JEE MAIN Permutations and Combinations Previous Year Question Paper and Solution with PDF

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JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Permutations And Combinations PYQ

Qus : 1 JEE MAIN PYQ

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

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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (25 July Evening Shift) PYQ

Solution

Qus : 2 JEE MAIN PYQ

Let $a \in \left(0, \dfrac{\pi}{2}\right)$ be fixed. If $\displaystyle \int \dfrac{\tan x + \tan a}{\tan x - \tan a} , dx = A(x)\cos 2a + B(x)\sin 2a + C,$ where $C$ is a constant of integration, then the functions $A(x)$ and $B(x)$ are respectively:

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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 April Evening Shift) PYQ

Solution

Qus : 3 JEE MAIN PYQ

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 family members are not separated?

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 6 September 2020 (Morning) PYQ

Solution

Let there be two families with 3 members each (say Family A and Family B), and one family with 4 members (Family C).

Step 1: Since members of the same family must sit together, treat each family as a single block.
Thus, there are 3 blocks: A, B, and C.
They can be arranged in $3! = 6$ ways.

Step 2: Now arrange members within each family:
Family A (3 members): $3!$ ways
Family B (3 members): $3!$ ways
Family C (4 members): $4!$ ways

Step 3: Total number of arrangements = $3! \times 3! \times 3! \times 4!$

Step 4: Simplify:
$3! = 6$ and $4! = 24$
$\Rightarrow (3!)^3\times4!$

∴ Total number of ways = $\boxed{5184}$

Qus : 4 JEE MAIN PYQ

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 such that there is at least one boy and at least one girl in each team is $1750$, then $n$ is equal to:

1
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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 April Evening Shift) PYQ

Solution

Qus : 5 JEE MAIN PYQ

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 :

1
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3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2013 (Offline) PYQ

Solution

Qus : 6 JEE MAIN PYQ

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

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3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

Qus : 7 JEE MAIN PYQ

From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowlers. One batsmen and one bowler who are captain and vice-captain respectively of the team should be included. Then the total number of ways such a selection can be made, is

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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (7 April Morning Shift) PYQ

Solution

Qus : 8 JEE MAIN PYQ

Let $A={1,3,7,9,11}$ and $B={2,4,5,7,8,10,12}$. The total number of one–one maps $f:A\to B$ such that $f(1)+f(3)=14$ is:

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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (5 April Morning Shift) PYQ

Solution

Qus : 9 JEE MAIN PYQ

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 the value of $n$ is :

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4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2013 (Offline) PYQ

Solution

Qus : 10 JEE MAIN PYQ

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 serial number of the word PUBLIC is :

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4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (6 April Evening Shift) PYQ

Solution

Qus : 11 JEE MAIN PYQ

The number of four letter words that can be formed using the letters of the word $\text{BARRACK}$ is :

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4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

Qus : 12 JEE MAIN PYQ

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

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4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (8 April Morning Shift) PYQ

Solution

Qus : 13 JEE MAIN PYQ

$ \text{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:} $

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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (8 April Morning Shift) PYQ

Solution

Qus : 14 JEE MAIN PYQ

A fair die is tossed until six is obtained on it. Let x be the number of required tosses, then the conditional probability P(x $\ge$ 5 | x > 2) is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (26 August Evening Shift) PYQ

Solution

Qus : 15 JEE MAIN PYQ

Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote the total number of one-one functions form the set A to the set A $\times$ B. Then :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (25 February Evening Shift) PYQ

Solution

Qus : 16 JEE MAIN PYQ

Let the set $S={2,4,8,16,\ldots,512}$ be partitioned into three sets $A,B,C$ having equal number of elements such that $A\cup B\cup C=S$ and $A\cap B=B\cap C=A\cap C=\phi$. Then the maximum number of such possible partitions of $S$ is:

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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (5 April Evening Shift) PYQ

Solution

Qus : 17 JEE MAIN PYQ

60 words can be formed using all the letters of the word BHBJO (with or without meaning). If these words are arranged in dictionary order, then the 50^th word is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (5 April Evening Shift) PYQ

Solution

Qus : 18 JEE MAIN PYQ

Let $p$ be the number of all triangles that can be formed by joining the vertices of a regular $n$-gon $P$, and $q$ be the number of all quadrilaterals that can be formed by joining the vertices of $P$. If $p+q=126$, then the eccentricity of the ellipse $\dfrac{x^2}{16}+\dfrac{y^2}{n}=1$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (7 April Evening Shift) PYQ

