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JEE Main

Permutations and Combinations

Mathematics

Previous Years Questions

Numerical

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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...
JEE Main 2022 (Online) 26th July Evening Shift
The number of 5-digit natural numbers, such that the product of their digits is 36 , is __________.
JEE Main 2022 (Online) 26th July Morning Shift
The letters of the word 'MANKIND' are written in all possible orders and arranged in serial order as in an English dicti...
JEE Main 2022 (Online) 25th July 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...
JEE Main 2022 (Online) 30th June Morning Shift
In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are ...
JEE Main 2022 (Online) 24th June Morning 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 Evening 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
The total number of three-digit numbers, with one digit repeated exactly two times, is ______________.
JEE Main 2022 (Online) 25th 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 Evening Shift
There are ten boys B1, B2, ......., B10 and five girls G1, G2, ........, G5 in a class. Then the number of ways of formi...
JEE Main 2022 (Online) 26th 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 an...
JEE Main 2022 (Online) 27th June Morning 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 Evening Shift
Let b1b2b3b4 be a 4-element permutation with bi $$\in$$ {1, 2, 3, ........, 100} for 1 $$\le$$ i $$\le$$ 4 and bi $$\ne$...
JEE Main 2022 (Online) 29th June Morning Shift
All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two R appearin...
JEE Main 2021 (Online) 1st September Evening Shift
The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all...
JEE Main 2021 (Online) 31st August Morning Shift
A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is a six digit pali...
JEE Main 2021 (Online) 27th August Morning Shift
The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed...
JEE Main 2021 (Online) 26th August Morning Shift
If $${}^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...
JEE Main 2021 (Online) 26th August Morning 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...
JEE Main 2021 (Online) 27th July Evening 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 ...
JEE Main 2021 (Online) 25th July Morning 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 n...
JEE Main 2021 (Online) 22th July Evening 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...
JEE Main 2021 (Online) 20th July Morning 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 Evening Shift
The missing value in the following figure is ...
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 total number of numbers, lying between 100 and 1000 that can be formed with the digits 1, 2, 3, 4, 5, if the repetit...
JEE Main 2021 (Online) 25th February Morning Slot
The sum of first four terms of a geometric progression (G. P.) is $${{65} \over {12}}$$ and the sum of their respective ...
JEE Main 2021 (Online) 24th February Evening Slot
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...
JEE Main 2021 (Online) 24th February Evening Slot
The number of words (with or without meaning) that can be formed from all the letters of the word “LETTER” in which vowe...
JEE Main 2020 (Online) 6th September Evening 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 w...
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 o...
JEE Main 2020 (Online) 5th September Morning Slot
A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The numb...
JEE Main 2020 (Online) 4th September Evening Slot
The total number of 3-digit numbers, whose sum of digits is 10, is ______.
JEE Main 2020 (Online) 3rd September Evening 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 ...
JEE Main 2020 (Online) 2nd September Morning Slot
The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATI...
JEE Main 2020 (Online) 8th January Evening 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 dr...
JEE Main 2020 (Online) 8th January Morning Slot

MCQ (Single Correct Answer)

