# GATE ME 2017 SET-2

 Question 1
Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is _______
 A 0.5 B 0.65 C 0.75 D 0.8
Engineering Mathematics   Probability and Statistics
Question 1 Explanation:
Total four possibilities {HH. HT, TH, TT}
The probability of getting at least one head is $\frac{3}{4}$.
 Question 2
The divergence of the vector -yi+xj______
 A 0 B 1 C 2 D 0.5
Engineering Mathematics   Calculus
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 _____.
 A 5 B 6 C 7 D 8
Engineering Mathematics   Linear Algebra
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}
 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
 A 4 B 13 C 17 D 20
Industrial Engineering   PERT and CPM
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
 A $\frac{s}{(s+1)^{2}}$ B $\frac{1}{(s-1)^{2}}$ C $\frac{1}{(s+1)^{2}}$ D $\frac{s}{s-1}$
Engineering Mathematics   Calculus
Question 5 Explanation:
$f ( t ) = t e ^ { t }$
$L ( t ) = \frac { 1 } { s ^ { 2 } }$
By first shifting rule
$L\left( t e ^ { t } \right) = \frac { 1 } { ( s - 1 ) ^ { 2 } }$

There are 5 questions to complete.