`(a+2b)^2+101( a+2b)+100`

Factorise a^(2) b - b^(3) . Using this result, find the value of 101^(2) xx 100 - 100^(3)

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

The HCF of 100 and 101 is 10100 (b) 1001 (c) 10101 (d) None of these

The HCF of 100 and 101 is (a)10100 (b) 1001 (c) 10101 (d) None of these

The number of whole numbers between the smallest whole number and the greatest 2-digit number is 101 (b) 100 (c) 99 (d) 98

Evaluate : 101^(2) - 100^(2)

If the coefficient of x^100 is in 1+(1+x)+(1+x)^2+(1+x)^3+………+(1+x)^n , (n >= 100) is ^201C_101 then n (A) 100 (B) 200 (C) 101 (D) none of these