose an option for each question to see instant feedback and deep step-by-step explanations.

Question 1 of 10 Live App Practice

What is ∫₀¹ ln(1/x − 1) dx equal to?

Question 2 of 10 Live App Practice

What is the range of the function f(x) = l - sin x defined on entire real line?

Question 3 of 10 Live App Practice

Consider the following statements in respect of the function

f(x) = sin(1/x²), x ≠ 0 :

1. It is continuous at x = 0, if f(0) = 0.
2. It is continuous at x = 2/√π.

Which of the above statements is/are correct?

Question 4 of 10 Live App Practice

If f(x) = [x]/|x|, x ≠ 0 where [ ] denotes the greatest integer function, then what is the right-hand limit of f(x) at x = 1?

Question 5 of 10 Live App Practice

Consider the following statements in respect of
f(x) = |x| − 1 :

1. f(x) is continuous at x = 1.
2. f(x) is differentiable at x = 0.

Which of the above statements is/are correct?

Question 6 of 10 Live App Practice

Question 7 of 10 Live App Practice

What is lim(n→∞) (aⁿ + bⁿ)/(aⁿ − bⁿ) where a > b > 1, equal to?

Question 8 of 10 Live App Practice

Let f(x) be a polynomial function such that f(x) = x⁴. What is f′(1) equal to?

Question 9 of 10 Live App Practice

Question 10 of 10 Live App Practice

If y = (1 + x)(1 + x²)(1 + x⁴)(1 + x⁸)(1 + x¹⁶), then what is dy/dx at x = 0 equal to?

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Frequently Asked Questions

Which is more important: differential or integral calculus?

Both are equally important and deeply linked. Differential calculus contributes ~12 questions, and Integral calculus contributes ~10 questions in Paper 1.