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GATE CSE previous year questions · Engineering Mathematics

Calculus

39 questions

PYQ Hub · Previous year questions, organised for practice.Every question lists its source.

Calculus (Engineering Mathematics): GATE CSE PYQs | PYQ Hub

Programming & Data Structures195

Theory of Computation122

Compiler Design95

Computer Organization & Architecture131

Digital Logic91

Discrete Mathematics133

Engineering Mathematics139

General Aptitude260

Home
Previous Year
GATE
CSE
Engineering Mathematics
Calculus

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GATE CSE previous year questions · Engineering Mathematics

Calculus

39 questions

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2026 2025 2024 2023 2022 2021 2020 2019

GATE CSE 2026 | Set 1 | Question 32

Calculus

NAT1 mark

Consider the function

f: \mathbb{R} \to \mathbb{R}

defined as follows:

f(x) = \begin{cases} c_1 e^x - c_2 \log_e\left(\dfrac{1}{x}\right), & \text{if } x > 0 \\ 3 & \text{otherwise} \end{cases}

where

c_1, c_2 \in \mathbb{R}

. If

f

is continuous at

x = 0

, then

c_1 + c_2 =

_________. (*answer in integer*)

Numerical answer

Your answer

Source: GATE CSE 2026 Set 1 (CS1), IIT Guwahati. Official question paper.

GATE CSE 2026 | Set 2 | Question 64

Calculus

NAT2 marks

Consider a function

f: (0,1) \to \{0, 1\}

defined as follows. For a real number

r \in (0,1)

f(r) = 1

if the second digit after the decimal point in

r

is one of the four digits 2, 3, 6 and 7. Otherwise,

f(r)

is equal to 0. The number of points in

(0,1)

at which

f

is discontinuous is ___________. (*answer in integer*)

Numerical answer

Your answer

Source: GATE CSE 2026 Set 2 (CS2), IIT Guwahati. Official question paper.

GATE CSE 2025 | Set 1 | Question 31

Calculus

NAT1 mark

Consider the given function

f(x)

f(x) = \begin{cases} ax + b & \text{for } x < 1 \\ x^3 + x^2 + 1 & \text{for } x \ge 1 \end{cases}

If the function is differentiable everywhere, the value of

b

must be ________. (rounded off to one decimal place)

Numerical answer

Your answer

Source: GATE CSE 2025 Set 1 (CS1), IIT Roorkee. Official question paper.

GATE CSE 2023 | Question 31

Calculus

NAT1 mark

The value of the definite integral

\int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1} \left(4x^2 y - z^3\right) dz\, dy\, dx

is __________. (Rounded off to the nearest integer)

Numerical answer

Your answer

Answer key coming soon

Source: GATE CSE 2023, IIT Kanpur. Official question paper.

GATE CSE 2022 | Question 34

Calculus

NAT1 mark

The value of the following limit is __________

\lim_{x \to 0^+} \frac{\sqrt{x}}{1 - e^{2\sqrt{x}}}

Numerical answer

Your answer

Answer key coming soon

Source: GATE CSE 2022, IIT Kharagpur. Official question paper.

GATE CSE 2021 | Set 1 | Question 20

Calculus

NAT1 mark

Consider the following expression.

\lim_{x \to -3} \frac{\sqrt{2x + 22} - 4}{x + 3}

The value of the above expression (rounded to 2 decimal places) is __________.

Numerical answer

Your answer

Answer key coming soon

Source: GATE CSE 2021 Set 1 (CS1), IIT Bombay. Official question paper.

GATE CSE 2021 | Set 2 | Question 25

Calculus

NAT1 mark

Suppose that

f : \mathbb{R} \to \mathbb{R}

is a continuous function on the interval

[-3, 3]

and a differentiable function in the interval

(-3, 3)

such that for every

x

in the interval,

f'(x) \le 2

. If

f(-3) = 7

, then

f(3)

is at most __________.

Numerical answer

Your answer

Answer key coming soon

Source: GATE CSE 2021 Set 2 (CS2), IIT Bombay. Official question paper.

GATE CSE 2018 | Question 16

Calculus

NAT1 mark

The value of

\displaystyle\int_0^{\pi/4} x\cos(x^2)\,dx

correct to three decimal places (assuming that

\pi = 3.14

) is _____.

Numerical answer

Your answer

Source: GATE CSE 2018, IIT Guwahati. Official question paper and answer key.

GATE CSE 2016 | Set 1 | Question 3

Calculus

NAT1 mark

\lim_{x \to 4} \frac{\sin(x - 4)}{x - 4} = \underline{\qquad\qquad}.

Numerical answer

Your answer

Answer key coming soon

Source: GATE CSE 2016 Set 1, IISc Bengaluru. Official question paper.

GATE CSE 2016 | Set 2 | Question 2

Calculus

NAT1 mark

Let

f(x)

be a polynomial and

g(x) = f'(x)

be its derivative. If the degree of

(f(x) + f(-x))

is 10, then the degree of

(g(x) - g(-x))

is ________.

Numerical answer

Your answer

Answer key coming soon

Source: GATE CSE 2016 Set 2, IISc Bengaluru. Official question paper.

GATE CSE 2015 | Set 1 | Question 41

Calculus·Combinatorics

NAT2 marks

\displaystyle\sum_{x=1}^{99} \frac{1}{x(x+1)}

= _____.

Numerical answer

Your answer

Source: GATE CSE 2015 Set 1, IIT Kanpur. Official question paper and answer key.

GATE CSE 2015 | Set 1 | Question 58

Calculus

NAT2 marks

\displaystyle\int_{1/\pi}^{2/\pi} \frac{\cos(1/x)}{x^2}\,dx

= _____.

Numerical answer

Your answer

Source: GATE CSE 2015 Set 1, IIT Kanpur. Official question paper and answer key.

GATE CSE 2014 | Set 1 | Question 46

Calculus

NAT2 marks

The function

f(x) = x \sin x

satisfies the following equation:

f''(x) + f(x) + t\cos x = 0

. The value of

t

is _____.

Numerical answer

Your answer

Source: GATE CSE 2014 Set 1, IIT Kharagpur. Official question paper and answer key.

GATE CSE 2014 | Set 3 | Question 6

Calculus

NAT1 mark

\int_0^{2\pi} |x \sin x|\,dx = k\pi

, then the value of

k

is equal to _____.

Numerical answer

Your answer

Source: GATE CSE 2014 Set 3, IIT Kharagpur. Official question paper and answer key.

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