# Permutations and Combinations · Mathematics · JEE Main

Start Practice## Numerical

JEE Main 2024 (Online) 9th April Evening Shift

Let $$A=\{(x, y): 2 x+3 y=23, x, y \in \mathbb{N}\}$$ and $$B=\{x:(x, y) \in A\}$$. Then the number of one-one functions from $$A$$ to $$B$$ is equal ...

JEE Main 2024 (Online) 9th April Evening Shift

The number of integers, between 100 and 1000 having the sum of their digits equals to 14 , is __________.

JEE Main 2024 (Online) 1st February Morning Shift

The number of elements in the set $\mathrm{S}=\{(x, y, z): x, y, z \in \mathbf{Z}, x+2 y+3 z=42, x, y, z \geqslant 0\}$ equals __________.

JEE Main 2024 (Online) 31st January Morning Shift

The total number of words (with or without meaning) that can be formed out of the letters of the word 'DISTRIBUTION' taken four at a time, is equal to...

JEE Main 2024 (Online) 30th January Evening Shift

In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : $$A, B$$ and $$C...

JEE Main 2024 (Online) 29th January Morning Shift

All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The ser...

JEE Main 2023 (Online) 15th April Morning Shift

A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the ...

JEE Main 2023 (Online) 13th April Evening Shift

Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits $$1,2,3,4,5$$ with repetition, is _________.

JEE Main 2023 (Online) 13th April Morning Shift

The number of seven digit positive integers formed using the digits $$1,2,3$$ and $$4$$ only and sum of the digits equal to $$12$$ is ___________....

JEE Main 2023 (Online) 12th April Morning Shift

Let the digits a, b, c be in A. P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are ...

JEE Main 2023 (Online) 11th April Morning Shift

In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sits on the ...

JEE Main 2023 (Online) 10th April Evening Shift

The sum of all the four-digit numbers that can be formed using all the digits 2, 1, 2, 3 is equal to __________.

JEE Main 2023 (Online) 10th April Morning Shift

The number of permutations, of the digits 1, 2, 3, ..., 7 without repetition, which neither contain the string 153 nor the string 2467, is ___________...

JEE Main 2023 (Online) 10th April Morning Shift

Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match, is 840, then ...

JEE Main 2023 (Online) 6th April Evening Shift

The number of 4-letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word ...

JEE Main 2023 (Online) 6th April Morning Shift

The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is ___________.

JEE Main 2023 (Online) 1st February Evening Shift

Number of integral solutions to the equation $$x+y+z=21$$, where $$x \ge 1,y\ge3,z\ge4$$, is equal to ____________.

JEE Main 2023 (Online) 1st February Evening Shift

The total number of six digit numbers, formed using the digits 4, 5, 9 only and divisible by 6, is ____________.

JEE Main 2023 (Online) 1st February Morning Shift

The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7, is ____________.

JEE Main 2023 (Online) 1st February Morning Shift

The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is...

JEE Main 2023 (Online) 31st January Evening Shift

Let $\mathrm{A}=\left[\mathrm{a}_{i j}\right], \mathrm{a}_{i j} \in \mathbb{Z} \cap[0,4], 1 \leq i, j \leq 2$.
The number of matrices A such that the ...

JEE Main 2023 (Online) 31st January Evening Shift

If ${ }^{2 n+1} \mathrm{P}_{n-1}:{ }^{2 n-1} \mathrm{P}_{n}=11: 21$,
then $n^{2}+n+15$ is equal to :

JEE Main 2023 (Online) 31st January Morning Shift

Let 5 digit numbers be constructed using the digits $$0,2,3,4,7,9$$ with repetition allowed, and are arranged in ascending order with serial numbers. ...

JEE Main 2023 (Online) 31st January Morning Shift

Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to ____________.

JEE Main 2023 (Online) 30th January Evening Shift

The number of seven digits odd numbers, that can
be formed using all theseven digits 1, 2, 2, 2, 3, 3,
5 is ____________.

JEE Main 2023 (Online) 30th January Morning Shift

Number of 4-digit numbers (the repetition of digits is allowed) which are made using the digits 1, 2, 3 and 5, and are divisible by 15, is equal to __...

