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Previous year question hub

Limits Continuity And Differentiability - Calculus - Mathematics Previous Year Questions

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

15Papers
14Years
83Questions
1Topics

Limits Continuity And Differentiability question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Limits Continuity And Differentiability. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Not classified 83 100%

Question type distribution

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

Multiple Choices 79 95.2%
Subjective 4 4.8%

Subject weightage

Top subjects by unique question coverage.

Mathematics
83 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
83 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Limits Continuity And Differentiability
83 Qs

Paper coverage

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

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

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
VITEEE 202520251View paper
WB JEE 2025202510View paper
WB JEE 202420242View paper
WB JEE 202320236View paper
WB JEE 202220225View paper
WB JEE 202120215View paper
WB JEE 202020206View paper
WB JEE 201920198View paper
WB JEE 201820185View paper
WB JEE 201720176View paper
WB JEE 201620163View paper
WB JEE 201120118View paper
WB JEE 2010201010View paper
WB JEE 200920093View paper
WB JEE 200820085View paper

All Limits Continuity And Differentiability previous year questions

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

1
2016 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2016
\(\mathop {\lim }\limits_{x \to 1} {\left( {{{1 + x} \over {2 + x}}} \right)^{{{(1 - \sqrt x )} \over {(1 - x)}}}}\) is equal to
A
1
B
does not exist
C
\(\sqrt {{2 \over 3}}\)
D
2
Open complete paper
2
2016 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2016
If \(y = (1 + x)(1 + {x^2})(1 + {x^4})...(1 + {x^{2n}})\), then the value of \(\left( {{{dy} \over {dx}}} \right)\) at x = 0 is
A
0
B
\(-\)1
C
1
D
2
Open complete paper
3
2016 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2016
The value of

\(\mathop {\lim }\limits_{n \to \infty } \left\{ {{{\sqrt {n + 1} + \sqrt {n + 2} + ... + \sqrt {2n - 1} } \over {{n^{3/2}}}}} \right\}\) is
A
\({2 \over 3}(2\sqrt 2 - 1)\)
B
\({2 \over 3}(\sqrt 2 - 1)\)
C
\({2 \over 3}(\sqrt 2 + 1)\)
D
\({2 \over 3}(2\sqrt 2 + 1)\)
Open complete paper
4
2017 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2017
Let \(f(x) = \left\{ {\matrix{ \[{{{{x^p}} \over {{{(\sin x)}^q}}},} & {if\,0 < x \le {\pi \over 2}} \cr\] {0,} & {if\,x = 0} \cr } } \right.\), \((p,q \in R)\). Then, Lagrange's mean value theorem is applicable to f(x) in closed interval [0, x]
A
for all p, q
B
only when p > q
C
only when p < q
D
for no value of p, q
Open complete paper
5
2017 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2017
\(\mathop {\lim }\limits_{x \to 0} {(\sin x)^{2\tan x}}\) is equal to
A
2
B
1
C
0
D
does not exist
Open complete paper
6
2017 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2017
If f'' (0) = k, k \(\ne\) 0, then the value of

\(\mathop {\lim }\limits_{x \to 0} {{2f(x) - 3f(2x) + f(4x)} \over {{x^2}}}\) is
A
k
B
2k
C
3k
D
4k
Open complete paper
7
2017 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2017
Let f : R \(\to\) R be twice continuously differentiable. Let f(0) = f(1) = f'(0) = 0. Then,
A
f''(x) \(\ne\) 0 for all x
B
f''(c) = 0 for some c \(\in\) R
C
f''(x) \(\ne\) 0 if x \(\ne\) 0
D
f'(x) > 0 for all x
Open complete paper
8
2017 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2017
Let for all x > 0, \(f(x) = \mathop {\lim }\limits_{n \to \infty } n({x^{1/n}} - 1)\), then
A
\(f(x) + f\left( {{1 \over x}} \right) = 1\)
B
f(xy) = f(x) + f(y)
C
f(xy) = xf(y) + yf(x)
D
f(xy) = xf(x) + yf(y)
Open complete paper
9
2017 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2017
Consider the non-constant differentiable function f one one variable which obeys the relation \({{f(x)} \over {f(y)}} = f(x - y)\). If f' (0) = p and f' (5) = q, then f' (\(-\)5) is
A
\({{{p^2}} \over q}\)
B
\({q \over p}\)
C
\({p \over q}\)
D
q
Open complete paper
10
2018 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2018
Let f : [a, b] \(\to\) R be such that f is differentiable in (a, b), f is continuous at x = a and x = b and moreover f(a) = 0 = f(b). Then
A
there exists at least one point c in (a, b) such that f'(c) = f(c)
B
f'(x) = f(x) does not hold at any point in (a, b)
C
at every point of (a, b), f'(x) > f(x)
D
at every point of (a, b), f'(x) < f(x)
Open complete paper
11
2018 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2018
Let \(f(x) = 3{x^{10}} - 7{x^8} + 5{x^6} - 21{x^3} + 3{x^2} - 7\).