Solution

Qus : 19 JEE MAIN PYQ

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 dictionary is always in the middle. The number of such arrangements is :

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4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

Qus : 20 JEE MAIN PYQ

Group $A$ consists of $7$ boys and $3$ girls, while group $B$ consists of $6$ boys and $5$ girls. The number of ways $4$ boys and $4$ girls can be invited for a picnic if $5$ of them must be from group $A$ and the remaining $3$ from group $B$, is equal to:

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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (24 January Evening Shift) PYQ

Solution

Qus : 21 JEE MAIN PYQ

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

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (27 January Evening Shift) PYQ

Solution

Qus : 22 JEE MAIN PYQ

If the number of words (with or without meaning) that can be formed using all the letters of the word MATHEMATICS — in which C and S do not come together — is $(6!)k$, then $k$ is equal to:

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4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (8 April Evening Shift) PYQ

Solution

Qus : 23 JEE MAIN PYQ

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 :

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4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (26 February Morning Shift) PYQ

Solution

Qus : 24 JEE MAIN PYQ

The number of different $5$-digit numbers greater than $50000$ that can be formed using the digits $0,1,2,3,4,5,6,7$, such that the sum of their first and last digits is not more than $8$, is

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (28 January Morning Shift) PYQ

Solution

Qus : 25 JEE MAIN PYQ

The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is:

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4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (6 April Morning Shift) PYQ

Solution

Qus : 26 JEE MAIN PYQ

The number of numbers between $2000$ and $5000$ that can be formed with the digits $0,1,2,3,4$ (repetition of digits is not allowed) and are multiples of $3$ is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

Solution

Qus : 27 JEE MAIN PYQ

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

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3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (29 January Evening Shift) PYQ

Solution

Qus : 28 JEE MAIN PYQ

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 the number of ways, in which they can be transported, is :

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4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (10 April Evening Shift) PYQ

Solution

Qus : 29 JEE MAIN PYQ

Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is:

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4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (28 January Evening Shift) PYQ

Solution

Qus : 30 JEE MAIN PYQ

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 common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is:

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4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (Offline) PYQ

Solution

Qus : 31 JEE MAIN PYQ

If all words (with or without meaning) formed using all the letters of the word NAGPUR are arranged in dictionary order, then the word at the 315^th position is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (6 April Evening Shift) PYQ

Solution

Qus : 32 JEE MAIN PYQ

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 triangles having these points from different sides as vertices and $\beta$ be the number of quadrilaterals having these points from different sides as vertices. Then ($\beta$ $-$ $\alpha$) is equal to :

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4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (16 March Evening Shift) PYQ

Solution

Qus : 33 JEE MAIN PYQ

The number of triplets , where are distinct non negative integers satisfying , is :

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4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (11 April Morning Shift) PYQ

Solution

Qus : 34 JEE MAIN PYQ

An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (11 April Morning Shift) PYQ

Solution

Qus : 35 JEE MAIN PYQ

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

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3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (24 January Evening Shift) PYQ

Solution

Qus : 36 JEE MAIN PYQ

There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total number of triangles that can be formed with the vertices at any three of these 12 points is

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4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (8 April Evening Shift) PYQ

Solution

Qus : 37 JEE MAIN PYQ

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 number of the word THAMS is :

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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (11 April Evening Shift) PYQ

Solution

Qus : 38 JEE MAIN PYQ

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 straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is 99 times the number of blue lines, then the value of n is :

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Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2 September 2020 (Evening) PYQ

Solution

There are $n$ stations on a circle. Each pair is connected by a straight track.

Blue lines connect nearest neighbours, so the number of blue lines is

Blue $ = n. $

Total lines is $ \binom{n}{2} = \frac{n(n-1)}{2}. $

Hence red lines are $ \text{Red} = \binom{n}{2} - n. $

Given Red =$ 99 \times \text{Blue} $

$ \binom{n}{2} - n = 99n $

$ \;\;\Longrightarrow\;\; \frac{n(n-1)}{2} - n = 99n$

$ \;\;\Longrightarrow\;\; \frac{n(n-1)}{2} = 100n$

$ \;\;\Longrightarrow\;\; n-1 = 200$

$ \;\;\Longrightarrow\;\; n = 201.$

Final Answer: $\boxed{201}$

Qus : 39 JEE MAIN PYQ

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 occupy even places is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (8 April Morning Shift) PYQ

