Q JEE MAIN 2026

A person has three different bags and four different books. The number of ways, in which he can put these...

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Q JEE MAIN 2026

A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The...

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Q JEE MAIN 2026

Let $A=\{1,4,7\}$ and $B=\{2,3,8\}$. Then the number of elements, in the relation $...

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Q JEE MAIN 2026

The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be...

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Q JEE MAIN 2026

A box contains 5 blue, 6 yellow and 4 red balls. The number of ways, of drawing 8 balls containing...

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Q JEE MAIN 2026

Two players A and B play a series of games of badminton. The player, who wins 5 games first, wins...

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Q JEE MAIN 2026

$\mathrm{A}=\{(a, b, c): a, b, c$ are non-negative integers and $a+b+2 c=22\}$. Then $n(\mathrm{~A})$ is equal to:

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Q Jee Main 2026

The number of ways, of forming a queue of 4 boys and 3 girls such that all the girls are...

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Q Jee Main 2026

Let $p_n$ denote the total number of triangles formed by joining the vertices of an $n$-side regular polygon. If $p_{n+1}-p_n=66$,...

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Q JEE Main 2024

Let the set $S=\{2,4,8,16, \ldots, 512\}$ be partitioned into 3 sets $\mathrm{A}, \mathrm{B}, \mathrm{C}$ with equal number of elements such...

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Q JEE Main 2024

60 words can be made using all the letters of the word BHBJO, with or without meaning. If these words...

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Q JEE Main 2024

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

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Q JEE Main 2024

There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If...

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Q JEE MAIN 2024

The lines $\mathrm{L}_1, \mathrm{~L}_2, \ldots, \mathrm{I}_{20}$ are distinct. For $\mathrm{n}=1,2,3, \ldots, 10$ all the lines $\mathrm{L}_{2 \mathrm{n}-1}$ are parallel to...

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Q JEE MAIN 2024

In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into...

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Q JEE-Main 2024

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

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Q Jee Main 2024

If for some $\mathrm{m}, \mathrm{n} ;{ }^6 \mathrm{C}_{\mathrm{m}}+2\left({ }^6 \mathrm{C}_{\mathrm{m}+1}\right)+{ }^6 \mathrm{C}_{\mathrm{m}+2}>{ }^8 \mathrm{C}_3$ and $...

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Q Jee Main 2024

The number of ways in which 21 identical apples can be distributed among three children such that each child gets...

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Q Jee Main 2024

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

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Q JEE MAIN 2026

Three persons enter in a lift at the ground floor. The lift will go upto $...

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Q JEE MAIN 2026

Let $\mathrm{S}=\left\{x^3+a x^2+b x+c: a, b, c \in \mathrm{~N}\right.$ and $\left.a, b, c \leq 20\right\}$ be a set of polynomials....

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Q JEE MAIN 2026

Let . Let be the number of 9 -digit numbers formed using the digits of the set S such that...

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Q JEE MAIN 2026

Let S denote the set of 4-digit numbers abcd such that $a>b>c>d$ and P denote the set of 5-digit numbers...

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Q JEE MAIN 2026

The number of ways, in which 16 oranges can be distributed to four children such that each child gets at...

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Q JEE MAIN 2026

The number of $3 \times 2$ matrices A , which can be formed using the elements of the set $\{-2,-1,0,1,2\}$...

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Q JEE MAIN 2026

The number of numbers greater than 5000 , less than 9000 and divisible by 3, that can be formed using...

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Q JEE MAIN_2026_

The number of 4 -letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is ______.

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Q JEE MAIN 2026

Let $S$ be the set of the first 11 natural numbers. Then the number of elements in $...

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Q JEE MAIN_2026

Let ABC be a triangle. Consider four points $\mathrm{p}_1, \mathrm{p}_2, \mathrm{p}_3, \mathrm{p}_4$ on the side AB , five points $...

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Q JEE MAIN 2026

Let $S=\{(m, n): m, n \in\{1,2,3, \ldots, 50\}\}$. If the number of elements ( $\mathrm{m}, \mathrm{n}$ ) in S such...