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The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple ...
JEE Main 2022 (Online) 28th June Morning Shift
The number of ways to distribute 30 identical candies among four children C1, C2, C3 and C4 so that C2 receives at least...
JEE Main 2022 (Online) 28th June 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...
JEE Main 2021 (Online) 1st September 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) 25th July Evening 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) 18th March Morning 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 tria...
JEE Main 2021 (Online) 17th March Evening 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 arra...
JEE Main 2021 (Online) 17th March Morning Shift
Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA respectively. Let...
JEE Main 2021 (Online) 16th March 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$$-$$...
JEE Main 2021 (Online) 26th February Evening 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) 26th February Morning Shift
The total number of positive integral solutions (x, y, z) such that xyz = 24 is :
JEE Main 2021 (Online) 25th February Morning Slot
A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the...
JEE Main 2021 (Online) 24th February 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 th...
JEE Main 2020 (Online) 6th September Morning Slot
There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 q...
JEE Main 2020 (Online) 5th September Evening 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) 3rd September Morning Slot
Let n > 2 be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair o...
JEE Main 2020 (Online) 2nd September Evening 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) 9th January Morning Slot
If a, b and c are the greatest value of 19Cp, 20Cq and 21Cr respectively, then...
JEE Main 2020 (Online) 8th January Morning 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 Evening 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 2020 (Online) 7th January Morning 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 b...
JEE Main 2019 (Online) 12th April Evening Slot
The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct,...
JEE Main 2019 (Online) 12th April Morning Slot
Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of eac...
JEE Main 2019 (Online) 10th April Evening 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 d...
JEE Main 2019 (Online) 10th 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...
JEE Main 2019 (Online) 9th April Morning 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 ...
JEE Main 2019 (Online) 8th April Evening 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 numbe...
JEE Main 2019 (Online) 8th April Morning Slot
There are m men and two women participating in a chess tournament. Each participant plays two games with every other par...
JEE Main 2019 (Online) 12th January Evening Slot
Consider three boxes, each containing, 10 balls labelled 1, 2, … , 10. Suppose one ball is randomly drawn from each of t...
JEE Main 2019 (Online) 12th January Morning Slot
The number of functions f from {1, 2, 3, ...., 20} onto {1, 2, 3, ...., 20} such that f(k) is a multiple of 3, whenever ...
JEE Main 2019 (Online) 11th January Evening Slot
If  $$\sum\limits_{r = 0}^{25} {\left\{ {{}^{50}{C_r}.{}^{50 - r}{C_{25 - r}}} \right\} = K\left( {^{50}{C_{25...
JEE Main 2019 (Online) 10th January Evening Slot
The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repitition of digit...
JEE Main 2019 (Online) 9th January Evening Slot
Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie o...
JEE Main 2019 (Online) 9th January Evening Slot
Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be forme...
JEE Main 2019 (Online) 9th January Morning Slot
The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4 (repetition of digits is ...
JEE Main 2018 (Online) 16th April Morning Slot
The number of four letter words that can be formed using the letters of the word BARRACK is :
JEE Main 2018 (Online) 15th April Evening Slot
n$$-$$digit numbers are formed using only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct ...
JEE Main 2018 (Online) 15th April Morning Slot
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row...
JEE Main 2018 (Offline)
The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy B1 and a particular g...
JEE Main 2017 (Online) 9th April Morning Slot
If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in Englis...
JEE Main 2017 (Online) 8th April Morning Slot
A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are...
JEE Main 2017 (Offline)
The sum $$\sum\limits_{r = 1}^{10} {\left( {{r^2} + 1} \right) \times \left( {r!} \right)} $$ is equal to :
JEE Main 2016 (Online) 10th April Morning Slot
If    $${{{}^{n + 2}C{}_6} \over {{}^{n - 2}{P_2}}}$$ = 11, then n satisfies the equation :
JEE Main 2016 (Online) 10th April Morning Slot
The value of $$\sum\limits_{r = 1}^{15} {{r^2}} \left( {{{{}^{15}{C_r}} \over {{}^{15}{C_{r - 1}}}}} \right)$$ is equal ...
JEE Main 2016 (Online) 9th April Morning Slot
If the four letter words (need not be meaningful ) are to be formed using the letters from the word “MEDITERRANEAN” such...
JEE Main 2016 (Online) 9th April Morning Slot
If all the words (with or without meaning) having five letters,formed using the letters of the word SMALL and arranged a...
JEE Main 2016 (Offline)
The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is:
JEE Main 2015 (Offline)
Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A $$ \times $$ B hav...
JEE Main 2013 (Offline)
Let $${T_n}$$ be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If $${T_...
JEE Main 2013 (Offline)
Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can b...
AIEEE 2012
Statement - 1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is emply is...
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 po...
AIEEE 2011
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 take...
AIEEE 2010
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row...
AIEEE 2009
How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?
AIEEE 2008
In a shop there are five types of ice-cream available. A child buys six ice-cream. Statement - 1: The number of diffe...
AIEEE 2008
The set S = {1, 2, 3, ........., 12} is to be partitioned into three sets A, B, C of equal size. Thus $$A \cup B \cup C ...
AIEEE 2007
At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 c...
AIEEE 2006
If the letter of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, the...
AIEEE 2005
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is
AIEEE 2004
How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order
AIEEE 2004
If $${}^n{C_r}$$ denotes the number of combination of n things taken r at a time, then the expression $$\,{}^n{C_{r + 1}...
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 ...
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
Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4 and 5 without repetition. Total number of such numbers ar...
AIEEE 2002
The sum of integers from 1 to 100 that are divisible by 2 or 5 is
AIEEE 2002
Number greater than 1000 but less than 4000 is formed using the digits 0, 1, 2, 3, 4 (repetition allowed). Their number ...
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

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