Mechanical engineering Questions and solutions set - 17. Free gate, DRDO, BHEL questions answers and solutions

Question:-

Match List-I with List-II and select the correct answer using the codes given below the lists:
List-I
A.Newton-Raphson method
B.Rung-kutta method equations
C. Simpson's Rule equations
D. Gauss elimination
List-II
1.Solving nonlinear equations
2.Solving simultaneous linear equations
3.Solving ordinary differential
4.Numerical integration
5.Interpolation
6.Calculation of Eigen values

Option (A)

A B C D
6 1 5 3

Option (B)

A B C D
1 6 4 3

Option (C)

A B C D
1 3 4 2

Option (D)

A B C D
5 3 4 1

Correct Option:

C

Question:-

Section - I (Technical)
Question No. 1 to Question No. 25 carry 1 mark each.
where P is a vector is equal to

Option (A)

Option (B)

Option (C)

Option (D)

Correct Option:

D

Question Solution:

From vector triple product.
A × (B × C) = B (A.C) - C(A.B)

=

Question:-

The order of the differential equation is

Option (A)

1

Option (B)

2

Option (C)

3

Option (D)

4

Correct Option:

B

Question Solution:

Highest derivative of differential equation is 2.

Question:-

The system of linear equations
4x + 2y = 7
2x + y = 6
has

Option (A)

a unique solution

Option (B)

no solution

Option (C)

an infinite number of solutions

Option (D)

exactly two distinct solutions

Correct Option:

B

Question Solution:

The system can be written in matrix from as
=
The Augmented matrix [A|B] is given by

Performing Gauss elimination on this [A|B] as follows:

NowRank [A|B] = 2
(The number of non-zero rows in [A|B]
Rank [A] = 1
(The number of non-zero rows in [A])
Since,Rank [A|B]≠Rank[A],
The system has no solution.