Beta Question Bank for Engineering: Mathematics>Chapter 9 - Permutation and Combination>EXERCISE-2>Q 17

MEDIUM

JEE Main/Advance

IMPORTANT

Earn 100

Total number of even divisors of $2079000$ which are divisible by $15$ are -

100% studentsanswered this correctly

Important Questions on Permutation and Combination

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 9 - Permutation and Combination>EXERCISE-2>Q 18

The number of five digit numbers that can be formed using all the digits

0, 1, 3, 6, 8

which are -

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 9 - Permutation and Combination>EXERCISE-2>Q 19

All the

7

digit numbers containing each of the digits

1, 2, 3, 4, 5, 6, 7

exactly once and not divisible by

5

are arranged in the increasing order. Then -

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 9 - Permutation and Combination>EXERCISE-2>Q 20

There are

(p + q)

different books on different topics in Mathematics.

(p \neq q)

If $L =$ the number of ways in which these books are distributed between two students $X$ and $Y$ such that $X$ get $p$ books and $Y$ gets $q$ books.

$M =$ The number of ways in which these books are distributed between two students $X$ and $Y$ such that one of them gets $p$ books and another gets $q$ books.

$N =$ The number of ways in which these books are divided into two groups of $p$ books and $q$ books then -

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 9 - Permutation and Combination>EXERCISE-2>Q 21

Number of dissimilar terms in the expansion of

{(x_{1} + x_{2} + \dots \dots + x_{n})}^{3}

is -

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 9 - Permutation and Combination>EXERCISE-2>Q 22

A persons wants to invite one or more of his friend for a dinner party. In how many ways can he do so if he has eight friends :-

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 9 - Permutation and Combination>EXERCISE-2>Q 23

If

P (n, n)

denotes the number of permutations of

n

different things taken all at a time then

P (n, n)

is also identical to :-

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 9 - Permutation and Combination>EXERCISE-2>Q 24

Which of the following statement(s) is/are true :-

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 9 - Permutation and Combination>EXERCISE-3>Q 3

If

{}^{n + 1}C_{2} + 2 ({}^{2}C_{2} + {}^{3}C_{2} + {}^{4}C_{2} + . . . + {}^{n}C_{2}) = 1^{2} + 2^{2} + 3^{2} + . . . . . + 100^{2},

then the value of

n

is