Engineering Mathematics - Online Test
Q1. If 
then the initial and final values of f(t) are
respectively
then the initial and final values of f(t) are
respectively
Answer : Option B
Explaination / Solution:
No Explaination.
Q2. A numerical solution of the equation 
can be obtained using
Newton- Raphson method. If the starting value is x = 2 for the iteration, the
value of x that is to be used in the next step is
can be obtained using
Newton- Raphson method. If the starting value is x = 2 for the iteration, the
value of x that is to be used in the next step is
Answer : Option C
Explaination / Solution:
Substituting x0 = 2 we get
Newton Raphson Method
Substituting all values we have
Q3. The system of equations
x + Y + z = 6
x + 4y + 6y = 20
x + 4y + λz = μ
has NO solution for values of λ and μ given by
Answer : Option B
Explaination / Solution:
Writing A:B we have
Apply R3⟶R3 – R2
For equation to have solution, rank of A and A:B must be same. Thus for no
solution; λ = 6, μ ≠ 20
Q4. A fair dice is tossed two times. The probability that the second toss results in a value that is higher than the first toss is
Answer : Option C
Explaination / Solution:
Total outcome are 36 out of which favorable outcomes are :
(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6);
(3, 4), (3, 5), (3, 6), (4, 5), (4, 6), (5, 6) which are 15.
P(E) = (No of favourable outcomes/No of total outcomes) = 15/36
= 5/12
Q5. Three friends, R, S and T shared toffee from a bowl. R took 1/3rd of the toffees, but returned four to the bowl. S took 1/4th of what was left but returned three toffees to the bowl. T took half of the remainder but returned two back into the bowl. If the bowl had 17 toffees left, how many toffees-were originally there in the bowl?
Answer : Option C
Explaination / Solution:
Let total no of toffees be x . The following table shows the all calculations.
Q6. Given that 
and q is any non-zero real number, the value
of |f(q) - f(-q)| is
and q is any non-zero real number, the value
of |f(q) - f(-q)| is
Answer : Option D
Explaination / Solution:
Q7. The sum of n terms of the series 4 + 44 + 444 + .... is
Answer : Option C
Explaination / Solution:
Q8. Let M4 = I, (where I denotes the identity matrix) and M ≠ I, M2 ≠ I and M3 ≠ I. Then, for any
natural number k, M-1 equals:
Answer : Option C
Explaination / Solution:
D is not correct
Q9. Given the following statements about a function
f : R⟶R, select the right option
P: If f(x) is continuous at x = x0, then it is also differentiable at x = x0.
Q: If f(x) is continuous at x = x0, then it may not be differentiable at x = x0.
R: If f(x) is differentiable at x = x0, then it is also continuous at x = x0.
Answer : Option B
Explaination / Solution:
We know that every differentiable function is continuous but converse need not be True
Q10. Which one of the following is a property of the solutions to the Laplace equation: Δ2f = 0?
Answer : Option A
Explaination / Solution:
No Explaination.
