Civil Engineering - Online Test
Q1. For matrices of same dimension M , N and scalar c, which one of these properties DOES NOT ALWAYS hold ?
Answer : Option D
Explaination / Solution:
Let the matrices
i.e. the property holds always
i.e. property does not hold always.
Q2. Consider two RCC beams, P and Q, each having the section 400 mm × 750 mm (effective depth, d = 750 mm) made with concrete having a τcmax = 2.1 N /mm2.
For the reinforcement provided and the grade of concrete used, it may be assumed
that the τc = 0.75 N/mm2. The design shear in beam P is 400 kN and in beam
Q is 750 kN. Considering the provisions of IS 456-2000, which of the following
statements is TRUE?
Answer : Option A
Explaination / Solution:
No Explaination.
Q3. C is a closed path in the z -plane by |z| = 3 The value of the integral 
is
is
Answer : Option C
Explaination / Solution:
Integral,
So, we have the singularity
z j + 2 = 0
z =- 2j
Since, z = -2j lies inside |z| = 3. Therefore, using cauchy’s integral, we get
Q4. The adjoining figure shows a schematic representation of a steel plate girder to
be used as a simply supported beam with a concentrated load. For stiffeners, PQ
(running between the top and bottom flanges) which of the following pairs of
statements will be TRUE?
Answer : Option B
Explaination / Solution:
No Explaination.
Q5. The 4-point Discrete Fourier Transform (DFT) of a discrete time sequence {1,0,2,3} is
Answer : Option D
Explaination / Solution:
Q6. A singly under-reamed, m8 long, RCC pile (shown in the adjoining figure) weighing
20 kN with 350 mm shaft diameter and 750 mm under-ream diameter is installed
within stiff, saturated silty clay (undrained shear strength is 50 kPa, adhesion
factor is 0.3, and the applicable bearing capacity factor is 9) to counteract the
impact of soil swelling on a structure constructed above. Neglecting suction and
the contribution of the under-ream to the adhesive shaft capacity, what would be
the estimated ultimate tensile capacity (rounded off to the nearest integer value
of kN) of the pile?
Answer : Option B
Explaination / Solution:
No Explaination.
Q7. The Taylor series expansion of 3 sin x + 2 cos x is
Answer : Option A
Explaination / Solution:
Given the function
f(x) = 3 sin x + 2 cos x
Now, we have the Taylor’s expansion for the trigonometric function as
Substituting it in equation (1), we get
Q8. A rigid beam is hinged at one end and supported on linear elastic springs (both having
a stiffness of ‘k ’) at points ‘1’ and ‘2’, and an inclined load acts at ‘2’, as shown.
Which of the following options represents the deflections δ1 and δ2 at points ‘1’
and ‘2’?
Answer : Option B
Explaination / Solution:
No Explaination.
Q9. For a function g (t), it is given that 
for any real value 𝜔. If 
is
for any real value 𝜔. If is
Answer : Option B
Explaination / Solution:
Given the relations
The Fourier transformation of f (t) is defined as
Now, from equation (2), we have
where u (t) is unit step function. Taking Fourier transform both the sides, we have
Q10. A rigid beam is hinged at one end and supported on linear elastic springs (both having a stiffness of ‘k ’) at points ‘1’ and ‘2’, and an inclined load acts at ‘2’, as shown.
If the load P equals 100 kN, which of the following options represents forces R1 and R2 is the springs at points ‘1’ and ‘2’?
Answer : Option D
Explaination / Solution:
No Explaination.
