Take timed practice tests on Calculus Mixed Practice for JEE Main and JEE Advanced with session-wise drills, score review, and explanation-led revision.
Six 20-question timed sessions plus one 60-question module test. Each question is original and calibrated from the uploaded material pattern without copying PDF wording.
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1. ∫₀^(π/2) (sin x + cos x) dx equals:
Explanation: [−cos x + sin x]₀^(π/2) = (0 + 1) − (−1 + 0) = 1 + 1 = 2.
2. lim(x→0) (sin x − x)/x³ equals:
Explanation: Using L'Hôpital or Taylor series: sin x = x − x³/6 + ... → (sin x − x)/x³ → −x³/6 / x³ = −1/6.
3. The equation of the curve whose slope at (x,y) is 3x² and which passes through (1,2) is:
Explanation: dy/dx = 3x² → y = x³ + C. At (1,2): 2 = 1 + C → C = 1. Curve: y = x³ + 1.
4. The area bounded by y = x², y = 0, x = 1, x = 2 is:
Explanation: ∫₁² x² dx = [x³/3]₁² = 8/3 − 1/3 = 7/3.
5. If ∫₀^a x dx = ∫ₐ^1 x dx, then a equals:
Explanation: ∫₀^a x dx = a²/2. ∫ₐ^1 x dx = (1−a²)/2. Setting equal: a²/2 = (1−a²)/2 → a² = 1−a² → 2a² = 1 → a = 1/√2.
6. lim(x→∞) x sin(1/x) equals:
Explanation: Let t = 1/x → as x→∞, t→0. x sin(1/x) = sin(t)/t → 1 as t→0 (standard limit).