Class 11

Math

JEE Main Questions

Permutations and Combinations

The total number of ways of selecting two numbers from the set ${1,2,3,4,……..3n}$ so that their sum is divisible by 3 is equal to a. $22n_{2}−n $ b. $23n_{2}−n $ c. $2n_{2}−n$ d. $3n_{2}−n$

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How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?

If the number of selections of 6 different letters that can be made from the words SUMAN and DIVYA so that each selection contains 3 letters from each word is $N_{2},$ then the value of $N$ is________.

Compute $6!×2!8! $

The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order s in an English dictionary. The number of words that appear before the word COCHIN is a.$360$ b. $192$ c. $96$ d. $48$

If $a$ denotes the number of permutations of $(x+2)$ things taken all at a time, $b$ the number of permutations of $x$ things taken $11$ at a time and $c$ the number of permutations of $x−11$ things taken all at a time such that $a=182bc,$ find the value of $x˙$

The value of $r=0∑n−1 _{n}C_{r}/(_{n}C_{r}+_{n}C_{r+1})$ equals a. $n+1$ b. $n/2$ c. $n+2$ d. none of these

A forecast is to be made of the results of five cricket matches, each of which can be a win or a draw or a loss for Indian team. Let $p=$ number of forecasts with exactly 1 error $q=$ number of forecasts with exactly 3 error $r=$ number of forecasts with all five error Then the correct statement(s) is/are a. $2q=5r$ b. $8p−q$ c. $8p−r$ d. $2(p+r)>q$

Let $S={1,2,3,4}$ . The total number of unordered pairs of disjoint subsets of $S$ is equal a.$25$ b. $34$ c. $42$ d. $41$