Question
1
The differential equation for the family of curves x2 + y2 - 2ay=0, where a is an arbitrary constant is
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2(x2 - y2)y' = xy
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(x2 - y2)y' = 2xy
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2(x2 + y2)y' = xy
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(x2 + y2)y' = 2xy
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Question
2
The range of the function f(x)= 7-x P
x-3 is
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{1, 2, 3, 4, 5}
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{1, 2, 3}
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{1, 2, 3, 4}
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{1, 2, 3, 4, 5, 6}
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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
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transitive
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not symmetric
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a function
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reflexive
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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
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(3a, 3a, 3a), (a, a, a)
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(3a, 2a, 3a), (a, a, a)
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(3a, 2a, 3a), (a, a, 2a)
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(2a, 3a, 3a), (2a, a, a)
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Question
7
The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is
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219/256
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37/256
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128/256
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28/256
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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?
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only (a)
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only (b)
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only (a) and (b)
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(a), (b) and (c)
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