Question 1 |
If E denotes expectation, the variance of a random variable X is given by
E[X^{2}]-E^{2}[X] | |
E[X^{2}]+E^{2}[X] | |
E[X^{2}] | |
E^{2}[X] |
Question 1 Explanation:
\begin{array}{l} \sigma_{X}^{2}=E\left[X^{2}\right]-E^{2}[X] \\ \text { AC. Power }=\text { Total power - DC power } \end{array}
Question 2 |
The following plot shows a function which varies linearly with x. The value of
the integral I=\int_{1}^{2} ydx is
1 | |
2.5 | |
4 | |
5 |
Question 2 Explanation:
\begin{aligned} y &=x+1 \\ I &=\int_{1}^{2} y d x \\ &=\int_{1}^{2}(x+1) d x=\left.\frac{(x+1)^{2}}{2}\right|_{1} \\ &=\frac{1}{2}(9-4)=2.5 \end{aligned}
Question 3 |
For |x| \lt \lt 1, \; coth (x) can be approximated as
x | |
x^{2} | |
\frac{1}{x} | |
\frac{1}{x^{2}} |
Question 3 Explanation:
\cot h x=\frac{\cos h x}{\sin h x}=\frac{1}{x}
Question 4 |
\lim_{\theta \rightarrow 0}\frac{sin(\frac{\theta }{2})}{\theta } is
0.5 | |
1 | |
2 | |
not defined |
Question 4 Explanation:
\lim _{\theta \rightarrow 0} \frac{\frac{1}{2} \times \sin \left(\frac{\theta}{2}\right)}{\theta \times \frac{1}{2}}=\frac{1}{2} \lim _{\theta \rightarrow 0} \frac{\sin \frac{\theta}{2}}{\frac{\theta}{2}}=\frac{1}{2}=0.5
Question 5 |
Which one of following functions is strictly bounded?
1/x^{2} | |
e^{x} | |
x^{2} | |
e^{-x^{2}} |
Question 5 Explanation:
y=\frac{1}{x^{2}}
y=\theta^{x}
y=x^{2}
y=e^{-x^{2}}
There are 5 questions to complete.