JEE Main 2023 (Online) 29th January Evening Shift

The total number of 4-digit numbers whose greatest common divisor with 54 is 2, is __________.

JEE Main 2023 (Online) 29th January Morning Shift

If all the six digit numbers $$x_1\,x_2\,x_3\,x_4\,x_5\,x_6$$ with $$0...

JEE Main 2023 (Online) 29th January Morning Shift

Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are written in descending order with serial numbers. For example, th...

JEE Main 2023 (Online) 25th January Evening Shift

A triangle is formed by X-axis, Y-axis and the line $$3x+4y=60$$. Then the number of points P(a, b) which lie strictly inside the triangle, where a is...

JEE Main 2023 (Online) 25th January Evening Shift

Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, a...

JEE Main 2023 (Online) 25th January Morning Shift

Let $$x$$ and $$y$$ be distinct integers where $$1 \le x \le 25$$ and $$1 \le y \le 25$$. Then, the number of ways of choosing $$x$$ and $$y$$, such t...

JEE Main 2023 (Online) 24th January Morning Shift

A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. If he can choose at most two language cours...

JEE Main 2023 (Online) 24th January Morning Shift

The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is ___...

JEE Main 2022 (Online) 29th July Evening Shift

The number of natural numbers lying between 1012 and 23421 that can be formed using the digits $$2,3,4,5,6$$ (repetition of digits is not allowed) and...

JEE Main 2022 (Online) 29th July Morning Shift

The number of matrices of order $$3 \times 3$$, whose entries are either 0 or 1 and the sum of all the entries is a prime number, is __________....

JEE Main 2022 (Online) 28th July Evening Shift

A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168 , then $$\mathrm{b}+3 \mathrm{~g}$$ i...

JEE Main 2022 (Online) 28th July Morning Shift

Let $$S$$ be the set of all passwords which are six to eight characters long, where each character is either an alphabet from $$\{A, B, C, D, E\}$$ or...

JEE Main 2022 (Online) 26th July Evening Shift

Numbers are to be formed between 1000 and 3000 , which are divisible by 4 , using the digits $$1,2,3,4,5$$ and 6 without repetition of digits. Then th...

JEE Main 2022 (Online) 26th July Morning Shift

The number of 5-digit natural numbers, such that the product of their digits is 36 , is __________.

JEE Main 2022 (Online) 25th July Morning Shift

The letters of the word 'MANKIND' are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number ...

JEE Main 2022 (Online) 30th June Morning Shift

The number of 6-digit numbers made by using the digits 1, 2, 3, 4, 5, 6, 7, without repetition and which are multiple of 15 is ____________.

JEE Main 2022 (Online) 29th June Evening Shift

The total number of four digit numbers such that each of first three digits is divisible by the last digit, is equal to ____________.

JEE Main 2022 (Online) 29th June Morning Shift

Let b1b2b3b4 be a 4-element permutation with bi $$\in$$ {1, 2, 3, ........, 100} for 1 $$\le$$ i $$\le$$ 4 and bi $$\ne$$ bj for i $$\ne$$ j, such tha...

JEE Main 2022 (Online) 27th June Evening Shift

Let A be a matrix of order 2 $$\times$$ 2, whose entries are from the set {0, 1, 2, 3, 4, 5}. If the sum of all the entries of A is a prime number p, ...

JEE Main 2022 (Online) 27th June Morning Shift

The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should b...

JEE Main 2022 (Online) 26th June Evening Shift

The total number of 3-digit numbers, whose greatest common divisor with 36 is 2, is ___________.

JEE Main 2022 (Online) 26th June Morning Shift

There are ten boys B1, B2, ......., B10 and five girls G1, G2, ........, G5 in a class. Then the number of ways of forming a group consisting of three...

JEE Main 2022 (Online) 25th June Evening Shift

The total number of three-digit numbers, with one digit repeated exactly two times, is ______________.

JEE Main 2022 (Online) 25th June Morning Shift

The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is _____________.

JEE Main 2022 (Online) 25th June Morning Shift

Let A be a 3 $$\times$$ 3 matrix having entries from the set {$$-$$1, 0, 1}. The number of all such matrices A having sum of all the entries equal to ...

