If `sum n^2=2870, then sumn^3=` (A) 44100 (B) 48400 (C) 52900 (D) none of these

If (2+x)(2+x^2)(2+x^3)………..(2+x^100)=sum_(r=0)^n k_rx^r, then n= (A) 2550 (B) 5050 (C) 2^8 (D) none of these

If C_r stands for ^nC_r and sum_(r=1)^n (r.C_r)/(C_(r-1)=210 then n= (A) 19 (B) 20 (C) 21 (D) none of these

If sum_(n=1)^k [1/3+n/90]=21 where [x] dentes the integeral part of x, then k= (A) 84 (B) 80 (C) 85 (D) none of these

If a=sum_(r=1)^oo(1/r)^2, b=sum_(r=1)^oo1/((2r-1)^2), then a/b= (A) 5/4 (B) 4/5 (C) 3/4 (D) none of these

If 1^2+2^2+3^2+n^2=1015 then the value of n is equal to (A) 13 (B) 14 (C) 15 (D) none of these

The sum of the coefficients in the expansion of (2+5x^2-7x^3)^2000= (A) 0 (B) 1 (C) 2 (D) none of these

If sum_(r=1)^20(r^2+1)r!=k!20 then sum of all divisors of k of the from 7^n, n epsilin N is (A) 7 (B) 58 (C) 350 (D) none of these

Let n be a positive integer such that sin (pi/(2n))+cos (pi/(2n))= sqrt(n)/2 then (A) n=6 (B) n=1,2,3,….8 (C) n=5 (D) none of these

If a,b,c are proper fractiion are in H.P. and x sum_(n=1)^oo a^n, y=sum_(n=1)^oo b^n, z= sum_(n=1)^oo c^n then x,y,z are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If n is a whole number such that n+n=n ,\ t h e n\ n=? (a) 1 (b) 2 (c) 3 (d) none of these