ME⏐ GATE Paper 2008
Answer keys
1
C
2
B
3
B
4
A
5
C
6
D
7
D
8
D
9
B
10
D
11
B
12
B
13
B
14
C
15
A
16
B
17
18
B
19
20
D
21
D
22
B
23
B
24
C
25
26
A
27
D
28
C
29
A
30
31
D
32
B
33
B
34
B
35
B
36
37
D
38
39
D
40
A
41
B
42
43
A
44
C
45
C
46
A
47
A
48
C
49
C
50
D
51
A
52
53
54
C
55
56
D
57
C
58
D
59
60
C
61
C
62
63
B
64
D
65
66
67
B
68
B
69
D
70
71
72
73
74
A
75
A
76
77
78
79
80
81
82
D
83
B
84
85
Explanation:-
3. 13x8xLtx8→−−, Applying L-Hospital’s Rule , we get, 23x81x13Lt11−→=
4. Required probability 331C1114224⎛⎞⎛⎞==⎜⎟⎜⎟⎝⎠⎝⎠
5. Given matrix is 12430611P⎡⎤⎢⎥⎢⎥⎢⎥⎣⎦
Let be the Eigen values of the above matrix 123,andλλλ()1Let3Givenλ=
12323Now,sumofdiagonalelements1PP13P2λ+λ+λ==+∴λ+λ=+−=−
6. ()()()ˆˆˆGivenvectorisFxyiyxjxyzk=−+−+++
FFFDivergence1113xyz∂∂∂=++=++=∂∂∂
8. Both young’s Modulus and shear Modulus are required as linear strain will be calculated by young modulus. Change in diameter can be calculated from Poisson’s ratio which depends on young’s modulus and shear modulus.
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10. Let W be the weight of counterweight. 0.5RWQ•20⋅75KgP
Taking moment about Q
752W0.5,W300Kg×=×=
11. Grubler’s criterion is applied to mechanism with only single degree of freedom.
Given conditions satisfy Grubler’s criterion i.e. 32j40where−−=