JEE Main 2022 (Online) 24th June Evening Shift

The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1, 2, 3, 4, 5, 7 and 9 is _____________.

JEE Main 2022 (Online) 24th June Morning Shift

In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks for each correct answe...

JEE Main 2021 (Online) 1st September Evening Shift

All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two R appearing together. The arrangements a...

JEE Main 2021 (Online) 31st August Morning Shift

The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come tog...

JEE Main 2021 (Online) 27th August Evening Shift

Let S = {1, 2, 3, 4, 5, 6, 9}. Then the number of elements in the set T = {A $$ \subseteq $$ S : A $$\ne$$ $$\phi$$ and the sum of all the elements of...

JEE Main 2021 (Online) 27th August Morning Shift

A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is a six digit palindrome. The number of six digi...

JEE Main 2021 (Online) 26th August Morning Shift

If $${}^1{P_1} + 2.{}^2{P_2} + 3.{}^3{P_3} + .... + 15.{}^{15}{P_{15}} = {}^q{P_r} - s,0 \le s \le 1$$, then $${}^{q + s}{C_{r - s}}$$ is equal to ___...

JEE Main 2021 (Online) 26th August Morning Shift

The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______________.

JEE Main 2021 (Online) 27th July Evening Shift

Let n be a non-negative integer. Then the number of divisors of the form "4n + 1" of the number (10)10 . (11)11 . (13)13 is equal to __________....

JEE Main 2021 (Online) 25th July Morning Shift

There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the number of ways, in which 10 students can be selected from ...

JEE Main 2021 (Online) 22th July Evening Shift

If the digits are not allowed to repeat in any number formed by using the digits 0, 2, 4, 6, 8, then the number of all numbers greater than 10,000 is ...

JEE Main 2021 (Online) 20th July Morning Shift

There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsman and 2 are wicketkeepers. The number of ways, a team of 11 players be...

JEE Main 2021 (Online) 18th March Evening Shift

If $$\sum\limits_{r = 1}^{10} {r!({r^3} + 6{r^2} + 2r + 5) = \alpha (11!)} $$, then the value of $$\alpha$$ is equal to ___________.

JEE Main 2021 (Online) 18th March Morning Shift

The number of times the digit 3 will be written when listing the integers from 1 to 1000 is :

JEE Main 2021 (Online) 18th March Morning Shift

The missing value in the following figure is ...

JEE Main 2021 (Online) 25th February Morning Shift

The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1, 2, 3, 4, 5, if the repetition of digits is not allowed a...

JEE Main 2021 (Online) 24th February Evening Shift

The students S1, S2, ....., S10 are to be divided into 3 groups A, B and C such that each group has at least one student and the group C has at most 3...

JEE Main 2020 (Online) 6th September Evening Slot

The number of words (with or without meaning)
that can be formed from all the letters of the
word “LETTER” in which vowels never come
together is ____...

JEE Main 2020 (Online) 5th September Morning Slot

Four fair dice are thrown independently 27 times. Then the expected number of times, at
least two dice show up a three or a five, is _________.

JEE Main 2020 (Online) 5th September Morning Slot

The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word ’SYLLABUS’ such that two l...

JEE Main 2020 (Online) 4th September Evening Slot

A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candida...

JEE Main 2020 (Online) 3rd September Evening Slot

The total number of 3-digit numbers, whose
sum of digits is 10, is __________.

JEE Main 2020 (Online) 2nd September Morning Slot

If the letters of the word 'MOTHER' be permuted
and all the words so formed (with or without
meaning) be listed as in a dictionary, then the
position ...

JEE Main 2020 (Online) 8th January Evening Slot

The number of 4 letter words (with or without
meaning) that can be formed from the eleven
letters of the word 'EXAMINATION' is
_______.

JEE Main 2020 (Online) 8th January Morning Slot

An urn contains 5 red marbles, 4 black marbles
and 3 white marbles. Then the number of ways
in which 4 marbles can be drawn so that at the
most three ...

## MCQ (Single Correct Answer)

JEE Main 2024 (Online) 1st February Morning Shift

If $\mathrm{n}$ is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of per...

