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# Engineering Mathematics : Nuclear Quiz 2

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Question 1

A continuous random variable x has a probability density function f (x) = e–x, 0 < x < ∞ the P (x > 1) is

Question 2

Let X be a random variable with probability density function

The probability p(0.5<x<5) is ________

Question 3

Find the probability of getting  in  of a unbiased coin.

Question 4

Possibility of Ajay clearing an exam or failing in that exam are equal. Find the probability that Ajay will clear this exam at most once in 6 trials.

Question 5

A fair six-sided dice is rolled twice. Assume six-sided dice is numbered as 0, 1, 2, 3, 4, 6. Given that the sum of values shown at first and second roll is 6, what is the probability that the value of the first rolled dice is less than or equal to the value of the second rolled dice?

Question 6

Let P(E) denote the probability of the occurrence of event E.
If P(A) = 0.5 and P(B) = 1, then the values of P(A/B) and P(B/A) respectively are

Question 7

If A and B are both non-singular n x n matrices, then which of the following statement is NOT TRUE. Note: det represents the determinant of a matrix.

Question 8

Let X be a square matrix. Consider the following two statements on X.

I. X is invertible.

II. Determinant of X is non-zero.

Which one of the following is TRUE?

Question 9

For the system of equations

the value of x and y are respectively:

Question 10

The value of a for which the following system has infinite solutions

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