The number `51^(49)+51^(48)+51^(47)+....+51+1` is divisible by a. 10 b. 20 c. `25` d. `50`

If x^(51)+ 51 is divided by x + 1 , then the remainder is

The remainder when 27^(10)+7^(51) is divided by 10

The value of ^15 C0 2-^(15)C12+^(15)C2 2-^(15)C 15 2 is 15 b. -15 c. 0 d. 51

The greatest integer by which 1+sum_(r=1)^(30)rxxr ! is divisible is a. composite number b. odd number c. divisible by 3 d. none of these

The value of sum_(r=0)^(50)(-1)^r((50)C_r)/(r+2) is equal to a . 1/(50xx51) b. 1/(52xx50) c. 1/(52xx51) d. none of these

A fair coin is tossed 99 times. If X is the number of times heads occur, then P(X=r) is maximum when r is a. 49 , 50 b. 50 , 51 c. 51 , 52 d. none of these

The coefficient x^5 in the expansion of (1+x)^(21)+(1+x)^(22)++(1+x)^(30) is a. "^51 C_5 b. "^9C_5 c. "^31 C_6 -"^(21)C_6 d. "^30 C_5 + "^(20)C_5