JEE Main 2024 (Online) 31st January Evening Shift

The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is

JEE Main 2024 (Online) 31st January Evening Shift

If for some $$m, n ;{ }^6 C_m+2\left({ }^6 C_{m+1}\right)+{ }^6 C_{m+2}>{ }^8 C_3$$ and $${ }^{n-1} P_3:{ }^n P_4=1: 8$$, then $${ }^n P_{m+1}+{ }^{\m...

JEE Main 2024 (Online) 29th January Evening Shift

Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to

JEE Main 2024 (Online) 27th January Evening Shift

Let $$\alpha=\frac{(4 !) !}{(4 !)^{3 !}}$$ and $$\beta=\frac{(5 !) !}{(5 !)^{4 !}}$$. Then :

JEE Main 2023 (Online) 15th April Morning Shift

The total number of three-digit numbers, divisible by 3, which can be formed using the digits $1,3,5,8$, if repetition of digits is allowed, is :

JEE Main 2023 (Online) 13th April Evening Shift

All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial numbers....

JEE Main 2023 (Online) 12th April Morning Shift

The number of five digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits $$0,1,3,5,7$$ and 9 without repetition,...

JEE Main 2023 (Online) 11th April Evening Shift

If the letters of the word MATHS are permuted and all possible words so formed are arranged as in a dictionary with serial numbers, then the serial nu...

JEE Main 2023 (Online) 11th April Morning Shift

The number of triplets $$(x, \mathrm{y}, \mathrm{z})$$, where $$x, \mathrm{y}, \mathrm{z}$$ are distinct non negative integers satisfying $$x+y+z=15$$...

JEE Main 2023 (Online) 10th April Evening Shift

Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then th...

JEE Main 2023 (Online) 8th April Evening Shift

If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which $$\mathrm{C}$$ and $$\mathrm...

JEE Main 2023 (Online) 8th April Morning Shift

The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is :

JEE Main 2023 (Online) 8th April Morning Shift

The number of ways, in which 5 girls and 7 boys can be seated at a round table so that no two girls sit together, is :

JEE Main 2023 (Online) 8th April Morning Shift

Let the number of elements in sets $$A$$ and $$B$$ be five and two respectively. Then the number of subsets of $$A \times B$$ each having at least 3 a...

JEE Main 2023 (Online) 6th April Evening Shift

All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the se...

JEE Main 2023 (Online) 1st February Morning Shift

The value of $$\frac{1}{1 ! 50 !}+\frac{1}{3 ! 48 !}+\frac{1}{5 ! 46 !}+\ldots .+\frac{1}{49 ! 2 !}+\frac{1}{51 ! 1 !}$$ is :

JEE Main 2023 (Online) 30th January Evening Shift

The number of ways of selecting two numbers $a$ and $b, a \in\{2,4,6, \ldots ., 100\}$ and $b \in\{1,3,5, \ldots . ., 99\}$ such that 2 is the remaind...

JEE Main 2023 (Online) 29th January Evening Shift

The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of...

JEE Main 2023 (Online) 29th January Evening Shift

The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is :

JEE Main 2023 (Online) 25th January Evening Shift

The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1, 3, 5, 7, 9 without repetition, is :

JEE Main 2023 (Online) 25th January Evening Shift

$$\sum\limits_{k = 0}^6 {{}^{51 - k}{C_3}} $$ is equal to :

JEE Main 2023 (Online) 24th January Evening Shift

The number of integers, greater than 7000 that can be formed, using the digits 3, 5, 6, 7, 8 without repetition is :

JEE Main 2023 (Online) 24th January Evening Shift

The number of square matrices of order 5 with entries from the set {0, 1}, such that the sum of all the elements in each row is 1 and the sum of all t...

JEE Main 2022 (Online) 28th June Evening Shift

The number of ways to distribute 30 identical candies among four children C1, C2, C3 and C4 so that C2 receives at least 4 and at most 7 candies, C3 r...

JEE Main 2022 (Online) 28th June Morning Shift

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is :

JEE Main 2021 (Online) 1st September Evening Shift

Let P1, P2, ......, P15 be 15 points on a circle. The number of distinct triangles formed by points Pi, Pj, Pk such that i +j + k $$\ne$$ 15, is : ...

