Civil Engineering - Online Test
Q1. Let x be a continuous variable defined over the interval (−∞, ∞), and 
Answer : Option B
Explaination / Solution:
Q2. For the function f(x) = a + bx, 0 ≤ x ≤ 1, to be a valid probability density function, which one of the following statements is correct?
Answer : Option B
Explaination / Solution:
f(x) = a + bx 0 ≤ x ≤1 iis a valid probability density function
a=0.5, b=1 satisfies the above relation
Q3. Consider the matrix 
Which one of the following statements is TRUE for the
eigenvalues and eigenvectors of this matrix?
Which one of the following statements is TRUE for the
eigenvalues and eigenvectors of this matrix?
Answer : Option A
Explaination / Solution:
e(A) = 1
Number of linearly independent eigen vectors corresponding to eigen value λ = 3 is
n-r=2-1=1 where n= no. of unknowns, r= rank of( A − λI)
One linearly independent eigen vector exists corresponding to λ = 3
Q4. The solution of the equation (dQ/dt) + Q = 1 with Q = 0 at t = 0 is
Answer : Option D
Explaination / Solution:
(dQ/dt) + Q = 1 and Q = 0 at t = 0
Comparing with first order linear differential equations
Q5. The following sequence of numbers is arranged in increasing order: 1, x, x, x, y, y,9,16,18.
Given that the mean and median are equal, and are also equal to twice the mode, the value of
y is
Answer : Option D
Explaination / Solution:
Given, Mean = Median = 2Mode
Mean = Median = 2x [Mode = x].............. (1)
Mean of the data = (3x + 2y + 44)/9
2x = (3x + 2y + 44)/9
15x - 2y = 44.............(2)
Median of the data = y.........(3)
y = 2x ..........(4)
From (2); 11x = 44
x = 4
y = 8
Q6. If the radius of a right circular cone is increased by 50%, its volume increases by
Answer : Option C
Explaination / Solution:
Given, radius of a right circular cone is increased by 50%. 
Let, height of the circular cone=(h)
Q7. In a process, the number of cycles to failure decreases exponentially with an increase
in load. At a load of 80 units, it takes 100 cycles for failure. When the load is halved, it
takes 10000 cycles for failure. The load for which the failure will happen in 5000
cycles is __________.
Answer : Option B
Explaination / Solution:
From the data given we assume
load = exp onent/log(cycles)
80 = x/log(10000)
x = 160
40 = x/log(10000)
x = 160
load = 160/log 5000 = 43.25
Q8. If f(x7) = 2x7 + 3x - 5, which of the following is a factor of f(x)?
Answer : Option B
Explaination / Solution:
from the option (b0 substitute x=1 in
2x7 + 3x - 5 = 0
2(1)7 + 3(1) - 5 = 0
5 - 5 = 0
So (x - 1) is a factor of f (x)
Q9. The type of partial differential equation 
Answer : Option C
Explaination / Solution:
Comparing the given equation with the general form of second order partial differential
equation, we have A=1, B=3, C=1
B2- 4AC = 5 > 0
P.D.E
is Hyperbola.
Q10. If the entries in each column of a square matrix M add up to 1, then an eigen value of M
is
Answer : Option D
Explaination / Solution:
Consider the '2x2 ' square matrix 
Characteristic equation of M is
Characteristic equation of M isλ2 - (a + d)λ + (ad - bc) = 0......................(1)
Put λ =1, weget
1 - (a + d) + ad - bc = 0
1 - a - d + ad - (1 - d)(1 - a) = 0
1 - a - d + ad - 1 + a + d - ad = 0
0 = 0,which is true
λ = 1
Satisfies the equation (1) but λ = 2,3,4
does not satisfy the equation (1). For all
possible values of a,d
