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Previous year question hub

Calculus - Mathematics Previous Year Questions

Practice Calculus - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

1Papers
1Years
19Questions
1Topics

Calculus question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Calculus. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Not classified 19 100%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 19 100%

Subject weightage

Top subjects by unique question coverage.

Mathematics
19 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
19 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Differentiation
4 Qs
Limits Continuity And Differentiability
3 Qs
Differential Equations
3 Qs
Functions
2 Qs
Indefinite Integration
2 Qs
Application Of Derivatives
2 Qs
Definite Integration
2 Qs
Area Under The Curves
1 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

KCET 2026
19 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
KCET 2026202619View paper

Sample previous year questions

A varied preview from the papers represented in this selection, with every available option.

1
2026 · Mathematics · Calculus · Area Under The Curves
KCET 2026
The area of the region bounded by the curve $y^2 = x^3$, the $y$-axis and the lines $y = 1$ and $y = 8$ is
A
$\dfrac{155}{3}$ sq. units
B
$\dfrac{93}{5}$ sq. units
C
$93$ sq. units
D
$155$ sq. units
Open complete paper
2
2026 · Mathematics · Calculus · Functions
KCET 2026
$f(x) = (x-1)^2$ for $x \geq 1$, $g(x)$ is a function whose graph is the reflection of the graph of $f(x)$ in the line $y = x$, then $g(x)$ is
A
$-\sqrt{x} + 1$
B
$\sqrt{x} - 1$
C
$\sqrt{x} + 1$
D
$\sqrt{x - 1}$
Open complete paper
3
2026 · Mathematics · Calculus · Limits Continuity And Differentiability
KCET 2026
If $f(x) = \begin{cases} ax + 7 & \text{if } x < 1 \\ 3x - 1 & \text{if } x = 1 \\ \dfrac{b}{x + 3} & \text{if } x > 1 \end{cases}$ is continuous at $x = 1$, then
A
$a = -5, b = 2$
B
$a = -5, b = -2$
C
$a = 5, b = -2$
D
$a = -5, b = 8$
Open complete paper
4
2026 · Mathematics · Calculus · Indefinite Integration
KCET 2026
If '$n$' is a natural number, then $\int \dfrac{\sin^n x}{\cos^{n+2} x}\,dx = $
A
$\dfrac{\tan^{n-1} x}{n - 1} + C$
B
$\dfrac{\tan^n x}{n} + C$
C
$\dfrac{\tan^{n+2} x}{n + 2} + C$
D
$\dfrac{\tan^{n+1} x}{n + 1} + C$
Open complete paper
5
2026 · Mathematics · Calculus · Differentiation
KCET 2026
The second order derivative of $\cos^{-1}(4x^3 - 3x)$ with respect to $\cos^{-1}(2x^2 - 1)$, where $\dfrac{1}{2} < x < 1$ is
A
$0$
B
$-\dfrac{1}{\sqrt{1 - x^2}}$
C
$\dfrac{3}{2}$
D
$-\dfrac{3}{2}$
Open complete paper
6
2026 · Mathematics · Calculus · Differential Equations
KCET 2026
Sum of the squares of the order and degree (if defined) of a differential equation $2 y^{\prime}+\left(y^{\prime \prime}\right)^2=\sqrt{y^{\prime \prime}-3}$ is
A
$3$
B
$20$
C
$8$
D
$16$
Open complete paper