JEE Main 2021 (Online) 25th July Evening Shift

If $${}^n{P_r} = {}^n{P_{r + 1}}$$ and $${}^n{C_r} = {}^n{C_{r - 1}}$$, then the value of r is equal to :

JEE Main 2021 (Online) 18th March Morning Shift

The sum of all the 4-digit distinct numbers that can be formed with the digits 1, 2, 2 and 3 is :

JEE Main 2021 (Online) 17th March Evening Shift

If the sides AB, BC and CA of a triangle ABC have 3, 5 and 6 interior points respectively, then the total number of triangles that can be constructed ...

JEE Main 2021 (Online) 17th March Morning Shift

Team 'A' consists of 7 boys and n girls and Team 'B' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams w...

JEE Main 2021 (Online) 16th March Evening Shift

Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA respectively. Let $$\alpha$$ be the number of t...

JEE Main 2021 (Online) 26th February Evening Shift

A natural number has prime factorization given by n = 2x3y5z, where y and z are such that y + z = 5 and y$$-$$1 + z$$-$$1 = $${5 \over 6}$$, y > z....

JEE Main 2021 (Online) 26th February Morning Shift

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 :

JEE Main 2021 (Online) 25th February Morning Shift

The total number of positive integral solutions (x, y, z) such that xyz = 24 is :

JEE Main 2021 (Online) 24th February Morning Shift

A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at
least 2 Indians and double the number of foreigners as India...

JEE Main 2020 (Online) 6th September Morning Slot

Two families with three members each and one family with four members are to be seated in a row.
In how many ways can they be seated so that the same ...

JEE Main 2020 (Online) 5th September Evening Slot

There are 3 sections in a question paper and
each section contains 5 questions. A candidate
has to answer a total of 5 questions, choosing
at least on...

JEE Main 2020 (Online) 3rd September Morning Slot

The value of (2.1P0
– 3.2P1 + 4.3P2 .... up to
51th term) + (1! – 2! + 3! – ..... up to 51th term)
is equal to :...

JEE Main 2020 (Online) 2nd September Evening Slot

Let n > 2 be an integer. Suppose that there are
n Metro stations in a city located along a
circular path. Each pair of stations is connected
by a s...

JEE Main 2020 (Online) 9th January Morning Slot

If the number of five digit numbers with distinct
digits and 2 at the 10th place is 336 k, then k
is equal to :

JEE Main 2020 (Online) 8th January Morning Slot

If a, b and c are the greatest value of 19Cp, 20Cq
and 21Cr respectively, then :

JEE Main 2020 (Online) 7th January Evening Slot

The number of ordered pairs (r, k) for which 6.35Cr
= (k2 - 3). 36Cr + 1, where k is an integer, is :
...

JEE Main 2020 (Online) 7th January Morning Slot

Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is :

JEE Main 2019 (Online) 12th April Evening Slot

A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can
randomly be selected from this group suc...

JEE Main 2019 (Online) 12th April Morning Slot

The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21
are distinct, is :

JEE Main 2019 (Online) 10th April Evening Slot

Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the
top of each pillar has been connected by...

JEE Main 2019 (Online) 10th April Morning Slot

The number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by
11 and no digit is repeated is :

JEE Main 2019 (Online) 9th April Morning Slot

A committee of 11 members is to be formed from
8 males and 5 females. If m is the number of ways
the committee is formed with at least 6 males and
n i...

JEE Main 2019 (Online) 8th April Evening Slot

The number of four-digit numbers strictly greater
than 4321 that can be formed using the digits
0,1,2,3,4,5 (repetition of digits is allowed) is :

JEE Main 2019 (Online) 8th April Morning Slot

All possible numbers are formed using the digits
1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number
of such numbers in which the odd digits occ...

JEE Main 2019 (Online) 12th January Evening Slot

There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of gam...

JEE Main 2019 (Online) 12th January Morning Slot

Consider three boxes, each containing, 10 balls labelled 1, 2, … , 10. Suppose one ball is randomly drawn from each of the boxes. Denote by ni, the la...

JEE Main 2019 (Online) 10th January Evening Slot

If $$\sum\limits_{r = 0}^{25} {\left\{ {{}^{50}{C_r}.{}^{50 - r}{C_{25 - r}}} \right\} = K\left( {^{50}{C_{25}}} \right)} ,\,\,$$ then K is...

