Loading…

Questions and solutions are free, always.

Humaaans by Pablo Stanley · CC BY 4.0

Illustrations by Storyset and Open Doodles.

Practise

Practice
Revision queue
Take a test
Build a test

Browse

All topics
Physics
Chemistry
Mathematics

Account

Your numbers
Study plan
Saved
Plus

Skip to content

Workspace

Topic explorer

Practice
Revise
Tests
Topics
More
My progress Study plan Saved questions Printables Explore Plus

JEE MainQuestion bank

Your workspace

Take a testPlus

Your library

Saved questions

Your next exam

112days to go

JEE Main 2027, Session 1 · Estimated

Alror PlusExplore Plus ↗

About Alror ↗

Definite Integration — previous year questions · Alror

Topics/Mathematics

Mathematics

Definite Integration

Appeared 210 times across 21 years of JEE Main papers — about 10.0 questions a year. Every one of them is below, with a full worked solution.

Questions per year

6’02

6’03

5’04

5’05

3’06

3’07

1’09

1’10

1’11

1’13

1’14

1’15

4’16

4’17

5’18

22’19

17’20

42’21

31’22

24’23

27’24

210 questions in the bank

Practise this topic →

01Easy210×since 2002Q3386

\int\limits_{ - \pi }^\pi {\left| {\pi - \left| x \right|} \right|dx}

is equal to :

JEE Main 2020 · 3 Sep, Morning shift · Q3386·Definite Integration

02Easy210×since 2002Q3289

The value of

\mathop {\lim }\limits_{n \to \infty } {1 \over n}\sum\limits_{r = 0}^{2n - 1} {{{{n^2}} \over {{n^2} + 4{r^2}}}}

is :

JEE Main 2021 · 26 Aug, Morning shift · Q3289·Definite Integration

03Easy210×since 2002Q3279

\mathop {\lim }\limits_{n \to \infty } {{{1^p} + {2^p} + {3^p} + ..... + {n^p}} \over {{n^{p + 1}}}}

is

JEE Main 2002 · Annual, Paper 1 · Q3279·Definite Integration

04Easy210×since 2002Q3288

The value of

\mathop {\lim }\limits_{n \to \infty } {1 \over n}\sum\limits_{j = 1}^n {{{(2j - 1) + 8n} \over {(2j - 1) + 4n}}}

is equal to :

JEE Main 2021 · 27 Jul, Morning shift · Q3288·Definite Integration

05Medium210×since 2002Q3280

\mathop {\lim }\limits_{n \to \infty } {{1 + {2^4} + {3^4} + .... + {n^4}} \over {{n^5}}}

-

\mathop {\lim }\limits_{n \to \infty } {{1 + {2^3} + {3^3} + .... + {n^3}} \over {{n^5}}}

JEE Main 2003 · Annual, Paper 1 · Q3280·Definite Integration

06Easy210×since 2002Q3281

\mathop {Lim}\limits_{n \to \infty } \sum\limits_{r = 1}^n {{1 \over n}{e^{{r \over n}}}}

is

JEE Main 2004 · Annual, Paper 1 · Q3281·Definite Integration

07Medium210×since 2002Q3282

\mathop {\lim }\limits_{n \to \infty } \left[ {{1 \over {{n^2}}}{{\sec }^2}{1 \over {{n^2}}} + {2 \over {{n^2}}}{{\sec }^2}{4 \over {{n^2}}}.... + {1 \over n}{{\sec }^2}1} \right]

equals

JEE Main 2005 · Annual, Paper 1 · Q3282·Definite Integration

08Medium210×since 2002Q3283

\mathop {\lim }\limits_{n \to \infty } {\left( {{{\left( {n + 1} \right)\left( {n + 2} \right)...3n} \over {{n^{2n}}}}} \right)^{{1 \over n}}}

is equal to:

JEE Main 2016 · Session, Shift 1 · Q3283·Definite Integration

09Hard210×since 2002Q3284

If

\mathop {\lim }\limits_{n \to \infty } \,\,{{{1^a} + {2^a} + ...... + {n^a}} \over {{{(n + 1)}^{a - 1}}\left[ {\left( {na + 1} \right) + \left( {na + 2} \right) + ..... + \left( {na + n} \right)} \right]}} = {1 \over {60}}

for some positive real number a, then a is equal to :

JEE Main 2017 · 9 Apr, Morning shift · Q3284·Definite Integration

10Easy210×since 2002Q3285

\mathop {\lim }\limits_{x \to \infty } \left( {{n \over {{n^2} + {1^2}}} + {n \over {{n^2} + {2^2}}} + {n \over {{n^2} + {3^2}}} + ..... + {1 \over {5n}}} \right)

is equal to :

