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.

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