JEE Main 2019 (Online) 9th January Evening Slot

Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integra...

JEE Main 2019 (Online) 9th January Evening Slot

The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repitition of digits allowed) is equal to :

JEE Main 2019 (Online) 9th January Morning Slot

Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can
be formed from this class, if there ar...

JEE Main 2018 (Online) 16th April Morning Slot

The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4 (repetition of digits is not allowed) and are multiple ...

JEE Main 2018 (Offline)

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and
arranged in a row on a shelf so that the dictio...

JEE Main 2018 (Online) 15th April Evening Slot

The number of four letter words that can be formed using the letters of the word BARRACK is :

JEE Main 2018 (Online) 15th April Morning Slot

n$$-$$digit numbers are formed using only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct numbers can be formed, is :

JEE Main 2017 (Online) 9th April Morning Slot

The number of ways in which 5 boys and 3 girls can be seated on a round table if a
particular boy B1 and a particular girl G1 never sit adjacent to e...

JEE Main 2017 (Online) 8th April Morning Slot

If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the positio...

JEE Main 2017 (Offline)

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are
ladies and 4 are men. Assume X and Y have no c...

JEE Main 2016 (Online) 10th April Morning Slot

If $${{{}^{n + 2}C{}_6} \over {{}^{n - 2}{P_2}}}$$ = 11, then n satisfies the
equation :

JEE Main 2016 (Online) 10th April Morning Slot

The sum $$\sum\limits_{r = 1}^{10} {\left( {{r^2} + 1} \right) \times \left( {r!} \right)} $$ is equal to :

JEE Main 2016 (Online) 9th April Morning Slot

If the four letter words (need not be meaningful ) are to be formed using the
letters from the word “MEDITERRANEAN” such that the first letter is R an...

JEE Main 2016 (Online) 9th April Morning Slot

The value of $$\sum\limits_{r = 1}^{15} {{r^2}} \left( {{{{}^{15}{C_r}} \over {{}^{15}{C_{r - 1}}}}} \right)$$ is equal to :

JEE Main 2016 (Offline)

If all the words (with or without meaning) having five letters,formed using the letters of the word SMALL and arranged as in a dictionary, then the po...

JEE Main 2015 (Offline)

The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is:

JEE Main 2013 (Offline)

Let $${T_n}$$ be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If $${T_{n + 1}} - {T_n}$$ = 10, then ...

JEE Main 2013 (Offline)

Let A and B be two sets containing 2 elements and
4 elements respectively. The number of subsets of
A $$ \times $$ B having 3 or more elements is :

AIEEE 2012

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 gr...

AIEEE 2011

These are 10 points in a plane, out of these 6 are collinear, if N is the number of triangles formed by joining these points. then:

AIEEE 2011

Statement - 1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is emply is $${}^9{C_3}$$.
Statement -...

AIEEE 2010

There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then trans...

AIEEE 2009

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictio...

AIEEE 2008

In a shop there are five types of ice-cream available. A child buys six ice-cream.
Statement - 1: The number of different ways the child can buy th...

AIEEE 2008

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

AIEEE 2007

The set S = {1, 2, 3, ........., 12} is to be partitioned into three sets A, B, C of equal size. Thus $$A \cup B \cup C = S,\,A \cap B = B \cap C = A ...

AIEEE 2006

At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be sele...

AIEEE 2005

If the letter of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at s...

AIEEE 2004

How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order

AIEEE 2004

The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

AIEEE 2003

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choic...

AIEEE 2003

The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by

AIEEE 2003

If $${}^n{C_r}$$ denotes the number of combination of n things taken r at a time, then the expression $$\,{}^n{C_{r + 1}} + {}^n{C_{r - 1}} + 2\, \tim...

AIEEE 2002

Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are :

AIEEE 2002

Number greater than 1000 but less than 4000 is formed using the digits 0, 1, 2, 3, 4 (repetition allowed). Their number is :

AIEEE 2002

Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4 and 5 without repetition. Total number of such numbers are :

AIEEE 2002

The sum of integers from 1 to 100 that are divisible by 2 or 5 is :