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Q JEE MAIN 2019

A committee of 11 members is to be formed from 8 males and 5 females. If m is the number...

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Q JEE MAIN_2019_

The number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9...

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Q JEE Main 2020

If the letters of the word ‘MOTHER’ be permuted and all the words so formed (with or without meaning) be...

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Q JEE MAIN 2020

Let $n>2$ be an integer. Suppose that there are $n$ Metro stations in a city located along a circular path....

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Q JEE MAIN 2019

A group of students comprises of 5 boys and n girls. If the number of ways, in which a team...

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Q JEE MAIN 2019

The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7,9...

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Q JEE-MAIN 2019

Consider three boxes, each containing 10 balls labelled 1, 2, ...,10. Suppose one ball is randomly drawn from each of...

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Q JEE MAIN 2020

If the number of five digit numbers with distinct digits and 2 at the $10^{\text {th }}$ place is 336...

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Q JEE MAIN 2020

The number of words, with or without meaning, that can be formed by taking 4 letters at a time from...

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Q JEE MAIN 2019

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

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Q JEE MAIN 2020

Two families with three members each and one family with four members are to be seated in a row. In...

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Q JEE MAIN 2019

The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7,9...

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Q JEE MAIN 2020

In a bombing attack, there is 50% chance that a bomb will hit the target. Atleast two independent hits are...

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Q JEE MAIN 2020

An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which...

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Q JEE MAIN 2019

Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the...

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Q JEE-MAIN 2020

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a...

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Q JEE MAIN 2020

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

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Q JEE-MAIN 2020

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

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Q JEE MAIN 2019

The number of function f from {1, 2, 3, ...,20} onto {1, 2, 3, ..., 20} such that f(k) is...

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Q JEE MAIN 2020

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

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Q JEE MAIN 2019

Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the...

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Q JEE Main 2021

The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is ______.

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Q JEE MAIN 2021

The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so...

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Q JEE MAIN 2020

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

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Q JEE Main 2021

The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of...

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Q JEE Main 2021

If ${ }^1 \mathrm{P}_1+2 \cdot{ }^2 \mathrm{P}_2+3 \cdot{ }^3 \mathrm{P}_3+\ldots+15 \cdot{ }^{15} \mathrm{P}_{15}={ }^9 \mathrm{P}_{\mathrm{r}}-\mathrm{s}, 0 \leq \mathrm{s} \leq 1$,...

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Q JEE MAIN 2021

A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is...

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Q JEE MAIN_2021_

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

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Q JEE MAIN 2019

The sum of all natural numbers ' $n$ ' such that $100< n1$ is :

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Q JEE MAIN 2021

The sum of all 3-digit numbers less than or equal to 500, that are formed without using the digit "1"...

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Q JEE MAIN 2019

All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at...

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Q JEE Main 2019

Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3...

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Q JEE MAIN 2021

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

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Q JEE MAIN 2021

Let $\mathrm{P}_1, \mathrm{P}_2 \ldots \ldots, \mathrm{P}_{15}$ be 15 points on a circle. The number of distinct triangles formed by points...

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Q _JEE MAIN_2021_

There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the...

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Q JEE MAIN 2021 S2

Let $n$ be a non-negative integer. Then the number of divisors of the form " $4 n+1$ " of the...

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Q JEE MAIN 2021

The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is

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Q JEE MAIN 2021

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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Q JEE MAIN 2019

The number of four-digit numbers strictly greater than 4321 that can be formed using the digits 0, 1, 2, 3,...

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Q JEE MAIN 2021

There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are...

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Q JEE MAIN 2021

Let x denote the total number of one-one functions from a set A with 3 elements to a set B...

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Q JEE-MAIN 2021

If the sides AB, BC and CA of a triangle ABC have 3, 5 and 6 interior points respectively, then...

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Q JEE MAIN_2021_

Team 'A' consists of 7 boys and n girls and Team 'B' has 4 boys and 6 girls. If a...

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Q JEE MAIN 2021

Consider a rectangle ABCD having $5,7,6,9$ points in the interior of the line segments $...

