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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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214
Total Questions
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2
Easy
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208
Medium
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4
Hard
Practice by Exam:Mathematics(210)Physics(4)

About Calculus — practice questions, PYQs & concepts

Calculus is a frequently-tested topic on Mathematics, Physics. ExamTest.live currently lists 214 Calculus questions spanning previous-year papers from 2004 to 2026, each with worked solutions and a step-by-step explanation. Use the filters on this page to focus on a specific exam, difficulty level or year — every answer key is free, no sign-up required.

Calculus weight in competitive exams

Across our Calculus question bank, the largest sources are Mathematics (210) and Physics (4). Click any exam chip above to drill down to that exam-specific question set.

How to use this page

  • Start easy: 2 easy Calculus questions are available — build fluency before moving up.
  • Target weak years: Use the year filter to focus on the most recent 2026 paper or older PYQs you have not attempted.
  • Time yourself: Every question shows the average solve time so you can benchmark your speed against other students.
  • Read every explanation: Even on questions you got right — the explanation often surfaces a faster approach you can reuse.

All Calculus Questions(1–100 of 214)

3 pages
Filter:
Q1mediummcqMathematicsMathematics Mock Test - 62026
11% accuracy
The value of is equal to:
Q2mediummcqMathematicsMathematics Mock Test - 62026
7% accuracy
At which point does the line touch the curve ?
Q3mediummcqMathematicsMathematics Mock Test - 62026
19% accuracy
The value of in satisfying the Mean Value Theorem for the function is equal to:
Q4mediummcqMathematicsMathematics Mock Test - 62026
11% accuracy
What is the solution of the differential equation ?
Q5mediummcqMathematicsMathematics Mock Test - 62026
11% accuracy
The solution of the differential equation is:
Q6mediummcqMathematicsMathematics Mock Test - 62026
15% accuracy
The function is monotonically decreasing for:
Q7mediummcqMathematicsMathematics Mock Test - 62026
4% accuracy
If is continuous at , then the value of is:
Q8mediummcqMathematicsMathematics Mock Test - 62026
15% accuracy
If , then the derivative of the composite function is equal to:
Q9mediummcqMathematicsMathematics Mock Test - 62026
19% accuracy
The value of the integral is:
Q10mediummcqMathematicsMathematics Mock Test - 62026
11% accuracy
The sum of two numbers is fixed. Their product is maximum when:
Q11mediummcqMathematicsMathematics Mock Test - 12026
8% accuracy
For the function , the value of for Lagrange's Mean Value Theorem is:
Q12mediummcqMathematicsMathematics Mock Test - 102026
17% accuracy
If , then at is:
Q13mediummcqMathematicsMathematics Mock Test - 12026
17% accuracy
The value of ' ' in Rolle's Theorem for the function on the interval is:
Q14mediummcqMathematicsMathematics Mock Test - 102026
25% accuracy
The critical points of the function are:
Q15mediummcqMathematicsMathematics Mock Test - 102026
8% accuracy
For the function , the area formed by the tangent to the curve at with the coordinate axes is:
Q16mediummcqMathematicsMathematics Mock Test - 102026
8% accuracy
Complete solution set of is given by:
Q17mediummcqMathematicsMathematics Mock Test - 102026
8% accuracy
For the function , has:
Q18mediummcqMathematicsMathematics Mock Test - 102026
25% accuracy
The maximum value of the function is:
Q19mediummcqMathematicsMathematics Mock Test - 102026
8% accuracy
The normal to the curve at meets the curve again at two points and . The length of the line segment is:
Q20mediummcqMathematicsMathematics Mock Test - 102026
8% accuracy
If , then at is:
Q21mediummcqMathematicsMathematics Mock Test - 102026
0% accuracy
The value of so that decreases for all real values of is given by:
Q22mediummcqMathematicsMathematics Mock Test - 102026
8% accuracy
If , then the value of is:
Q23mediummcqMathematicsMathematics Mock Test - 102026
17% accuracy
If , then the value of at is:
Q24mediummcqMathematicsMathematics Mock Test - 102026
0% accuracy
A function satisfies the equation for all ; . Suppose that the function is differentiable at and . If , then the value of is:
Q25mediummcqMathematicsMathematics Mock Test - 102026
0% accuracy
Let for every real number , where is the greatest integer less than or equal to . Then the value of is:
Q26easymcqMathematicsMathematics Mock Test - 102026
25% accuracy
The cost of a cricket ball is Rs 500. If the price remains constant, its marginal revenue in Rs will be:
