Question
1
The differential equation for the family of curves x^{2} + y^{2}  2ay=0, where a is an arbitrary constant is
(x^{2}  y^{2})y' = 2xy


2(x^{2}  y^{2})y' = xy


(x^{2} + y^{2})y' = 2xy


2(x^{2} + y^{2})y' = xy


Question
2
The range of the function f(x)= ^{7}^{}^{x} P _{
x3 is}
{1, 2, 3, 4, 5}


{1, 2, 3, 4}


{1, 2, 3}


{1, 2, 3, 4, 5, 6}


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
transitive


not symmetric


a function


reflexive


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 coplanar then λ equals
Question
5
If (1 – p) is a root of quadratic equation x^{2} + 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 coordinates of each of the point of intersection are given by
(3a, 2a, 3a), (a, a, 2a)


(3a, 2a, 3a), (a, a, a)


(2a, 3a, 3a), (2a, 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
219/256


28/256


128/256


37/256


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)


only (a) and (b)


(a), (b) and (c)



