Civil Engineering - Online Test
Q1. 
is equal to
is equal to
Answer : Option D
Explaination / Solution:
Q2. The two Eigen values of the matrix 
have a ratio of 3 : 1 for p = 2. What is another value
of p for which the Eigen values have the same ratio of 3 : 1?
have a ratio of 3 : 1 for p = 2. What is another value
of p for which the Eigen values have the same ratio of 3 : 1?
Answer : Option D
Explaination / Solution:
Let A = 
Given that two eigen values of A are in 3:1
Ratio for p = 2
⇒ Characteristic equation λ2 -4λ+3 = 0 (by substituting p=2)
⇒ λ=1,3
Eigen values 5, 5/3 are in ratio 3:1
P = 14/3
Q3. A fair (unbiased) coin was tossed four times in succession and resulted in the following
outcomes: (i) Head, (ii) Head, (iii) Head, (iv) Head. The probability of obtaining a 'Tail' when
the coin is tossed again is
Answer : Option B
Explaination / Solution:
No Explaination.
Q4. 
can be expressed as
can be expressed as
Answer : Option C
Explaination / Solution:
Q5. The integrating factor for the differential equation 
Answer : Option D
Explaination / Solution:
The standard form of Linear differential equations is
Q6. If {x} is a continuous, real valued random variable defined over the interval (−∞,+∞) and its occurrence is defined by the density function given as: 
where ‘a’ and
‘b’ are the statistical attributes of the random variable {x}. The value of the integral 
dx is
where ‘a’ and
‘b’ are the statistical attributes of the random variable {x}. The value of the integral dx is
Answer : Option B
Explaination / Solution:
Q7. The expression 
is equal to
is equal to
Answer : Option A
Explaination / Solution:
By L’ Hospital rule,
Q8. If |4x − 7| = 5 then the value of 2 |x| − |−x| is
Answer : Option B
Explaination / Solution:
|4x − 7| = 5; 4x − 7 = 5 or 4x − 7 = −5 ⇒ x = 3 or 0.5
2 |x| − |−x| = 2×3-3= 3 or 2 |x| − |−x| = 2×1/2-1/2 = 1/2
Q9.
[A] is a square matrix which is neither symmetric nor skew-symmetric and [A]T is its transpose. The sum and difference of these matrices are defined as [S]=[A]+ [A]T and [D]=[A]+ [A]T , respectively. Which of the following statements is TRUE?
Answer : Option D
Explaination / Solution:
No Explaination.
Q10. The square root of a number N is to be obtained by applying the Newton Raphson iterations to the equation x2- N = 0. If i denotes the iteration index, the correct iterative scheme will be
Answer : Option A
Explaination / Solution:
No Explaination.
