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
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
C.
Given that will lie on the circle (from the given figure). Since, point lies on the region containing origin.
So, point will be on the shaded region.
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