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Mechanical engineering Questions and solutions set - 16

Mechanical engineering Questions and solutions set - 16
Question:-
Option (A)
D-1 C-1 A-1
Option (B)
CDA
Option (C)
ADC
Option (D)
does not necessarily exist
Correct Option:
B
Question Solution:
A, B, C, D is n x n matrix.
Given,ABCD=I
=> ABCDD-1 C-1=D-1 C-1
=> AB=D-1 C-1
=> A-1 AB=A-1 D-1 C-1
=> B=A-1 D-1 C-1
B-1=(A-1 D-1 C-1)-1
=(C-1)-1x(D-1)-1x(A-1)-1
=CDA
Question:-
Option (A)
monotonically increases
Option (B)
monotonically decreases
Option (C)
increases to a maximum value and then decreases
Option (D)
decreases to a minimum value and then increases
Correct Option:
A
Question Solution:
f'(x) = =
since ex is +ve for all values of x, f'(x) is +ve for all values of x and hence f(x) monotonically increases.
Question:-
Option (A)
1 and - 1
Option (B)
1 and i
Option (C)
1 and - i
Option (D)
i and - i
Correct Option:
D
Question Solution:
f(z)=
=
therefore, The singularities arc at
z=i and -i
Question:-
Option (A)
0
Option (B)
1
Option (C)
2
Option (D)
3
Correct Option:
C
Question Solution:
Perform, R3 -> R1 - R3
=>
therefore, Rank=2
Since,=-2 ≠ 0