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Q JEE MAIN 2021

A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and...

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Q JEE MAIN 2021

The students $S_1, S_{2, \ldots \ldots}, S_{10}$ are to be divided into 3 groups $\mathrm{A}, \mathrm{B}$ and C such that...

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Q JEE MAIN 2021

The number of times the digit 2 will be written when listing the integers from 1 to 1000 is

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Q JEE MAIN 2021

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

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Q JEE MAIN 2021

A natural number has prime factorization given by $\mathrm{n}=2^{\mathrm{x}} 3^{\mathrm{y}} 5^{\mathrm{z}}$, where y and z are such that $\mathrm{y}+\mathrm{z}=5$ and...

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Q JEE MAIN 2021

The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits...

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Q JEE MAIN 2021

The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1, 2, 3,...

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Q JEE MAIN 2021

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

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Q JEE MAIN_2022

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

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Q JEE MAIN 2022

The letters of the word ‘MANKIND’ are written in all possible orders and arranged in serial order as in an...

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Q JEE MAIN 2022

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

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Q JEE MAIN 2022

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

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Q JEE MAIN 2022

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

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Q JEE MAIN 2022

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

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Q JEE MAIN 2022

The number of ways to distribute 30 identical candies among four children $\mathrm{C}_1, \mathrm{C}_2, \mathrm{C}_3$ and $\mathrm{C}_4$ so that $\mathrm{C}_2$...

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Q JEE MAIN 2022

Let $\mathrm{b}_1 \mathrm{~b}_2 \mathrm{~b}_3 \mathrm{~b}_4$ be a 4 -element permutation with $\mathrm{b}_{\mathrm{i}} \in\{1,2,3, \ldots \ldots \ldots, 100\}$ for $...

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Q JEE MAIN 2022

The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in...

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Q JEE MAIN 2022

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

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Q JEE MAIN 2022

There are ten boys $\mathrm{B}_1, \mathrm{~B}_2, \ldots ., \mathrm{B}_{10}$ and five girls $\mathrm{G}_1, \mathrm{G}_2, \ldots ., \mathrm{G}_5$ in a class....

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Q JEE MAIN 2022

Let A be a 3 × 3 matrix having entries from the set {–1, 0, 1}. The number of all...

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Q JEE MAIN 2022

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

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Q JEE MAIN 2022

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

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Q JEE MAIN 2022

The number of one-one function $f:\{a, b, c, d\} \rightarrow\left\{0,1,2_{\text {sui. }} .10\right\}$ such that $2 f(a) . f(b)+3 f(c)+f(d)=0$...

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Q JEE MAIN 2023

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

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Q JEE MAIN 2023

Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2,...

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Q JEE MAIN 2023

The number of points, where the curve $y=x^5-20 x^3+50 x+2$ crosses the $x$-axis, is $\_\_\_\_$ .

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Q JEE-Main 2023

If the number of words, with or without meaning, which can be made using all the letters of the word...

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Q JEE MAIN 2023

All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written...

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Q JEE MAIN 2025

There are 12 points in a plane, no three of which are in the same straight line, except 5 points...

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Q JEE MAIN 2023

All the letters of the word PUBLIC are written in all possible orders and these words are written as in...

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Q JEE MAIN_2025

Let $p$ be the number of all triangles that can be formed by joining the vertices of a regular polygon...

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Q JEE MAIN 2023

Eight persons are to be transported from city A to city B in three cars of different makes. If each...

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Q JEE MAIN 2025

Let m and $\left.\mathrm{n}_{( } \mathrm{m}

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Q JEE MAIN 2025

Line $L_1$ of slope 2 and line $L_2$ of slope $\frac{1}{2}$ intersect at the origin $O$. In the first quadrant,...

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Q JEE MAIN 2025

The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes...

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Q JEE MAIN 2023

The number of seven digit positive integers formed using the digits 1,2,3 and 4 only and sum of the digits...

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Q JEE MAIN 2023

A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different,...

