Practice Questions on Engineering Mathematics

Q6.

Find the limit

\(X(s)=\dfrac{10(s+1)}{s(s^2+4s+3)}\)

A.

\(10/3\)

B.

\(17/3\)

C.

\(10/7\)

D.

\(3/7\)

 View Ans

Q7.

Consider two independent random variables $ X $  and $ Y $  with identical distributions. 

The  variables  $ X $ and $ Y $ take values 0, 1 and  2 with probabilities $ 1/2$, $1/4 $, $1/4 $ respectively.

What is the conditional probability,
\[ \text P(X+Y=2|X-Y=0)\]

A.

3.455

B.

2.144

C.

1.098

D.

0.166

 View Ans

Q8.

The residues of a complex function
\[x(z)=\dfrac{(1-3z)}{z(z-1)(z-3)}\]
at it's poles

A.

$ 1, 2, -1 $

B.

$\dfrac{1}{2}, 0, -1  $

C.

$  \dfrac{1}{3}, 1, -\dfrac{4}{3}$

D.

$ -\dfrac{1}{3}, 0, 1 $

 View Ans

Q9.

What is value of the integral

\[\text I=\dfrac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}\exp\left(-\dfrac{x^2}{32}\right)dx\]

A.

2

B.

3

C.

4

D.

6

 View Ans

Q10.

A box contains 3 white cards and 2 black cards. Another bag contains 2 white and 4 black cards. A box and a card are picked random. The probability that the card will be white is:

A.

3/11

B.

6/7

C.

7/15

D.

9/11

 View Ans


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