Question 1 |
At least one eigenvalue of a singular matrix is
positive | |
zero | |
negative | |
imaginary |
Question 1 Explanation:
For singular matrix
|A|=0
According to properties of eigen value
Product of eigen values =|A|=0
\Rightarrow Atleast one of the eigen value is zero.
|A|=0
According to properties of eigen value
Product of eigen values =|A|=0
\Rightarrow Atleast one of the eigen value is zero.
Question 2 |
At x = 0, the function f(x)=\left | x \right | has
a minimum | |
a maximum | |
a point of inflexion | |
neither a maximum nor minimum |
Question 2 Explanation:
The graph of |x| is
from the graph we can say that
|x| has minimum at x=0
from the graph we can say that
|x| has minimum at x=0
Question 3 |
Curl of vector V(x,y,z)= 2x^{2}i+3z^{2}j+y^{3}k at x=y=z=1 is
-3i | |
3i | |
3i-4j | |
3i-6k |
Question 3 Explanation:
Curl of vector =\left|\begin{array}{ccc} i & j & k \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ 2 x^{2} & 3 z^{2} & y^{3} \end{array}\right|
=i\left[\frac{\partial}{\partial x}\left(y^{3}\right) \frac{\partial}{\partial z}\left(3 z^{2}\right)\right]+j\left[\frac{\partial}{\partial x}\left(y^{3}\right) \frac{\partial}{\partial z}\left(2 x^{2}\right)\right]
+k\left[\frac{\partial}{\partial x}\left(3z^{2}\right) \frac{\partial}{\partial z}\left(2 x^{2}\right)\right]
=i\left[3 y^{2}-6 z\right]-[10]+k[0+0]
\text { At } x=1, y=1 \text { and } z=1
\text { Curl }=i\left(3 \times 1^{2}-6 \times 1\right)=-3 i
=i\left[\frac{\partial}{\partial x}\left(y^{3}\right) \frac{\partial}{\partial z}\left(3 z^{2}\right)\right]+j\left[\frac{\partial}{\partial x}\left(y^{3}\right) \frac{\partial}{\partial z}\left(2 x^{2}\right)\right]
+k\left[\frac{\partial}{\partial x}\left(3z^{2}\right) \frac{\partial}{\partial z}\left(2 x^{2}\right)\right]
=i\left[3 y^{2}-6 z\right]-[10]+k[0+0]
\text { At } x=1, y=1 \text { and } z=1
\text { Curl }=i\left(3 \times 1^{2}-6 \times 1\right)=-3 i
Question 4 |
The Laplace transform of e^{i5t} where i=\sqrt{-1} is
(s-5i)/(s^{2}-25) | |
(s+5i)/(s^{2}+25) | |
(s+5i)/(s^{2}-25) | |
(s-5i)/(s^{2}+25) |
Question 4 Explanation:
\begin{aligned}
e^{j 5 t} &=\cos 5 t+i \sin 5 t \\
L\left\{e^{(i 5 f)}\right\}&=\frac{s}{s^{2}+25}+\frac{5 i}{s^{2}+25} \\
&=\frac{s+5 i}{s^{2}+25} 2 e^{-x^{2}}
\end{aligned}
Question 5 |
Three vendors were asked to supply a very high precision component. The respective probabilities of their meeting the strict design specifications are 0.8, 0.7 and 0.5. Each vendor supplies one component. The probability that out of total three components supplied by the vendors, at least one will meet the design specification is ___________
0.12 | |
0.97 | |
0.65 | |
1 |
Question 5 Explanation:
Probability of atleast one meet the specification
\begin{aligned} &=1-(\bar{A} \cap \bar{B} \cap \bar{C}) \\ &=1-(0.2 \times 0.3 \times 0.5) \\ &=0.97 \end{aligned}
\begin{aligned} &=1-(\bar{A} \cap \bar{B} \cap \bar{C}) \\ &=1-(0.2 \times 0.3 \times 0.5) \\ &=0.97 \end{aligned}
There are 5 questions to complete.