Le S. 1+2 +2 1+2+3 +2+3 100 S, n. then n is equal 1+2+ +2+ (c) 200 199 99 (d) 19

Let S_n=1+q+q^2 +...+q^n and T_n =1+((q+1)/2)+((q+1)/2)^2+...((q+1)/2)^n If alpha T_100=^101C_1 +^101C_2 x S_1 ...+^101C_101 x S_100, then the value of alpha is equal to (A) 2^99 (B) 2^101 (C) 2^100 (D) -2^100

Let S_n=1+q+q^2 +?+q^n and T_n =1+((q+1)/2)+((q+1)/2)^2+?+((q+1)/2)^n If alpha T_100=^101C_1 +^101C_2 xS_1 +^101C_101 xS_100, then the value of alpha is equal to (A) 2^99 (B) 2^101 (C) 2^100 (D) -2^100

If S_n=sum_(r=1)^n(1+2+2^2+ .......+2^r)/(2^r), then S_n is equal to (a) 2^n n-1 (b) 1-1/(2^n) (c) n -1+1/(2^n) (d) 2^n-1

In a series of 2n observations, half of them equal a end remaining half equal -a. If the S.D. of the observationsis 2, then |a| equals (1) 1/n (2) sqrt2 (3) 2 (4) sqrt2/n

In a series of 2n observations, half of them equal a end remaining half equal -a. If the S.D. of the observationsis 2, then |a| equals (1) 1/n (2) sqrt2 (3) 2 (4) sqrt2/n

If S= tan^-1 (1/(n^2+n+1))+tan^-1 (1/(n^2+3n+3))+…+tan^-1 (1/(1+(n+19)(n+20))) then tan S is equal to (A) 20/(401+20n) (B) n/(n^2+20n+1) (C) n(401+20n) (D) 20/(n^2+n-1)

If S= tan^-1 (1/(n^2+n+1))+tan^-1 (1/(n^2+3n+3))+…+tan^-1 (1/(1+(n+19)(n+20))) then tan S is equal to (A) 20/(401+20n) (B) n/(n^2+20n+1) (C) n(401+20n) (D) 20/(n^2+n-1)

Let S_(n)=1+q+q^(2)+?+q^(n) and T_(n)=1+((q+1)/(2))+((q+1)/(2))^(2)+?+((q+1)/(2)) If alpha T_(100)=^(101)C_(1)+^(101)C_(2)xS_(1)+^(101)C_(101)xS_(100), then the value of alpha is equal to (A) 2^(99)(B)2^(101)(C)2^(100) (D) -2^(100)

Let A = [[1, (-1-isqrt(3))/(2)],[(-1+isqrt(3))/(2),1]] . Then , A^(100) is equal to a) 2^(100)A b) 2^(99)A c) 2^(98)A d)A

If S_(n)=sum_(r=1)^(n)(1+2+2^(2)+......+2^(r))/(2^(r)), then S_(n) is equal to (a)2^(n)n-1( b) 1-(1)/(2^(n))(c)2n-1+(1)/(2^(n))(d)2^(n)-1