GATE/ISRO/BARC/DRDO EXAM QUESTION AND ANSWER

(1)-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 ______.
Solution:Probability of A speaking a truth, P (A) =

Probability of B speaking a truth,P (B) =

Now, we needed

(2)-The Laplace transformation of is

Solution:

We know that

but,

(3)-If a function is defined in the interval (0, a), then definite integral of f(x) i.e. is called improper integral when;

Solution:

Range of integration is infinite and integrand is bounded & Range of integration is definite and integrand is unbounded. An improper integral is a definite integral that has either or both limits infinite or an integrand that approaches infinity at one or more points in the range of integration

(4)-The value of k for which the lines 2x+y-1=0, 4x+3y-3=0 and 3x+ky-2=0, are concurrent is..?

Solution:

For concurrent the coefficient determinant should be zero, so

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