Class 11

Math

JEE Main Questions

Permutations and Combinations

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. $∣x−y∣=54$

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There are $n$ straight lines in a plane in which no two are parallel and no three pass through the same point. Their points of intersection are joined. Show that the number of fresh lines thus introduced is $81 n(n−1)(n−2)(n−3)$

If $_{n}C_{9}=_{n}C_{8},$find $_{n}C_{17}$

Evaluate (i) $8!$ (ii) $4!3!$

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of:(i) exactly 3 girls ? (ii) atleast 3 girls ? (iii) atmost 3 girls ?

The total number of flags with three horizontal strips in order, which can be formed using 2 identical red, 2 identical green, and 2 identical whit strips is equal to a. $4!$ b. $3×(4!)$ c. $2×(4!)$ d. none of these

Number of permutations of 1, 2, 3, 4, 5, 6, 7, 8, and 9 taken all at a time are such that the digit 1 appearing somewhere to the left of 2 3 appearing to the left of 4 and 5 somewhere to the left of 6, is $k×7!$ Then the value of $k$ is _________.

In how many ways can 4 red, 3 yellow and 2 green discs be arranged in a row if the discs of the same colour are indistinguishable?

$n$ lines are drawn in a plane such that no two of them are parallel and no three of them are concurrent. The number of different points at which these lines will cut is a. $k=1∑n−1 k$ b. $n(n−1)$ c. $n_{2}$ d. none of these