ME GATE 2016 - Online Test
Q1. The solution to the system of equations 
Answer : Option D
Explaination / Solution:
On comparing the matrix, we get
2x + 5y = 2 ………………(1)
-4x + 3y = -30 ………….(2)
By solving the equation (1) and (2)
We get
x = 6, y = -2
Q2. If f(t) is a function defined for all t ≥ 0, its Laplace transform F(s) is
defined is
Answer : Option B
Explaination / Solution:
As we know that, the Laplace transform of the function f(t) is given
by,
Q3. f(z) = u(x,y) + iv(x,y) is an analytic function of complex variable z =
x + i y where 𝑖 = √−1. If u(x,y) = 2xy, then v(x,y) may be expressed
as
Answer : Option A
Explaination / Solution:
Given that f(z) = u(x,y) + iν (x,y) is analytic function of complex
variable z = x + iy. Then the function derivatives can be given as,
Q4. Consider a Poisson distribution for the tossing of a biased coin. The
mean for this distribution is μ. The standard deviation for this
distribution is given by
Answer : Option A
Explaination / Solution:
As we know that, for the poisson distribution,
mean = variance = μ
And also, we know that,
Standard deviation =√𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒
⇒ Standard deviation= √μ
Q5. Point mass M is released from rest and slides down a spherical bowl
(of radius R) from a height H as shown in the figure below. The
surface of the bowl is smooth (no friction). The velocity of the mass
at the bottom of the bowl is
Answer : Option C
Explaination / Solution:
From the principle of energy conservation,
Kinetic energy at the bottom = Potential energy at height H
1/2 mv2 = mgH ⇒ v = √2gH
Q6. Maximize Z=15X1 + 20X2 subject to
12X1 + 4X2 ≥ 36
12X1 – 6X2 ≤ 24
Xv X2 ≥ 0
The above linear programming problem has
Answer : Option B
Explaination / Solution:
Max z = 15x1 + 20x2 
Converting constraints equation, we get
12x1 + 4x2 = 36 ___________(1)
12x1 - 6x2 = 24 ___________(2)
We cannot optimize the constraints, as these does not have any
bounded region.
Hence, solution is unbounded.
