The coefficient t²⁴ in (1 + t²)¹² (1 + t¹²) (1 + t²⁴) is

For natural number m, n if (1 – y)m (1 + y)n = 1 + a₁ y + a₂ y² +….. and a₁ = a₂ = 10, them (m, n) is

If x is + ive, the first – ive term in the expansion of (1 + x)^27/5 is:

Coefficients of x¹¹ in the expansion of (2x² + x – 3)⁶ is

Coefficients of x¹⁰ in the expansion of (1 + x² – x³)⁸ is

The expression [x + (x³ - 1)^1/2]⁵ + [x – (x³ – 1)^1/2]⁵ is a polynomial of degree

The degree of the polynomial

              is equal to

 where {x} = Fractional part of x then the value of sec ^–1 (8θ) is

The remainder left out when 82n – (62)²ⁿ⁺¹ is divided by 9 is