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Q JEE MAIN 2023

The total number of three-digit numbers, divisible by 3, which can be formed using the digits 1, 3, 5, 8,...

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Q JEE MAIN 2023

In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in...

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Q JEE-Main_2023

If ${ }^{2 n} C_3 \cdot{ }^n C_3=10: 1$, then the ratio $\left(n^2+3 n\right):\left(n^2-3 n+4\right)$ is

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Q JEE MAIN 2023

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

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Q JEE MAIN 2023

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

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Q JEE MAIN 2023

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

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Q JEE MAIN 2023

The number of triplets (x, y, z). where x, y, z are distinct non negative integers satisfying x + y...

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Q JEE MAIN 2023

The number of five digit numbers, greater than 40000 and divisible by 5, which can be formed using the digits...

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Q JEE MAIN 2023

The number of arrangements of the letter of the word “INDEPENDENCE” in which all the vowels always occur together is-

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Q JEE MAIN 2023

The number of ways, in which 5 girls and 7 boys can be seated at a round table so that...

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Q JEE-Main 2023

The number of ways of giving 20 distinct oranges to 3 children such that each child gets atleast one orange...

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Q JEE-Main 2023

If ${ }^{2 n} C_3 \cdot{ }^n C_3=10: 1$, then the ratio $\left(n^2+3 n\right):\left(n^2-3 n+4\right)$ is

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Q JEE MAIN 2024

The number of ways of getting a sum 16 on throwing a dice four times is

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Q JEE MAIN 2024

The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits...

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Q JEE-Main

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

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Q JEE MAIN 2024

There are 5 points $\mathrm{P}_1, \mathrm{P}_2, \mathrm{P}_3, \mathrm{P}_4, \mathrm{P}_5$ on the side AB , excluding A and B , of...

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Q JEE MAIN 2024

The total number of words (with or without meaning) that can be formed out of the letters of the word...

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Q JEE MAIN

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

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Q JEE-Main 2024

If n is the number of ways five different employees can sit into four indistinguishable offices where any office may...

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Q JEE MAIN 2025

If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as...

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Q JEE MAIN 2025

The number of natural numbers, between 212 and 999 , such that the sum of their digits is 15 ,...

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Q JEE MAIN 2025

For $n \ge 2$, let ${S_n}$ denote the set of all subsets of $\{ 1,2, \ldots ,n\} $ with no...

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Q JEE MAIN 2025

From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should...

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Q JEE MAIN 2025

If the number of seven-digit numbers, such that the sum of their digits is even, is $...

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Q JEE MAIN 2025

Number of functions $f:\{1,2, \ldots, 100\} \rightarrow\{0,1\}$, that assign 1 to exactly one of the positive integers less than or...

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Q JEE MAIN 2025

Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The...

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Q JEE MAIN 2025

The largest $n \in N$ such that ${3^n}$ divides 50 ! is :

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Q JEE MAIN 2025

The number of sequences of ten terms, whose terms are either 0 or 1 or 2 , that contain exactly...

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Q JEE MAIN 2025

The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys...

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Q JEE MAIN 2025

The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS...

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Q JEE MAIN 2025

Let P be the set of seven digit numbers with sum of their digits equal to 11 . If the...

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Q JEE MAIN 2025

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,...

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Q JEE MAIN 2025

Let $S = \left\{ {{p_1},{p_2} \ldots ,{p_{10}}} \right\}$ be the set of first ten prime numbers. Let $...

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Q JEE MAIN 2025

The number of 3-digit numbers, that are divisible by 2 and 3, but not divisible by 4 and 9, is

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Q JEE MAIN 2025

The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the...

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Q JEE MAIN 2025

Let $A=\{1,2,3, \ldots, 10\}$ and $B = \left\{ {\frac{m}{n}:m,n \in A,m < n} \right.$ and $\left. {gcd(m,n) = 1} \right\}$....

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Q JEE MAIN 2025

In a group of 3 girls and 4 boys, there are two boys $B_1$ and $B_2$. The number of ways,...

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Q JEE MAIN 2025

From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways,...

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