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Previous year question hub

Functions - Calculus - Mathematics Previous Year Questions

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

15Papers
14Years
50Questions
1Topics

Functions question pattern

Every graph below is calculated only from this selection.

Questions by year

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

Difficulty distribution

How the classified questions are distributed by difficulty.

Not classified 50 100%

Question type distribution

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

Multiple Choices 49 98%
Subjective 1 2%

Subject weightage

Top subjects by unique question coverage.

Mathematics
50 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
50 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Functions
50 Qs

Paper coverage

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

WB JEE 2025
4 Qs
VITEEE 2025
2 Qs
WB JEE 2024
5 Qs
WB JEE 2023
1 Qs
WB JEE 2022
7 Qs
WB JEE 2021
5 Qs
WB JEE 2020
4 Qs
WB JEE 2019
3 Qs
WB JEE 2018
4 Qs
WB JEE 2017
2 Qs
WB JEE 2016
1 Qs
WB JEE 2011
3 Qs
WB JEE 2010
3 Qs
WB JEE 2009
2 Qs
WB JEE 2008
4 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
VITEEE 202520252View paper
WB JEE 202520254View paper
WB JEE 202420245View paper
WB JEE 202320231View paper
WB JEE 202220227View paper
WB JEE 202120215View paper
WB JEE 202020204View paper
WB JEE 201920193View paper
WB JEE 201820184View paper
WB JEE 201720172View paper
WB JEE 201620161View paper
WB JEE 201120113View paper
WB JEE 201020103View paper
WB JEE 200920092View paper
WB JEE 200820084View paper

All Functions previous year questions

Practice every matching question in batches of 20, with every available option.

1
2016 · Mathematics · Calculus · Functions
WB JEE 2016
Let f : X \(\to\) X be such that f [f(x)] = x, for all x\(\in\)X and X\(\subseteq\)R, then
A
f is one-to-one
B
f is onto
C
f is one-to-one but not onto
D
f is onto but not one-to-one
Open complete paper
2
2017 · Mathematics · Calculus · Functions
WB JEE 2017
Let \(f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 19\). Then, f(x) = 0 has
A
13 real roots
B
only one positive and only two negative real roots
C
not more than one real root
D
has two positive nd one negative real rot
Open complete paper
3
2017 · Mathematics · Calculus · Functions
WB JEE 2017
Let \(f:R \to R\) be such that f is injective and \(f(x)f(y) = f(x + y)\) for \(\forall x,y \in R\). If f(x), f(y), f(z) are in G.P., then x, y, z are in
A
AP always
B
GP always
C
AP depending on the value of x, y, z
D
GP depending on the value of x, y, z
Open complete paper
4
2018 · Mathematics · Calculus · Functions
WB JEE 2018
The domain of definition of \(f(x) = \sqrt {{{1 - |x|} \over {2 - |x|}}}\) is
A
\(( - \infty , - 1) \cup (2,\infty )\)
B
\([ - 1,1] \cup (2,\infty ) \cup ( - \infty , - 2)\)
C
\(( - \infty ,1) \cup (2,\infty )\)
D
\([ - 1,1] \cup (2,\infty )\)

