Embibe Experts Solutions for Chapter: Permutation and Combination, Exercise 1: JEE Main - 1 February 2023 Shift 2

The number of ways of selecting two numbers $a$ and $b$, $a\in \left\{2,4,6,\dots \dots ,100\right\}$ and $b\in \left\{1,3,5,\dots \dots ,99\right\}$ such that $2$ is the remainder when $a+b$ is divided by $23$ is

The number of seven digits odd numbers, that can be formed using all the seven digits $1, 2, 2, 2, 3, 3, 5$ is

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. Then the serial number of the number $42923$ is _____ .

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

If ${}^{2n+1}P_{n-1}:{}^{2n-1}P_n=11:21$, then $n^2+n+15$ is equal to :

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 _____ .

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

Number of integral solutions to the equation $x+y+z=21$, where $x\ge 1,y\ge 3,z\ge 4$, is equal to _____ .