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.

A 2n digit number starts with 2 and all its digits are prime, then the probability that the sum of all 2 consecutive digits of the number is prime is a. 4xx2^(3n) b. 4xx2^(-3n) c. 2^(3n) 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

Number of divisors of the form 4n+2(nge0) of the integer 240 is

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

A four figure number is formed of the figures 1, 2, 3, 4, 5 with no repetitions. The probability that the number is divisible by 5 is 3//4 b. 1//4 c. 1//8 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 0 b. 4 c. 2 d. none of these

The number of distinct real roots of the equation tan(2pix)/(x^2+x+1)=-sqrt(3) is (a) 4 (b) 5 (c) 6 (d) none of these

Coefficient of x^(18) in (1+x+2x^2+3x^3++18 x^(18))^2 equal to 995 b. 1005 c. 1235 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