Mechanical Engineering - Online Test
Q1. The integral 
when evaluated by using Simpson’s 1/3 rule on two equal
subintervals each of length 1, equals
when evaluated by using Simpson’s 1/3 rule on two equal
subintervals each of length 1, equals
Answer : Option C
Explaination / Solution:
Q2. Consider the differential equation 
. The general solution with
constant c is
. The general solution with
constant c is
Answer : Option D
Explaination / Solution:
No Explaination.
Q3. An unbiased coin is tossed five times. The outcome of each toss is either a head
or a tail. The probability of getting at least one head is
Answer : Option D
Explaination / Solution:
P(at least one head) = 1- P (no heads) = 1 - (1/25) = 31/32
Q4. Consider the following system of equations
2x1 + x2 + x3 = 0,
x2 - x3 = 0,
x1 + x2 = 0.
This system has
Answer : Option C
Explaination / Solution:
No Explaination.
Q5. The Laplace transform of tet is
Answer : Option B
Explaination / Solution:
Q6. If f(z) = (x2 +ay2) + ibxy is a complex analytic function of z = x + iy, where i = √-1, then
Answer : Option B
Explaination / Solution:
Clearly for b = 2 and a= –1 above Cauchy-Riemann equations holds
Q7. 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
Q8. 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,
Q9. 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,
Q10. 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
