A vehicle registration number consists of 2 letters of English alphabet followed by 4 digits, where the first digit is not zero. Then, the total number of vehicles with distinct registration numbers is
Four speakers will address a meeting where speaker Q will always speak P. Then, the number of ways in which the order of speakers can be prepared is
256
128
24
12
Let the coefficients of powers of x in the 2nd, 3rd and 4th terms in the expansion of (1 + x)n, where n is a positive integer, be in arithmetic progression. Then, the sum of the coefficients of odd powers of x in the expansion is
32
64
128
256
Let f(x) = ax2 + bx + c, g(x) = px2 + qx + r such that f(1) = g(1), f(2) = g(2) and f(3) - g(3) = 2. Then, f(4) - g(4) is
4
5
6
7
The sum 1 x 1! + 2 x 2! + ... + 50 x 50! equals
51!
51! + 1
51! + 1
2 51!
B.
51! + 1
1 x 1! + 2 x 2! + ... + 50 x 50!
= (2 - 1)1! + (3 - 1)2! + (4 - 1)3! + ... + (51 - 1)50!
= (2! - 1!) + (3! - 2!) + (4! - 3!) + ... + (51! - 50!)
= 51! - 1!
= 51! - 1
Six numbers are in AP such that their sum is 3. The first term is 4 times the third term. Then, the fifth term is
- 15
- 3
9
- 4
The equations x2 + x + a= 0 and x2 + ax + 1 = 0 have a common real root
for no value of a
for exactly one value of a
for exactly two value of a
for exactly three value of a