# Mechanical engineering Questions and solutions set - 12

Mechanical engineering Questions and solutions set - 12
Question:-
Option (A)
&α = 1, ε ≠ 1
Option (B)
&α ≠ 1, ε = 1
Option (C)
&α ≠ 1 , ε ≠ 1
Option (D)
&α = 1, ε = 1
where &α = absorptivity
ε = emissivity
Correct Option:
D
Question:-
Option (A)
0
Option (B)
1/2
Option (C)
1
Option (D)
∞
Correct Option:
D
Question Solution:  Question:-
Option (A)
-30 and -5
Option (B)
-37 and -1
Option (C)
-7 and 5
Option (D)
17.5 and -2
Correct Option:
C
Question Solution:
Let matrix  A = The trace of matrix
t(A) = tr(A) = sum of its diagonal element
(=sum of its eigen value)
a + d = -2...(i)
Determinant of matrix A
|A| = => ad - bc = -35...(ii)
Assume eigen value is λ
|A - λI| = 0
=> => (a - λ) (d - λ) - bc = 0
=> ad - λ(a + d) + λ2 - bc = 0
=> λ2 - λ(a + d) + (ad -bc) = 0
=> λ2 + 2λ - 35 = 0
(λ +7) (λ - 5) = 0
Therefore, eigen values are λ = -7 and 5.
Question:-
Option (A)
0
Option (B)
1
Option (C)
1
Option (D)
1/e
Correct Option:
B
Question Solution:
P = Integrating by parts:
Letu = x
dv = exdx
du = dx
v = Now, therefore, = xex - ex + c = (1 x e1 - e1) - (0 × e0 - e0)
= 0 - (-1)
= 1