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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
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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 2018

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 1 | Question 46

Calculus

MSQ2 marks

Let

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

be defined as follows:

f(x) = \left(\frac{|x|}{2} - x\right)\left(x - \frac{|x|}{2}\right)

Which of the following statements is/are true?

One or more correct

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

GATE CSE 2026 | Set 2 | Question 27

Calculus

MSQ1 mark

For a real number

a

, let

I(a) = \int_{-1}^{1} (3x^2 - ax + 1)\, dx

. Which of the following statements is/are true?

One or more correct

Source: GATE CSE 2026 Set 2 (CS2), 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 2025 | Set 2 | Question 12

Calculus

MCQ1 mark

The value of

x

such that

x > 1

, satisfying the equation

\displaystyle\int_1^x t \ln t\, dt = \frac{1}{4}

Single correct

Source: GATE CSE 2025 Set 2 (CS2), IIT Roorkee. Official question paper.

GATE CSE 2024 | Set 1 | Question 11

Calculus

MCQ1 mark

Let

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

be a function such that

f(x) = \max\{x, x^3\}

x \in \mathbb{R}

, where

\mathbb{R}

is the set of all real numbers. The set of all points where

f(x)

is NOT differentiable is

Single correct

Source: GATE CSE 2024 Set 1 (CS1), IISc Bengaluru. Official question paper.

GATE CSE 2024 | Set 2 | Question 16

Calculus

MCQ1 mark

Let

f(x)

be a continuous function from

\mathbb{R}

\mathbb{R}

such that

f(x) = 1 - f(2 - x)

Which one of the following options is the CORRECT value of

\int_0^2 f(x)\,dx

Single correct

Source: GATE CSE 2024 Set 2 (CS2), IISc Bengaluru. Official question paper.

GATE CSE 2023 | Question 28

Calculus

MSQ1 mark

Let

f(x) = x^3 + 15x^2 - 33x - 36

be a real-valued function. Which of the following statements is/are TRUE?

One or more correct

Answer key coming soon

Source: GATE CSE 2023, IIT Kanpur. 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 2020 | Question 1

Calculus

MCQ1 mark

Consider the functions I.

e^{-x}

II.

x^2 - \sin x

III.

\sqrt{x^3 + 1}

Which of the above functions is/are increasing everywhere in

[0,1]

Single correct

Answer key coming soon

Source: GATE CSE 2020, IIT Delhi. Official question paper.

GATE CSE 2019 | Question 13

Calculus

MCQ1 mark

Compute

\displaystyle\lim_{x \to 3} \frac{x^4 - 81}{2x^2 - 5x - 3}

Single correct

Source: GATE CSE 2019, IIT Madras. Official question paper and answer key.

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 2017 | Set 1 | Question 28

Calculus

MCQ2 marks

The value of

\displaystyle\lim_{x \to 1} \frac{x^7 - 2x^5 + 1}{x^3 - 3x^2 + 2}

Single correct

Answer key coming soon

Source: GATE CSE 2017 Set 1, IIT Roorkee. Official question paper.

GATE CSE 2017 | Set 2 | Question 10

Calculus

MCQ1 mark

f(x) = R \sin\left(\frac{\pi x}{2}\right) + S

f'\left(\frac{1}{2}\right) = \sqrt{2}

and

\int_0^1 f(x)\, dx = \frac{2R}{\pi}

, then the constants

R

and

S

are, respectively

Single correct

Answer key coming soon

Source: GATE CSE 2017 Set 2, IIT Roorkee. Official question paper.

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.

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