If the coefficients of (2r+1)^th term and (4r+5)^th term in the expansion of (1+x)¹⁰ are equal then r=

If the 3^rd, 4^th and 5^th terms of (x+a)ⁿ are 720, 1080 and 810 respectively then (x,a,n)=

xⁿ-1 is divisible by x-k. Then the least +ve integral value of K is

The point which divides the line segment joining the points( 1,-1,2), (2,3,7) in the ratio -2:3 is

The first three terms in the expansion of (1+x+x²)¹⁰ are

C₀+4.C₁+7.C₂+……(n+1) terms =

The number of terms which are free from radical signs in the expansion of (x^1/5+y^1/10)⁵⁵ is

If the third term in the expansion of (1/x+ xlog₁₀ x)⁵ is 1, then x=

2.C₀+2².C₁/2+2³.C₃/3+……..+2ⁿ⁺¹.C_n/n+1 =

If n is odd then C₀²-C₁²+C₂²-……….+(-1)ⁿ C_n² =