Engineering Mathematics - Online Test
Q1. The integrating factor for the differential equation 
Answer : Option D
Explaination / Solution:
The standard form of Linear differential equations is
Q2. 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:
Q3. The expression 
is equal to
is equal to
Answer : Option A
Explaination / Solution:
By L’ Hospital rule,
Q4. 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
Q5.
[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.
Q6. 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.
Q7. There are two containers, with one containing 4 Red and 3 Green balls and the other containing 3 Blue and 4 Green balls. One ball is drawn at random from each container. The probability that one of the balls is Red and the other is Blue
will be
Answer : Option C
Explaination / Solution:
No Explaination.
Q8. 2D stress at a point is given by a matrix, 
MPa. The maximum shear stress in MPa is
MPa. The maximum shear stress in MPa is
Answer : Option A
Explaination / Solution:
Q10. x and y are two positive real numbers, such that equation
2x + y ≤ 6; x + 2y ≤ 8
For which values of (x, y), the function f (x, y) = 3x + 6y will give maximum value
Answer : Option A
Explaination / Solution:
2x + y ≤ 6; x + 2y ≤ 8
x ≤ 1.33; y ≤ 3.33; ∴ option(B) and (C) is rejected becuase x >1.33
Option (D) is rejected x >10 / 3
