If `A=[(1,1),(1,0)] and n epsilon N` then `A^n` is equal to (A) `2^(n-1)A` (B) `2^nA` (C) `nA` (D) none of these

The number of terms in the expansion of (x+1/x+1)^n is (A) 2n (B) 2n+1 (C) 2n-1 (D) none of these

IF A = [(1,0),(1,1)] then for all natural numbers n A^n is equal to (A) [(1,0),(1,n)] (B) [(n,0),(1,1)] (C) [(1,0),(n,1)] (D) none of these

If (1+x)^n=a_0+a_1x+a_2x^2+....+a_nx^n , then (a_0-a_2+.....)^2+(a_1-a_3+.....)^2 is equal to (A) 3^n (B) 2^n (C) ((1-2^n)/(1+2^n)) (D) none of these

Lt_(nrarroo) {(n!)/(kn)^n}^(1/n), k!=0 , is equal to (A) k/e (B) e/k (C) 1/(ke) (D) none of these

tan^(-1)n ,tan^(-1)(n+1) and tan^(-1)(n+2),n in N , are the angles of a triangle if n= 1 (b) 2 (c) 3 (d) None of these

If A=[(n,0 ,0),( 0,n,0),( 0, 0,n)] and B=[(a_1,a_2,a_3),(b_1,b_2,b_3),(c_1,c_2,c_3)] , then A B is equal to (A) B (B) n B (C) B^n (D) A+B

If S_n=[1/(1+sqrt(n))+1/(2+sqrt(2n))+....+1/(n+sqrt(n^2))] then (lim)_(n ->oo)S_n is equal to (A) log 2 (B) log4 (C) log8 (D) none of these

If m ,n in Na n dm^2-n^2=13 ,t h e n(m+1)(n+1) is equal to a. 42 b. 56 c. 50 d. none of these

Find sum of sum_(r=1)^n r . C (2n,r) (a) n*2^(2n-1) (b) 2^(2n-1) (c) 2^(n-1)+1 (d) None of these

The value of sum_(r=1)^(n+1)(sum_(k=1)^n "^k C_(r-1)) ( where r ,k ,n in N) is equal to a. 2^(n+1)-2 b. 2^(n+1)-1 c. 2^(n+1) d. none of these