Solution

Qus : 40 JEE MAIN PYQ

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 position of the word QUEEN is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (8 April Morning Shift) PYQ

Solution

Qus : 41 JEE MAIN PYQ

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

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 3 September 2020 (Morning) PYQ

Solution

Qus : 42 JEE MAIN PYQ

The number of five digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits 1, 3, 7 and 9 without repetition, is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (12 April Morning Shift) PYQ

Solution

Qus : 43 JEE MAIN PYQ

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

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (29 January Evening Shift) PYQ

Solution

Qus : 44 JEE MAIN PYQ

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 when a boy plays against a boy and a girl plays against a girl, then n is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (17 March Morning Shift) PYQ

Solution

Qus : 45 JEE MAIN PYQ

The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily distinct, is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (8 April Evening Shift) PYQ

Solution

Qus : 46 JEE MAIN PYQ

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

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (8 April Evening Shift) PYQ

Solution

Qus : 47 JEE MAIN PYQ

The number of ways in which $5$ boys and $3$ girls can be seated on a round table if a particular boy $B_1$ and a particular girl $G_1$ never sit adjacent to each other, is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (9 April Morning Shift) PYQ

Solution

Qus : 48 JEE MAIN PYQ

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 :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 June Morning Shift) PYQ

Solution

Qus : 49 JEE MAIN PYQ

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 Indians. Then the number of ways, the committee can be formed, is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (24 February Morning Shift) PYQ

Solution

Qus : 50 JEE MAIN PYQ

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

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (25 January Evening Shift) PYQ

Solution

Qus : 51 JEE MAIN PYQ

The term independent of x in the expansion of $(1 - {x^2} + 3{x^3}){\left( {{5 \over 2}{x^3} - {1 \over {5{x^2}}}} \right)^{11}},\,x \ne 0$ is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 June Evening Shift) PYQ

Solution

Qus : 52 JEE MAIN PYQ

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. The serial number of the word MONDAY is :

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2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (13 April Evening Shift) PYQ

Solution

Qus : 53 JEE MAIN PYQ

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 $n$ is the number of ways the committee is formed with at least $3$ females, then:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 April Morning Shift) PYQ

Solution

Qus : 54 JEE MAIN PYQ

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

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (18 March Morning Shift) PYQ

Solution

Qus : 55 JEE MAIN PYQ

The number of sequences of ten terms, whose terms are either $0$, $1$ or $2$, that contain exactly five $1$’s and exactly three $2$’s, is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (2 April Morning Shift) PYQ

Solution

Qus : 56 JEE MAIN PYQ

The total number of three-digit numbers, divisible by 3, which can be formed using the digits

, if repetition of digits is allowed, is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (15 April Morning Shift) PYQ

Solution

Qus : 57 JEE MAIN PYQ

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

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (31 January Evening Shift) PYQ

Solution

Qus : 58 JEE MAIN PYQ

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 the word TOUGH is :

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3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (29 January Evening Shift) PYQ

Solution

Qus : 59 JEE MAIN PYQ

Let S = {1, 2, 3, 4, 5, 6}. Then the probability that a randomly chosen onto function g from S to S satisfies g(3) = 2g(1) is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (31 August Evening Shift) PYQ

Solution

Qus : 60 JEE MAIN PYQ

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 position of the word SMALL is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

Qus : 61 JEE MAIN PYQ

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 $R$ and the fourth letter is $E$, then the total number of all such words is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

Qus : 62 JEE MAIN PYQ

If for some $m,n$, $\binom{6}{m}+2\binom{6}{m+1}+\binom{6}{m+2}>8\binom{6}{3}$ and $\,^{\,n-1}\!P_{3}:\,^{\,n}\!P_{4}=1:8$, then $\,^{\,n}\!P_{\,n+1}+\,^{\,n+1}\!C_{m}$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (31 January Evening Shift) PYQ

Solution

Qus : 63 JEE MAIN PYQ

The value of $\displaystyle \sum_{r=1}^{15} r^{2} \left( \dfrac{{}^{15}C_{r}}{{}^{15}C_{r-1}} \right)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

Qus : 64 JEE MAIN PYQ

Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (20 July Morning Shift) PYQ

Solution

Qus : 65 JEE MAIN PYQ

If $n$ is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons (including zero), then $n$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (1 February Morning Shift) PYQ

Solution

Qus : 66 JEE MAIN PYQ

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 are two specific boys $A$ and $B$ who refuse to be in the same team, is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 January Morning Shift) PYQ