Q27mediummcqMathematicsMathematics Mock Test - 102026
0% accuracy
The local maximum value of is:
Q28mediummcqMathematicsMathematics Mock Test - 102026
17% accuracy
is equal to:
Q29mediummcqMathematicsMathematics Mock Test - 102026
17% accuracy
The solution of is:
Q30mediummcqMathematicsMathematics Mock Test - 102026
0% accuracy
The integral is equal to:
Q31mediummcqMathematicsMathematics Mock Test - 102026
0% accuracy
Consider the function , where represents the greatest integer function. The function is decreasing in the interval:
Q32mediummcqMathematicsMathematics Mock Test - 102026
8% accuracy
The solution of the differential equation is:
Q33mediummcqMathematicsMathematics Mock Test - 102026
17% accuracy
The curves and intersect infinitely many times, forming bounded regions of equal areas. The area of one such region is:
Q34mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
Find the area bounded by the curves and .
Q35mediummcqMathematicsMathematics Mock Test - 52026
50% accuracy
If the tangent to the curve at a point is parallel to the line joining and , then:
Q36mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
The function , attains minimum value at:
Q37mediummcqMathematicsMathematics Mock Test - 52026
50% accuracy
If has critical points at and , then the values of the constants and are respectively:
Q38mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
If at a point on the curve the slope of the line tangent to the curve is equal to , then the function is:
Q39mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
Derivative of w.r.t. is:
Q40mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
is equal to:
Q41mediummcqMathematicsMathematics Mock Test - 52026
100% accuracy
Q42mediummcqMathematicsMathematics Mock Test - 52026
50% accuracy
The area under the curve and the lines and the -axis is:
Q43mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
If is an increasing function and is a decreasing function, then which of the following is correct for the real values and ? Given that for these values of , both functions are defined.
Q44mediummcqMathematicsMathematics Mock Test - 52026
50% accuracy
The value of is:
Q45mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
The normal to the curve at the point where the curve intersects the -axis passes through the point:
Q46mediummcqMathematicsMathematics Mock Test - 52026
50% accuracy
Find the area between the curve and the -axis from to .
Q47mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
Q48mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
Let the function be continuous on and differentiable on . If and for all , then for all such functions , lies in the interval:
Q49mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
The function has:
Q50mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
What is the area bound by the curve , -axis and the ordinates and where ?
Q51mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
The minimum area bounded by circle and straight line is:
Q52mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
If the slope of the tangent to curve at a point is equal to the ordinate of the point, then the point is:
Q53mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Area bounded by the region is:
Q54mediummcqMathematicsAIEEE 20072026
0% accuracy
The area enclosed between the curves and is:
image
Q55mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
For a certain curve satisfying , has a local minimum value when . The global maximum value of if , is:
Q56mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
The value of in Lagrange's theorem for the function in the interval is:
Q57mediummcqMathematicsAIEEE 20062026
0% accuracy
The value of the integral is:
Q58mediummcqMathematicsAIEEE 20062026
0% accuracy
The value of , where denotes the greatest integer not exceeding , is:
Q59mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Extract all possible values of for which the function has local maxima at :
Q60mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Let , and , then is:
Q61mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
A manufacturing firm has its variable cost given by . The price per unit is . Find the marginal revenue when units were in demand.
Q62mediummcqMathematicsAIEEE 20062026
0% accuracy
A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length . The maximum area enclosed by the park is:
Q63mediummcqMathematicsAIEEE 20062026
0% accuracy
is equal to:
Q64mediummcqMathematicsAIEEE 20062026
0% accuracy
If , then is:
Q65mediummcqMathematicsAIEEE 20062026
0% accuracy
The function has a local minimum at:
Q66mediummcqMathematicsAIEEE 20062026
0% accuracy
The set of points where is differentiable is:
Q67mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
