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ExamTest.live has 214+ Calculus questions with detailed explanations, covering easy, medium, and hard difficulty levels.

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Calculus Questions

Practice 214 Calculus questions with detailed answers and explanations. Free MCQs, PYQs, and mock test questions for NEET, JEE, GATE, SSC and more.

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Q201hardmcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026

The values of p and q for which the function f (x) = ⎩ ⎨ ⎧ \frac{s i n ( p + 1 ) x + s i n x}{x}, q, \frac{x + x ^{2} - x}{x ^{3/2}}, x < 0 x = 0 x > 0 is continuous for all x in R, are:

Q202mediummcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026

The area of the region enclosed by the curves y = x, x = e, y = 1/ x and the positive x -axis is:

Q203mediummcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026

For x \in (0, 5 π /2), define f (x) = \int_{0}^{x} t sin t d t . Then f has:

Q204mediummcqMathematicsAIEEE 20122026

If the integral \int \frac{5 t a n x}{t a n x - 2} d x = x + a ln ∣ sin x - 2 cos x ∣ + k, then a is equal to:

Q205mediummcqMathematicsAIEEE 20122026

The population p (t) at time t of a certain mouse species satisfies the differential equation \frac{d p ( t )}{d t} = 0.5 p (t) - 450 . If p (0) = 850, then the time at which the population becomes zero is:

Q206mediummcqMathematicsAIEEE 20122026

Let a, b \in R be such that the function f given by f (x) = ln ∣ x ∣ + b x^{2} + a x, x \neq = 0 has extreme values at x = - 1 and x = 2 .Statement 1: f has local maximum at x = - 1 and at x = 2 .Statement 2: a = \frac{1}{2} and b = - \frac{1}{4} .

Q207mediummcqMathematicsAIEEE 20122026

If f : R \to R is a function defined by f (x) = [x] cos (\frac{2 x - 1}{2} π), where [x] denotes the greatest integer function, then f is:

Q208mediummcqMathematicsAIEEE 20122026

If g (x) = \int_{0}^{x} cos^{4} t d t, then g (x + π) equals:

Q209mediummcqMathematicsAIEEE 20122026

Consider the function f (x) = ∣ x - 2∣ + ∣ x - 5∣, x \in R .Statement 1: f^{'} (4) = 0 Statement 2: f is continuous in [2, 5], differentiable in (2, 5) and f (2) = f (5) .

Q210mediummcqMathematicsAIEEE2026

Let f : R \to R be a continuous function defined by f (x) = \frac{1}{e ^{x} + 2 e ^{- x}} .Statement-1: f (c) = \frac{1}{3}, for some c \in R .Statement-2: 0 < f (x) \leq \frac{1}{2 2}, for all x \in R .

Q211hardmcqMathematicsAIEEE 20042004

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If x = e^{y + e^{y + ... t o \cdot \infty}}, x > 0 then \frac{d y}{d x} is

Q212mediummcqMathematicsAIEEE 20042004

0% accuracy

Let f (x) = \frac{1 - t a n x}{4 x - π}, x \neq = \frac{π}{4}, x \in [0, \frac{π}{2}] . If f (x) is continuous in [0, \frac{π}{2}], then f (\frac{π}{4}) is

Q213hardmcqMathematicsAIEEE 20042004

0% accuracy

A function y = f (x) has a second order derivative f^{''} (x) = 6 (x - 1) . If its graph passes through the point (2, 1) and at that point the tangent to the graph is y = 3 x - 5, then the function is

Q214easymcqPhysicsPhysics

The motion of a particle along a straight line is described by equation: x = 8 + 12 t - t^{3} where x is in metre and t in second. The retardation of the particle when its velocity becomes zero, is:

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Calculus questions are commonly asked in Mathematics, Physics. You can filter by exam using the links above.

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