Then \(\mathop {\lim }\limits_{h \to 0} {{f(1 - h) - f(1)} \over {{h^3} + 3h}}\)
A
does not exist
B
is \({{50} \over 3}\)
C
is \({{53} \over 3}\)
D
is \({{22} \over 3}\)
Open complete paper
12
2018 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2018
Let f : [a, b] \(\to\) R be differentiable on [a, b] and k \(\in\) R. Let f(a) = 0 = f(b). Also let J(x) = f'(x) + kf(x). Then
A
J(x) > 0 for all x \(\in\) [a, b]
B
J(x) < 0 for all x \(\in\) [a, b]
C
J(x) = 0 has at least one root in (a, b)
D
J(x) = 0 through (a, b)
Open complete paper
13
2018 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2018
Let f : R \(\to\) R be a twice continuously differentiable function such that f(0) = f(1) = f'(0) = 0. Then
A
f''(0) = 0
B
f''(c) = 0 for some c\(\in\)R
C
if c \(\ne\) 0, then f''(c) \(\ne\) 0
D
f'(x) > 0 for all x \(\ne\) 0
Open complete paper
14
2018 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2018
Let \(f(x) = \left\{ {\matrix{ \[{ - 2\sin x,} & {if\,x \le - {\pi \over 2}} \cr\] \[{A\sin x + B,} & {if\, - {\pi \over 2} < x < {\pi \over 2}} \cr\] \[{\cos x} & {if\,x \ge {\pi \over 2}} \cr\] } } \right.\). Then,
A
f is discontinuous for all A and B
B
f is continuous for all A = \(-\) 1 and B = 1
C
f is continuous for all A = 1 and B = \(-\) 1
D
f is continuous for all real values of A, B
Open complete paper
15
2019 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2019
$$\mathop {\lim }\limits_{x \to {0^ + }} ({x^n}\ln x),\,n > 0$$
A
does not exist
B
exists and is zero
C
exists and is 1
D
exists and is e\(-\)1
Open complete paper
16
2019 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2019
The limit of the interior angle of a regular polygon of n sides as n \(\to\) \(\infty\) is
A
\(\pi\)
B
\({\pi \over 3}\)
C
\({3\pi \over 2}\)
D
\({2\pi \over 3}\)
Open complete paper
17
2019 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2019
A particle starts at the origin and moves 1 unit horizontally to the right and reaches P1, then it moves \({1 \over 2}\) unit vertically up and reaches P2, then it moves \({1 \over 4}\) unit horizontally to right and reaches P3, then it moves \({1 \over 8}\) unit vertically down and reaches P4, then it moves \({1 \over 16}\) unit horizontally to right and reaches P5 and so on. Let Pn = (xn, yn) and \(\mathop {\lim }\limits_{n \to \infty } {x_n} = \alpha\) and \(\mathop {\lim }\limits_{n \to \infty } {y_n} = \beta\). Then, (\(\alpha\), \(\beta\)) is
A
(2, 3)
B
\(\left( {{4 \over 3},{2 \over 5}} \right)\)
C
\(\left( {{2 \over 5},1} \right)\)
D
\(\left( {{4 \over 3},3} \right)\)
Open complete paper
18
2019 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2019
$$\mathop {\lim }\limits_{x \to {0^ + }} {({e^x} + x)^{1/x}}$$
A
Does not exist finitely
B
is 1
C
is e2
D
is 2
Open complete paper
19
2019 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2019
Let \(f:[1,3] \to R\) be a continuous function that is differentiable in (1, 3) an

f'(x) = | f(x) |2 + 4 for all x\(\in\) (1, 3). Then,
A
f(3) \(-\) f(1) = 5 is true
B
f(3) \(-\) f(1) = 5 is false
C
f(3) \(-\) f(1) = 7 is false
D
f(3) \(-\) f(1) > 0 only at one point of (1, 3)
Open complete paper
20
2019 · Mathematics · Calculus · Limits Continuity And Differentiability
WB JEE 2019
The value of \(\mathop {\lim }\limits_{x \to {0^ + }} {x \over p}\left[ {{q \over x}} \right]\) is
A
\({{[q]} \over p}\)
B
0
C
1
D
\(\infty\)
Open complete paper

Showing 20 of 83 questions