[" 2.If "A=[[1,1],[1,1]]" ,then "A^(100)" is equal to "],[[" (A) "2^(100)" .A "," (B) "2^(99)" A "],[" (C) "100A," (D) "99A]]

A=[[1,11,1]] then prove that A^(100)=2^(99)A

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 A=det[[1,11,1]] and A^(100)=lambda^(99)A, then the value of lambda is

sin(tan^(-1)99 + cot^(-1)99) is equal to a) 0 b) -1 c) 1/2 d) 1

If f(x)=x^(100)+x^(99)++x+1, then f'(1) is equal to 5050 b.5049 c.5051 d.50051

If the remainder R(x)=ax+b is ontained by dividing the polynomial x^(100) by the polynomial x^(2)-3x+2 then (A) a=2^(100)-1 (B) b=2(2^(99)-1) (C) b=-2(2^(99)-1) (D) a=2^(100)

If the remainder R(x)=ax+b is ontained by dividing the polynomial x^(100) by the polynomial x^(2)-3x+2 then (A) a=2^(100)-1 (B) b=2(2^(99)-1) (C) b=-2(2^(99)-1) (D) a=2^(100)

If f(x)=x^(100)+x^(99)+...+x+1, then f^(prime)(1) is equal to a. 5050 b. 5049 c. 5051 d. 50051

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