Evaluate C1 – 2. C2 + 3. C3 – 4. C4 +….+ (– 1)n+1n. Cn 

Find the 11^th in the expression of 

Find the term independent of x in 

Show that 11ⁿ⁺² + 12²ⁿ⁺¹ is divisible by 133.

The digit at unit place in the number 17¹⁹⁹⁵ + 11¹⁹⁹⁵ – 7¹⁹⁹⁵ is

If the sum of the coefficients in the expression of (1 + 2x)ⁿ is 6561. The greatest term in the expression at x = 1/2 is

The number of terms in the expression of (a + b + c)ⁿ, where n Ïµ N, is

The number of terms which are free from fractional powers in the expansion of (a^1/5 + b^2/3)⁴⁵, a ≠ b is

If n is an odd natural, then  equals

The coefficient of x^m in (1 + x)^r + (1 + x)^r+1 + (1 + x)^r+2 +….+ (1 + x)ⁿ. r≤ m ≤ n is