Let d(n) denotes the number of divisors of n including 1 and itself. Then, d (225), d (1125) and d(640) are
in AP
in HP
in GP
consecutive integers
C.
in GP
Here,
If (2 + i) and are the roots of the equation (x2 + ax + b )(x2 + ex + d) = 0, where a, b, c and d are real constants, then product of all the roots of the equation is
40
9
45
35
Let S = , where N is the set of all natural numbers. Then, the number of elements in the set
6
7
13
14
If the point lies in the region between the lines x + y = 2 and x - y = 2 containing the origin, then 0 lies in
Number of points having distance from the straight line x - 2y + 1 = 0 and a distance is from the line 2x + 3y - 1 = 0, is
1
2
4
5
Let P(x) be a polynomial, which when divided by (x - 3) and (x - 5) leaves remainders 10 and 6, respectively. If the polynomial is divided by (x - 3) (x - 5), then the remainder is
- 2x + 16
16
2x - 16
60
A person goes to office by car, scooter, bus and train, probability of which are 1/7, 3/7, 2/7 and 1/7, respectively. Probability that he reaches office late, if he takes car, scooter, bus or train is 2/9, 1/9, 4/9, and 1/9, respectively. Given that he reached office in time, the probability that he travelled by a car, is
1/7
2/7
3/7
4/7
Let f : N R be such that f(1) = 1 and f(1) + 2f(2) + 3f(3) + ... + nf(n) = n(n+ 1) f(n), for all n N, n 2, where N is the set of natural numbers and R is the set of real numbers. Then, the value of f(500) is
1000
500
1/500
1/1000