Here (a, b) \(\equiv\) {x : a < x < b} and [a, b] \(\equiv\) {x : a \(\le\) x \(\le\) b}
Open complete paper
5
2018 · Mathematics · Calculus · Functions
WB JEE 2018
Consider the function \(y = {\log _a}(x + \sqrt {{x^2} + 1} ),a > 0,a \ne 1\). The inverse of the function
A
does not exist
B
is \(x = {\log _{1/a}}(y + \sqrt {{y^2} + 1} )\)
C
is \(x = \sinh (y\log a)\)
D
is \(x = \cosh \left( { - y\log {1 \over a}} \right)\)
Open complete paper
6
2018 · Mathematics · Calculus · Functions
WB JEE 2018
If f : R \(\to\) R be defined by f (x) = ex and g : R \(\to\) R be defined by g(x) = x2. The mapping gof : R \(\to\) R be defined by (gof) (x) = g[f(x)] \(\forall\)x\(\in\)R. Then,
A
gof is bijective but f is not injective.
B
gof is injective but g is injective
C
gof is injective but g is not bijective
D
gof is surjective and g is surjective
Open complete paper
7
2018 · Mathematics · Calculus · Functions
WB JEE 2018
For 0 \(\le\) p \(\le\) 1 and for any positive a, b; let I(p) = (a + b)p, J(p) = ap + bp, then
A
I(p) > J(p)
B
I(p) \(\le\) J(p)
C
I(p) < J(p) in \(\left[ {0,{p \over 2}} \right]\) and I(p) > J(p) in \(\left[ {{p \over 2},\infty } \right]\)
D
I(p) < J(p) in \(\left[ {{p \over 2},\infty } \right]\) and I(p) > J(p) in \(\left[ {0,{p \over 2}} \right]\)
Open complete paper
8
2019 · Mathematics · Calculus · Functions
WB JEE 2019
Let a > b > 0 and I(n) = a1/n \(-\) b1/n, J(n) = (a \(-\) b)1/n for all n \(\ge\) 2, then
A
I(n) < J(n)
B
I(n) > J(n)
C
I(n) = J(n)
D
I(n) + J(n) = 0
Open complete paper
9
2019 · Mathematics · Calculus · Functions
WB JEE 2019
Consider the function f(x) = cos x2. Then,
A
f is of period 2\(\pi\)
B
f is of period \(\sqrt {2\pi }\)
C
f is not periodic
D
f is of period \(\pi\)
Open complete paper
10
2019 · Mathematics · Calculus · Functions
WB JEE 2019
Let \(f:R \to R\) be defined by \(f(x) = {x^2} - {{{x^2}} \over {1 + {x^2}}}\) for all \(x \in R\). Then,
A
f is one-one but not onto mapping
B
f is onto but not one-one mapping
C
f is both one-one and onto
D
f is neither one-one nor onto
Open complete paper
11
2020 · Mathematics · Calculus · Functions
WB JEE 2020
Let \(f(x) = \sqrt {{x^2} - 3x + 2}\) and \(g(x) = \sqrt x\) be two given functions. If S be the domain of fog and T be the domain of gof, then
A
S = T
B
S \(\cap\) T = \(\phi\)
C
S \(\cap\) T is a singleton
D
S \(\cap\) T is an interval
Open complete paper
12
2020 · Mathematics · Calculus · Functions
WB JEE 2020
The domain of \(f(x) = \sqrt {\left( {{1 \over {\sqrt x }} - \sqrt {x + 1} } \right)}\) is
A
\(x > - 1\)
B
\(( - 1,\infty )\backslash \{ 0\}\)
C
\(\left( {0,{{\sqrt 5 - 1} \over 2}} \right]\)
D
\(\left[ {{{1 - \sqrt 5 } \over 2},0} \right)\)
Open complete paper
13
2020 · Mathematics · Calculus · Functions
WB JEE 2020
Let \(f(x) = 1 - \sqrt {({x^2})}\), where the square root is to be taken positive, then
A
f has no extrema at x = 0
B
f has minima at x = 0
C
f has maxima at x = 0
D
f' exists at 0
Open complete paper
14
2020 · Mathematics · Calculus · Functions
WB JEE 2020
Let \(A = \{ x \in R: - 1 \le x \le 1\}\) and \(f:A \to A\) be a mapping defined by \(f(x) = x\left| x \right|\). Then f is
A
injective but not surjective
B
surjective but not injective
C
neither injective nor surjective
D
bijective
Open complete paper
15
2021 · Mathematics · Calculus · Functions
WB JEE 2021
f(x) is real valued function such that 2f(x) + 3f(\(-\)x) = 15 \(-\) 4x for all x\(\in\)R. Then f(2) =
A
\(-\)15
B
22
C
11
D
0
Open complete paper
16
2021 · Mathematics · Calculus · Functions
WB JEE 2021
Consider the functions f1(x) = x, f2(x) = 2 + loge x, x > 0. The graphs of the functions intersect
A
once in (0, 1) but never in (1, \(\infty\))
B
once in (0, 1) and once in (e2, \(\infty\))
C
once in (0, 1) and once in (e, e2)
D
more than twice in (0, \(\infty\))
Open complete paper
17
2021 · Mathematics · Calculus · Functions
WB JEE 2021
Let f : R \(\to\) R be given by f(x) = | x2 \(-\) 1 |, x\(\in\)R. Then,
A
f has a local minimum at x = \(\pm\) 1 but no local maximum.
B
f has a local minimum at x = 0 but no local minimum.
C
f has a local minima at x = \(\pm\) 1 and a local maxima at x = 0.
D
f has neither a local maxima nor a local minima at any point.
Open complete paper
18
2021 · Mathematics · Calculus · Functions
WB JEE 2021
Given that f : S \(\to\) R is said to have a fixed point at c of S if f(c) = c. Let f : [1, \(\infty\)) \(\to\) R be defined by f(x) = 1 + \(\sqrt x\). Then
A
f has no fixed point in [1, \(\infty\))
B
f has unique fixed point in [1, \(\infty\))
C
f has to fixed points in [1, \(\infty\))
D
f has infinitely many fixed points in [1, \(\infty\))
Open complete paper
19
2021 · Mathematics · Calculus · Functions
WB JEE 2021
Let f and g be periodic functions with the periods T1 and T2 respectively. Then f + g is
A
periodic with period T1 + T2
B
non periodic
C
periodic with the period T1
D
periodic when T1 = T2
Open complete paper
20
2022 · Mathematics · Calculus · Functions
WB JEE 2022

Domain of \(y = \sqrt {{{\log }_{10}}{{3x - {x^2}} \over 2}}\) is

A
x < 1
B
2 < x
C
1 \(\le\) x \(\le\) 2
D
2 < x < 3
Open complete paper

Showing 20 of 50 questions