Question
1
The differential equation for the family of curves x2 + y2 - 2ay=0, where a is an arbitrary constant is
|
(x2 - y2)y' = 2xy
|
|
|
2(x2 + y2)y' = xy
|
|
|
2(x2 - y2)y' = xy
|
|
|
(x2 + y2)y' = 2xy
|
|
Question
2
The range of the function f(x)= 7-x P
x-3 is
|
{1, 2, 3, 4}
|
|
|
{1, 2, 3, 4, 5, 6}
|
|
|
{1, 2, 3, 4, 5}
|
|
|
{1, 2, 3}
|
|
Question
3
Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is
|
reflexive
|
|
|
a function
|
|
|
not symmetric
|
|
|
transitive
|
|
Question
4
If the straight lines x = 1 + s, y = –3 – λs, z = 1 + λs and x = t/2 , y = 1 + t, z = 2 – t with parameters s and t respectively, are co-planar then λ equals
Question
5
If (1 – p) is a root of quadratic equation x2 + px + (1 - p) = 0, then its roots are
Question
6
A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates of each of the point of intersection are given by
|
(2a, 3a, 3a), (2a, a, a)
|
|
|
(3a, 2a, 3a), (a, a, 2a)
|
|
|
(3a, 2a, 3a), (a, a, a)
|
|
|
(3a, 3a, 3a), (a, a, a)
|
|
Question
7
The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is
|
37/256
|
|
|
28/256
|
|
|
219/256
|
|
|
128/256
|
|
Question
8
The probability that A speaks truth is 4/5, while this probability for B is 3/4. The probability that they contradict each other when asked to speak on a fact is
Question
9
In a series of 2n observations, half of them equal a and remaining half equal –a. If the standard deviation of the observations is 2, then |a| equals
Question
10
Consider the following statements: (a) Mode can be computed from histogram (b) Median is not independent of change of scale (c) Variance is independent of change of origin and scale. Which of these is/are correct?
|
only (b)
|
|
|
only (a) and (b)
|
|
|
only (a)
|
|
|
(a), (b) and (c)
|
|
|
|