JEE Mains JEE Advance BITSAT
JEE Mains | PYQ

Year

All years 2026 2025 2024 2023 2022 2021

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 be at least \( 2 \) blue cubes, is _______.

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 ________.

The number of \( 3 \)-digit odd numbers, whose sum of digits is a multiple of \( 7 \), is ___________.

The number of one-one functions \( f : \{a, b, c, d\} \to \{0, 1, 2, \ldots, 10\} \) such that \( 2f(a) - f(b) + 3f(c) + f(d) = 0 \) is ________.

There are ten boys \( B_{1}, B_{2}, \ldots, B_{10} \) and five girls \( G_{1}, G_{2}, \ldots, G_{5} \) in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both \( B_{1} \) and \( B_{2} \) together should not be the members of a group, is __________ .

Let \( b_1 b_2 b_3 b_4 \) be a \( 4 \)-element permutation with \( b_i \in \{1, 2, 3, \ldots, 100\} \) for \( 1 \le i \le 4 \) and \( b_i \ne b_j \) for \( i \ne j \), such that either \( b_1, b_2, b_3 \) are consecutive integers or \( b_2, b_3, b_4 \) are consecutive integers. Then the number of such permutations \( b_1 b_2 b_3 b_4 \) is equal to ________.

The number of ways to distribute \(30\) identical candies among four children \(C_1, C_2, C_3\) and \(C_4\) so that \(C_2\) receives atleast \(4\) and atmost \(7\) candies, \(C_3\) receives atleast \(2\) and atmost \(6\) candies, is equal to:

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 divisible by \( 55 \) is ________.

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 \( b + 3g \) is equal to ______________.

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 answer, \( -2 \) marks for each wrong answer and \( 0 \) mark if the question is not attempted. Then, the number of ways a student appearing in the examination gets \( 5 \) marks is _________.

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 a number from \( \{1,2,3,4,5\} \) with the repetition of characters allowed. If the number of passwords in \( S \) whose at least one character is a number from \( \{1,2,3,4,5\} \) is \( \alpha \times 5^{6} \), then \( \alpha \) is equal to ________.

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

The letters of the word ‘\( \text{MANKIND} \)’ are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word ‘\( \text{MANKIND} \)’ is ______.

The number of bijective functions \( f:\{1,3,5,7,\ldots,99\}\to\{2,4,6,8,\ldots,100\} \), such that \( f(3)\ge f(9)\ge f(21)\ge \ldots \ge f(99) \), is ______________.

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:

Numbers are to be formed between \( 1000 \) and \( 3000 \), which are divisible by \( 4 \), using the digits \( 1,2,3,4,5, \text{and}\ 6 \) without repetition of digits. Then the total number of such numbers is ______.

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

← PreviousQuestion 14 of 17Next →

JEE Main 2022 25th July Evening Shift

The number of bijective functions \( f:\{1,3,5,7,\ldots,99\}\to\{2,4,6,8,\ldots,100\} \), such that \( f(3)\ge f(9)\ge f(21)\ge \ldots \ge f(99) \), is ______________.