JEE Main 2019 · 12 Jan, Evening shift · Q3285·Definite Integration

11Medium210×since 2002Q3286

\mathop {\lim }\limits_{n \to \infty } \left( {{{{{(n + 1)}^{1/3}}} \over {{n^{4/3}}}} + {{{{(n + 2)}^{1/3}}} \over {{n^{4/3}}}} + ....... + {{{{(2n)}^{1/3}}} \over {{n^{4/3}}}}} \right)

is equal to :

JEE Main 2019 · 10 Apr, Morning shift · Q3286·Definite Integration

12Medium210×since 2002Q3287

\mathop {\lim }\limits_{n \to \infty } \left[ {{1 \over n} + {n \over {{{(n + 1)}^2}}} + {n \over {{{(n + 2)}^2}}} + ........ + {n \over {{{(2n + 1)}^2}}}} \right]

is equal to :

JEE Main 2021 · 25 Feb, Evening shift · Q3287·Definite Integration

13Medium210×since 2002Q3305

Let f : R

\to

R be a continuously differentiable function such that f(2) = 6 and f'(2) =

{1 \over {48}}

. If

\int\limits_6^{f\left( x \right)} {4{t^3}} dt

= (x - 2)g(x), then

\mathop {\lim }\limits_{x \to 2} g\left( x \right)

is equal to :

JEE Main 2019 · 12 Apr, Morning shift · Q3305·Definite Integration

14Medium210×since 2002Q3290

If

{U_n} = \left( {1 + {1 \over {{n^2}}}} \right)\left( {1 + {{{2^2}} \over {{n^2}}}} \right)^2.....\left( {1 + {{{n^2}} \over {{n^2}}}} \right)^n

, then

\mathop {\lim }\limits_{n \to \infty } {({U_n})^{{{ - 4} \over {{n^2}}}}}

is equal to :

JEE Main 2021 · 27 Aug, Morning shift · Q3290·Definite Integration

15Medium210×since 2002Q3291

\mathop {\lim }\limits_{n \to \infty } \left( {{{{n^2}} \over {({n^2} + 1)(n + 1)}} + {{{n^2}} \over {({n^2} + 4)(n + 2)}} + {{{n^2}} \over {({n^2} + 9)(n + 3)}} + \,\,....\,\, + \,\,{{{n^2}} \over {({n^2} + {n^2})(n + n)}}} \right)

is equal to :

JEE Main 2022 · 24 Jun, Evening shift · Q3291·Definite Integration

16Medium210×since 2002Q3292

\mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {{r \over {2{r^2} - 7rn + 6{n^2}}}}

is equal to :

JEE Main 2022 · 30 Jun, Morning shift · Q3292·Definite Integration

17Medium210×since 2002Q3293

\mathop {\lim }\limits_{n \to \infty } {1 \over {{2^n}}}\left( {{1 \over {\sqrt {1 - {1 \over {{2^n}}}} }} + {1 \over {\sqrt {1 - {2 \over {{2^n}}}} }} + {1 \over {\sqrt {1 - {3 \over {{2^n}}}} }} + \,\,...\,\, + \,\,{1 \over {\sqrt {1 - {{{2^n} - 1} \over {{2^n}}}} }}} \right)

is equal to

JEE Main 2022 · 25 Jul, Evening shift · Q3293·Definite Integration

18Medium210×since 2002Q3294

If

a = \mathop {\lim }\limits_{n \to \infty } \sum\limits_{k = 1}^n {{{2n} \over {{n^2} + {k^2}}}}

and

f(x) = \sqrt {{{1 - \cos x} \over {1 + \cos x}}}

,

x \in (0,1)

, then :

JEE Main 2022 · 26 Jul, Morning shift · Q3294·Definite Integration

19Easy210×since 2002Q3295

\mathop {\lim }\limits_{n \to \infty } \left[ {{1 \over {1 + n}} + {1 \over {2 + n}} + {1 \over {3 + n}}\, + \,...\, + \,{1 \over {2n}}} \right]

is equal to

JEE Main 2023 · 1 Feb, Morning shift · Q3295·Definite Integration

20Easy210×since 2002Q3296

\lim\limits_{n \rightarrow \infty} \frac{3}{n}\left\{4+\left(2+\frac{1}{n}\right)^2+\left(2+\frac{2}{n}\right)^2+\ldots+\left(3-\frac{1}{n}\right)^2\right\}

is equal to :

JEE Main 2023 · 30 Jan, Evening shift · Q3296·Definite Integration

Showing the first 20 of 210. Practise this topic to work through the rest.