If , then the value of is equal to:
Q68mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Let be the inverse of an invertible function which is differentiable at , then equals:
Q69mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Solve:
Q70mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
If the line is a tangent to the curve , then:
Q71mediummcqPhysicsAIEEE 20062026
0% accuracy
A particle located at at time , starts moving along the positive -direction with a velocity that varies as . The displacement of the particle varies with time as:
Q72mediummcqMathematicsAIEEE 20062026
0% accuracy
Angle between the tangents to the curve at the points and is:
Q73mediummcqMathematicsAIEEE 20062026
0% accuracy
The differential equation whose solution is , where and are arbitrary constants, is of:
Q74mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
Let . Then which of the following is correct?
Q75mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
If and are differentiable functions in satisfying , and , then for some :
Q76mediummcqMathematicsAIEEE 20062026
0% accuracy
is equal to (where denotes the greatest integer function):
Q77mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
Find the area of the region (in sq. units) bounded by the curve for .
Q78mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
What is the interval over which the function is increasing?
Q79mediummcqMathematicsAIEEE 20072026
0% accuracy
Let , where . Then equals:
Q80mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
A cricket bat manufacturing firm assesses its variable cost to be , where is the number of bats produced, and the fixed cost incurred on storage is . How many bats should be manufactured for the minimum total cost?
Q81mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
If , then the function is:
Q82mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
If , then find .
Q83mediummcqMathematicsAIEEE 20072026
0% accuracy
A value of for which the conclusion of Mean Value Theorem holds for the function on the interval is:
Q84mediummcqMathematicsAIEEE 20072026
0% accuracy
equals:
Q85mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
Find the area under the curve , bounded by the x-axis and the y-axis.
Q86mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
Let be a differentiable function such that and for all . If , then is equal to:
Q87mediummcqMathematicsMathematics Mock Test - 42026
100% accuracy
What is the area of one of the loops between the curve and the x-axis?
Q88mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
The area enclosed between the curves and is:
Q89mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
Let and . If , then equals:
Q90mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
Evaluate:
Q91mediummcqMathematicsAIEEE 20072026
0% accuracy
The solution for of the equation is:
Q92mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
Calculate the value of:
Q93mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
Correct evaluation of (where is an arbitrary constant) is:
Q94mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
If and , then the value of at is:
Q95mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
The maximum slope of the curve occurs at the point:
Q96mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
If , then:
Q97mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
A piecewise-defined function is defined as:

Where and are constants. If the function is continuous everywhere, what is the value of ?
Q98mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
If is tangent to the curve at , then:
Q99mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
The area bounded by the curve , and the line is . Then is:
Q100mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
A manufacturing company has its variable cost given by where is the number of quantities produced. The price per unit is . The ratio of marginal cost and marginal revenue when 5 units were both produced and in demand is:
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How many Calculus questions are on ExamTest.live?▼
We have 214 Calculus questions spread across 3 pages, covering easy, medium, and hard difficulty levels with detailed explanations.
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Which exams include Calculus questions?▼
Calculus questions are commonly asked in Mathematics, Physics. You can filter by exam using the links above.
How do I practice Calculus questions effectively?▼
Start with easy questions to build confidence, then tackle medium and hard ones. Use the filter buttons to sort by difficulty. Reveal the answer only after attempting each question, and read the explanation thoroughly.