The number of even divisor of the number `N=12600=2^3 3^2 5^2 7` is a. `72` b. `54` c. `18` d. none of these

Find the number of divisors of the number N=2^3 .3^5 .5^7 .7^9 which are perfect squares.

The number of real solutions of the equation (9//10)^x=-3+x-x^2 is a. 2 b. 0 c. 1 d. none of these

The total number of divisor of 480 that are of the form 4n+2,ngeq0, is equal to a. 2 b. 3 c. 4 d. none of these

A four figure number is formed of the figures 1, 2, 3, 5 with no repetitions. The probability that the number is divisible by 5 is a. 3//4 b. 1//4 c. 1//8 d. none of these

If ^n C_3+^n C_4>^(n+1)C_3 , then a. n >6 b. n >7 c. n<6 d. none of these

If a ,b ,c are three distinct positive real numbers, the number of real and distinct roots of a |x^2|+2b|x|-c=0 is a. 0 b. 4 c. 2 d. none of these

The number of different seven-digit numbers that can be written using only the three digits 1, 2, and 3 with the condition that the digit 2 occurs twice in each number is a. 2P_5 2^5 b. 7C_2 2^5 c. 7C_2 5^2 d. none of these

Among the 8! [permutations of the digits 1, 2, 3..., 8, consider those arrangements which have the following property. If we take any five consecutive positions the product of the digits in these positions is divisible by 5. The number of such arrangements is equal to a. 7! b. 2.(7!) c. ^7C_4 d. none of these

The number of distinct natural numbers up to a maximum of four digits and divisible by 5, which can be formed with the digits 0, 1 , 2, 3, 4, 5, 6, 7, 8, 9 each digit not occurring more than once in each number, is a. 1246 b. 952 c. 1106 d. none of these

The number of irrational roots of the equation (4x)/(x^2+x+3)+(5x)/(x^2-5x+3)=-3/2 is (a) 4 b. 0 c. 1 d. 2