Calculus carries the largest share of marks in JEE Mathematics. This set covers the standard limits, continuity and differentiability, rules of differentiation, tangents and maxima and minima, standard integrals, definite integrals and the area between curves. Every answer comes with the working.
How to practise: read each question and tap the option you think is correct. You will see right away whether you got it, along with a short explanation, and your score is tracked at the bottom of the screen. This set has 15 questions.
Topics covered in this set
- Standard limits and the 1^∞ form
- Continuity and differentiability
- Product and chain rules, higher derivatives
- Tangents, maxima and minima, mean value theorems
- Standard and definite integrals
- Area between curves
JEE Mathematics MCQs with answers and explanations
Q1. What is lim(x→0) sin(3x)/x?
a) 0
b) 1/3
c) 1
d) 3
Q2. What is lim(x→0) (1 − cos x)/x²?
a) 2
b) 0
c) 1/2
d) 1
Q3. What is lim(x→∞) (1 + 2/x)ˣ?
a) 2
b) e²
c) 1
d) e
Q4. What is lim(x→2) (x² − 4)/(x − 2)?
a) 4
b) Does not exist
c) 2
d) 0
Q5. At x = 0, the function f(x) = |x| is:
a) Both continuous and differentiable
b) Neither continuous nor differentiable
c) Differentiable but not continuous
d) Continuous but not differentiable
Q6. What is d/dx (x² sin x)?
a) 2x sin x + x² cos x
b) x² cos x
c) 2x cos x
d) 2x sin x − x² cos x
Q7. What is d/dx ln(sin x)?
a) tan x
b) 1/sin x
c) cot x
d) cos x
Q8. If y = e^(2x), what is d²y/dx²?
a) e^(2x)
b) 2e^(2x)
c) 4xe^(2x)
d) 4e^(2x)
Q9. What is the slope of the tangent to y = x³ − 3x at x = 2?
a) 6
b) 12
c) 3
d) 9
Q10. What is the local maximum value of f(x) = x³ − 3x?
a) −2
b) 3
c) 2
d) 0
Q11. For f(x) = x² on [1, 3], at which c does Lagrange's Mean Value Theorem hold?
a) 1.5
b) 3
c) 2.5
d) 2
Q12. What is ∫ 1/(1 + x²) dx?
a) x/(1 + x²) + C
b) sin⁻¹ x + C
c) ln(1 + x²) + C
d) tan⁻¹ x + C
Q13. What is the value of ∫₀^π sin x dx?
a) 2
b) 1
c) 0
d) π
Q14. What is ∫₀^(π/2) sin² x dx?
a) 1
b) 1/2
c) π/2
d) π/4
Q15. What is the area enclosed between y = x and y = x²?
a) 1/6
b) 1/3
c) 1/2
d) 1
Quick revision notes
- sin x / x → 1, (1 − cos x)/x² → ½, (eˣ − 1)/x → 1.
- 1^∞ form: lim f^g = e^(lim g(f − 1)).
- Differentiable ⇒ continuous, not the reverse (|x| at 0).
- f′ = 0 and f″ < 0 ⇒ local maximum.
- Area between curves = ∫ (upper − lower) dx between intersection points.
Frequently asked questions
Are these JEE previous year questions?
No. They are original practice questions at the JEE Main level, with a few ideas used in JEE Advanced.
Which calculus topics carry the most marks?
Definite integration and its properties, application of derivatives and limits appear in almost every paper.
How do I handle the 1^∞ form quickly?
Use lim f(x)^g(x) = e^(lim g(x)·(f(x) − 1)). It solves most such questions in one line.
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