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

The middle term in the expansion of \({ \left( x+\frac { 1 }{ x } \right) }^{ 10 }\) is _______.

There are 10 true or false questions in an examination. Then these questions can be answered in ______.

The value of (5C₀ + 5C₁) + (5C₁ + 5C₂) + (5C₂ + 5C₃) + (5C₃ + 5C₄) + (5C₄ + 5C₅ ) is ________.

Number of words with or without meaning that can be formed using letters of the word "EQUATION" , with no repetition of letters is _____.

Evaluate the following using binomial theorem: (101)⁴

Evaluate the following using binomial theorem:(999)⁵

Evaluate the following expression.\(\frac { 8! }{ 5! } \)

Find n if 25 C_n+5 = 25 C_2n-1.

If 15C_3r = 15C_{r + 3} , find r

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

Find the middle terms in the expansion of \({ \left( 3x+\frac { { x }^{ 2 } }{ 2 } \right) }^{ 8 }\)

Find the number of arrangements that can be made out of the letters of the word "ASSASSINATION".

Find the Co-efficient of x¹¹ in the expansion of \({ \left( x+\frac { 2 }{ { x }^{ 2 } } \right) }^{ 17 }\)

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

In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?

In how many ways can the following prizes be given away to a class of 30 students, first and second in mathematics, first and second in physics, first in chemistry and first in English?

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

Resolve into partial fractions:\(\frac{2x+1}{(x-1)(x^2+1)}\)