# Permutations and Combinations · Mathematics · JEE Advanced

Start Practice## Numerical

JEE Advanced 2024 Paper 2 Online

If $n(X)={ }^m C_6$, then the value of $m$ is _____

JEE Advanced 2024 Paper 2 Online

If the value of $n(Y)+n(Z)$ is $k^2$, then $|k|$ is _________.

JEE Advanced 2024 Paper 1 Online

A group of 9 students, $s_1, s_2, \ldots, s_9$, is to be divided to form three teams $X, Y$, and $Z$ of sizes 2,3 , and 4 , respectively. Suppose that...

JEE Advanced 2022 Paper 1 Online

The number of 4-digit integers in the closed interval [2022, 4482] formed by using the digits $$0,2,3,4,6,7$$ is _________.

JEE Advanced 2020 Paper 2 Offline

An engineer is required to visit a factory for exactly four days during the first 15 days of every month and it is mandatory that no two visits take p...

JEE Advanced 2020 Paper 2 Offline

In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least ...

JEE Advanced 2019 Paper 2 Offline

Let |X| denote the number of elements in a set X. Let S = {1, 2, 3, 4, 5, 6} be a sample space, where each element is equally likely to occur. If A an...

JEE Advanced 2019 Paper 2 Offline

Five persons A, B, C, D and E are seated in a circular arrangement. If each of them is given a hat of one of the three colours red, blue and green, th...

JEE Advanced 2018 Paper 1 Offline

The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of digits is allowed, is ............

JEE Advanced 2017 Paper 1 Offline

Words of length 10 are formed using the letters A, B, C, D, E, F, G, H, I, J. Let x be the number of such words where no letter is repeated; and let y...

JEE Advanced 2015 Paper 1 Offline

Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m ...

JEE Advanced 2014 Paper 1 Offline

Let $${n \ge 2}$$ be an integer. Take n distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining ev...

JEE Advanced 2014 Paper 1 Offline

Let $${n_1}\, < {n_2}\, < \,{n_3}\, < \,{n_4}\, < {n_5}$$ be positive integers such that $${n_1}\, + {n_2}\, + \,{n_3}\, + \,{n_4}\, + {n_...

JEE Advanced 2013 Paper 1 Offline

Consider the set of eight vectors $$V = \left\{ {a\,\hat i + b\,\hat j + c\hat k:a,\,b,\,c\, \in \left\{ { - 1,\,1} \right\}} \right\}$$. Three non-co...

IIT-JEE 2009 Paper 2 Offline

Let $$\left( {x,\,y,\,z} \right)$$ be points with integer coordinates satisfying the system of homogeneous equation:
$$$\matrix{
{3x - y - z = 0} ...

## MCQ (Single Correct Answer)

JEE Advanced 2022 Paper 2 Online

Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls...

JEE Advanced 2018 Paper 2 Offline

In a high school, a committee has to be formed from a group of 6 boys M1, M2, M3, M4, M5, M6 and 5 girls G1, G2, G3, G4, G5.(i) Let $$\alpha $$1 be th...

JEE Advanced 2016 Paper 1 Offline

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be select from this club including the selection of a captain (from among thes...

JEE Advanced 2014 Paper 2 Offline

Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and ...

IIT-JEE 2012 Paper 2 Offline

Let $${{a_n}}$$ denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0.Le...

IIT-JEE 2012 Paper 2 Offline

Let $${{a_n}}$$ denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0.Le...

IIT-JEE 2012 Paper 1 Offline

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is

IIT-JEE 2009 Paper 1 Offline

The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is

IIT-JEE 2008 Paper 2 Offline

Consider all possible permutations of the letters of the word ENDEANOEL. Match the Statements/Expressions in Column I with the Statements/Expressions ...

IIT-JEE 2007

The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of ...

IIT-JEE 2005 Screening

A rectangle with sides of lenght (2m - 1) and (2n - 1) units is divided into squares of unit lenght by drawing parallel lines as shown in the diagram,...

IIT-JEE 2005 Screening

If the LCM of p, q is $${r^2}\,{r^4}\,{s^2}$$, where r, s, t are prime numbers and p, q are the positive integers then number of ordered pair (p, q) i...

IIT-JEE 2002 Screening

The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently is

IIT-JEE 2001 Screening

Let $${T_n}$$ denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If $${T_{n + 1}} - {T_n} = 21$$, ...

IIT-JEE 2000 Screening

How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions?

IIT-JEE 1989

A five-digit numbers divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be d...

IIT-JEE 1982

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the numbers of words which have at l...

IIT-JEE 1982

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs mar...

IIT-JEE 1982

The value of the expression $$\,{}^{47}{C_4} + \sum\limits_{j = 1}^5 {^{52 - j}\,{C_3}} $$ is equal to

IIT-JEE 1979

$${}^n{C_{r - 1}} = 36,{}^n{C_r} = 84\,\,and\,\,{}^n{C_{r + 1}} = 126$$, then r is :

## MCQ (More than One Correct Answer)

JEE Advanced 2021 Paper 2 Online

Let $${S_1} = \left\{ {(i,j,k):i,j,k \in \{ 1,2,....,10\} } \right\}$$,$${S_2} = \left\{ {(i,j):1 \le i < j + 2 \le 10,i,j \in \{ 1,2,...,10\} } \r...

IIT-JEE 1998

An n-digit number is a positive number with exactly digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5 an...

## Subjective

IIT-JEE 2005

If total number of runs scored in n matches is $$\left( {{{n + 1} \over 4}} \right)\,\,({2^{n + 1}} - n - 2)\,$$ where $$n > 1$$, and the runs scor...

IIT-JEE 2004

Prove by permulation or otherwise $${{({n^2})!} \over {{{(n!)}^n}}}$$ is an integer $$(n \in {1^ + })$$.

IIT-JEE 1994

A committee of 12 is to be formed from 9 women and 8 men. In how many ways this can be done if at least five women have to included in a committee? In...

IIT-JEE 1991

Eighteen guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on ...

IIT-JEE 1986

A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black bal...

IIT-JEE 1985

7 relatives of a man comprises 4 ladies and 3 gentlemen ; his wife has also 7 relatives ; 3 of them are ladies and 4 gentlemen. In how many ways can t...

IIT-JEE 1983

m men and n women are to be seated in a row so that no two women sit together. If $$m > n$$, then show that the number of ways in which they can be...

IIT-JEE 1981

Five balls of different colours are to be placed in there boxes of different size. Each box can hold all five. In how many different ways can be place...

IIT-JEE 1978

Six X' s have to be placed in the squares of figure below in such a way that each row contains at least one X. In how many different ways can this be ...

## Fill in the Blanks

IIT-JEE 1988

Total number of ways in which six ' + ' and four ' - ' signs can be arranged in a line such that no two ' - ' signs occur together is....................

IIT-JEE 1988

There are four balls of different colours and four boxes of colours, same as those of the balls. The number of ways in which the balls, one each in a ...

IIT-JEE 1984

The side AB, BC and CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. The number of triangles that can be constructed using t...

IIT-JEE 1982

In a certain test, $${a_i}$$ students gave wrong answers to atleast i questions, where i = 1, 2,..., k. No student gave more than k wrong answers. Th...

## True or False

IIT-JEE 1985

The product of any r consecutive natural numbers is always divisible by r!