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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