Solution

Qus : 67 JEE MAIN PYQ

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

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 April Morning Shift) PYQ

Solution

Qus : 68 JEE MAIN PYQ

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

1
2
3
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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (1 September Evening Shift) PYQ

Solution

Qus : 69 JEE MAIN PYQ

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 remainder when $a+b$ is divided by $23$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (30 January Evening Shift) PYQ

Solution

Qus : 70 JEE MAIN PYQ

From all the English alphabets, five letters are chosen and arranged in alphabetical order. The total number of ways in which the middle letter is M is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (22 January Morning Shift) PYQ

Solution

Qus : 71 JEE MAIN PYQ

The number of natural numbers less than 7000 which can be formed by using the digits 0,1,3,7,9 (repetition of digits allowed) is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 January Evening Shift) PYQ

Solution

Qus : 72 JEE MAIN PYQ

If $\dfrac{{}^{n+2}C_{6}}{{}^{n-2}P_{2}} = 11$, then $n$ satisfies the equation:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

Qus : 73 JEE MAIN PYQ

Line $L_1$ of slope $2$ and line $L_2$ of slope $\dfrac{1}{2}$ intersect at the origin $O$. In the first quadrant, $P_1,P_2,\ldots,P_{12}$ are $12$ points on line $L_1$ and $Q_1,Q_2,\ldots,Q_{9}$ are $9$ points on line $L_2$. Then the total number of triangles that can be formed having vertices at three of the $22$ points $O,P_1,P_2,\ldots,P_{12},Q_1,Q_2,\ldots,Q_{9}$ is

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (3 April Evening Shift) PYQ

Solution

Qus : 74 JEE MAIN PYQ

The sum $\displaystyle \sum_{r=1}^{10} (r^2 + 1)\,(r!)$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

Qus : 75 JEE MAIN PYQ

Let $S$ be the set of all triangles in the $xy$-plane, each having one vertex at the origin and the other two vertices on the coordinate axes with integral coordinates. If each triangle in $S$ has area $50$ sq. units, then the number of elements in the set $S$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 January Evening Shift) PYQ

Solution

Qus : 76 JEE MAIN PYQ

Suppose that $20$ pillars of the same height are erected along the boundary of a circular stadium. If the top of each pillar is connected by beams with the tops of all its non-adjacent pillars, then the total number of beams is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 April Evening Shift) PYQ

Solution

Qus : 77 JEE MAIN PYQ

The number of bijective functions $f:\{1,3,5,7,\ldots,99\}\to\{2,4,6,8,\ldots,100\}$ such that

$f(3)\ge f(9)\ge f(15)\ge f(21)\ge \cdots \ge f(99)$ is ________.

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (25 July Evening Shift) PYQ

Solution

Qus : 78 JEE MAIN PYQ

In a group of 3 girls and 4 boys, there are two boys $B_1$ and $B_2$. The number of ways in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but $B_1$ and $B_2$ are not adjacent to each other, is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (22 January Evening Shift) PYQ

Solution

Qus : 79 JEE MAIN PYQ

There are 5 points P₁, P₂, P₃, P₄, P₅ on the side AB, excluding A and B, of a triangle ABC. Similarly, there are 6 points P₆, P₇,..., P₁₁ on the side BC and 7 points P₁₂, P₁₃,..., P₁₈ on the side CA. The number of triangles that can be formed using the points P₁, P₂,..., P₁₈ as vertices is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (4 April Morning Shift) PYQ

Solution

Qus : 80 JEE MAIN PYQ

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

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 April Morning Shift) PYQ

Solution

Qus : 81 JEE MAIN PYQ

The number of words that can be formed using all the letters of the word "DAUGHTER" such that all the vowels never come together is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (23 January Morning Shift) PYQ

Solution

Qus : 82 JEE MAIN PYQ

The number of integers greater than $6000$ that can be formed, using the digits $3,5,6,7$ and $8$, without repetition, is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2015 (Offline) PYQ

Solution

Qus : 83 JEE MAIN PYQ

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 one question from each section. Then the number of ways, in which the candidate can choose the questions, is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 5 September 2020 (Evening) PYQ

Solution

Qus : 84 JEE MAIN PYQ

Let $A$ and $B$ be two sets containing four and two elements respectively. Then, the number of subsets of the set $A\times B$, each having at least three elements, are :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2015 (Offline) PYQ

Solution

JEE MAIN

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