Question 1 |
Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is _______
0.5 | |
0.65 | |
0.75 | |
0.8 |
Question 1 Explanation:
Total four possibilities {HH. HT, TH, TT}
The probability of getting at least one head is \frac{3}{4}.
The probability of getting at least one head is \frac{3}{4}.
Question 2 |
The divergence of the vector -yi+xj______
0 | |
1 | |
2 | |
0.5 |
Question 2 Explanation:
\begin{aligned} \vec { F } & = - y \bar { i } + x \bar { j } \\ \nabla \cdot \bar { F } & = \frac { \partial } { \partial x } ( - y ) + \frac { \partial } { \partial y } ( x ) \\ & = 0 + 0 = 0 \end{aligned}
Question 3 |
The determinant of a 2x2 matrix is 50. If one eigenvalue of the matrix is 10, the other eigenvalue is _____.
5 | |
6 | |
7 | |
8 |
Question 3 Explanation:
The product of eigen value of always equal to
the determinant value of the matrix.
\begin{aligned} \lambda_{1} &=10 \quad \lambda_{2}=\text { unknown } \quad|A|=50 \\ \lambda_{1} \cdot \lambda_{2} &=50 \\ 10\left(\lambda_{2}\right) &=50\\ \therefore \qquad \lambda_{2}&=5 \\ \end{aligned}
the determinant value of the matrix.
\begin{aligned} \lambda_{1} &=10 \quad \lambda_{2}=\text { unknown } \quad|A|=50 \\ \lambda_{1} \cdot \lambda_{2} &=50 \\ 10\left(\lambda_{2}\right) &=50\\ \therefore \qquad \lambda_{2}&=5 \\ \end{aligned}
Question 4 |
A sample of 15 data is follows: 17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3. The mode of the data is
4 | |
13 | |
17 | |
20 |
Question 4 Explanation:
Mode means highest number of observations
or occurrence of data most of the time as data
17, occurs four times, i.e., highest time. So
mode is 17.
Question 5 |
The Laplace transform of te^{t} is
\frac{s}{(s+1)^{2}} | |
\frac{1}{(s-1)^{2}} | |
\frac{1}{(s+1)^{2}} | |
\frac{s}{s-1} |
Question 5 Explanation:
f ( t ) = t e ^ { t }
L ( t ) = \frac { 1 } { s ^ { 2 } }
By first shifting rule
L\left( t e ^ { t } \right) = \frac { 1 } { ( s - 1 ) ^ { 2 } }
L ( t ) = \frac { 1 } { s ^ { 2 } }
By first shifting rule
L\left( t e ^ { t } \right) = \frac { 1 } { ( s - 1 ) ^ { 2 } }
There are 5 questions to complete.