Class 11

Math

JEE Main Questions

Permutations and Combinations

How many chords can be drawn through 21 points on a circle?

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If all the permutations of the letters in the word OBJECT are arranged (and numbered serially) in alphabetical order as in a dictionary, then the 717th word is a. TOJECB b. TOEJBC c. TOCJEB d. TOJCBE

From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?

If $6!1 +7!1 =8!x ,$find x

In a room there are 12 bulbs of the same wattage, each having separate switch. The number of ways to light the room with different amounts of illumination is (a)$12_{2}−1$ (b) $2_{12}$ (c) $2_{12}−1$ (d) none of these

Let $f(n,k)$ denote the number of ways in which $k$ identical balls can be colored with $n$ colors so that there is at least one ball of each color. Then $f(2n,n)$ must be equal to a. $_{2}nC_{n}$ b. $_{2}n−1C_{n+1}$ c. $_{2}n−1C_{n}$ d. none of these

A man has three friends. The number of ways he can invite one friend everyday for dinner on six successive nights so that no friend is invited more than three times is a. $640$ b. $320$ c. $420$ d. $510$

Computer (i) $5!7! $ (ii) $(10!)(2!)12! $

Find the value of n such that (i) $_{n}P_{5}=42_{n}P_{3},n>4$ (ii) $_{(n−1)}P_{4}_{n}P_{4} =35 ,n>4$