Class 11

Math

JEE Main Questions

Permutations and Combinations

Find $r$ if (i) $_{5}P_{r}=2_{6}P_{r−1}$ (ii) $_{5}P_{r}=_{6}P_{r−1}$

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How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?

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________.

Evaluate $r!(n−r)!n! $, when n = 5, r = 2.

How many words, with or without meaning, each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

If $N$ is the number of ways in which 3 distinct numbers canbe selected from the set ${3_{1},3_{2},3_{3},,3_{10}}$ so that they form a G.P. then the value of $N/5$ is ______.

There are 3 men and 7 women taking a dance class. If $N$ ils number of different ways in which each man be paired with a women partner, and the four remaining women be paired into two pairs each of two, then the value of $N/90$ is_________.

Let $n$ be a four-digit integer in which all the digits are different. If $x$ is number of odd integers and $y$ is number of even integers, then a. $x<y$ b. $x>y$ c. $x+y=4500$ d. $∣x−y∣=54$

How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?