If nC₃ = nC₂, then the value of nC₄ is _______.

The value of n, when nP₂ = 20 is _______.

The number of ways selecting 4 players out of 5 is _______.

If nP_r = 720 (nC_r), then r is equal to ______.

The possible out comes when a coin is tossed five times _________.

Expand the following by using binomial theorem.\(\left( x+\frac { 1 }{ y } \right) ^{ 7 }\)

Expand the following by using binomial theorem.\({ \left( x+\frac { 1 }{ { x }^{ 2 } } \right) }^{ 6 }\)

Evaluate the following using binomial theorem: (101)⁴

ResoIve into partial fractions :\(\frac { 12x-17 }{ (x-2)(x-1) } \)

In a railway compartment, 6 seats are vacant on a bench. In how many ways can 3 passengers sit on them?

Evaluate\(\frac { 1 }{ 5! } +\frac { 1 }{ 6! } +\frac { 1 }{ 7! } \)

Find the 5^th term in the expansion of (x - 2y)^13.

Resolve into partial fractions for the following : \(\frac{2 x^2-5 x-7}{(x-2)^3}\)

Resolve into partial fractions for the following : \(\frac{x^2-3}{(x+2)\left(x^2+1\right)}\)

There are 6 gentlemen and 4 ladies to line at a round table. In how many ways can they seat themselves so that no two ladies together?

In how many ways can n prizes be given to n boys, when a boy may receive any number of prizes?

In how many ways can 12 things be equally divided among 4 persons?

Prove that the term independent of x in the expansion of \({ \left( x+\frac { 1 }{ x } \right) }^{ 2n }is\quad \frac { 1.3.5.....,(2n-1){ 2 }^{ n } }{ n! } \)

If nP₄= 12(nP₂) find n.

If m parallel lines in a plane are intersected by a family of n parallel lines. Find the number of parallelogram formed?