MH SET 2016: 29 May, Paper III, Mathematical Sciences
Text of page 5
x
1 dx
1 x
0
sin x d x
2
0
1 x
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1
1
dx
1 x
0
1
1 x
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z2
dz
z3 2
C
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z pn 1
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1
2
1 if Y 0
Z =
X if Y 1
T12 a n d T22
T1 1 a n d T2 1
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#
1
n#
2 0 0 0 0 0
0 2 2 2 2 2 1
0 0 0 0 0 0 n#
1 1 1 1 1 1
1 1 1 1 1 1
!2 3 2 3 2 3" d
$$
p
2 1 0 0 0 0 $$
0 2 0 0 0 0 r
$$
0 0 2 1 0 0 a. s .
$$$
0 0 0 2 0 0
0 0 0 0 3 1
!0 0 0 0 0 3 "
2 1 0 0 0 0
0 2 0 0 0 0
0 0 2 1 0 0
0 0 0 2 0 0
0 0 0 0 3 1
!0 0 0 0 0 3 "
1 0 0 0 0 0
0 2 0 0 0 0
0 0 3 0 0 0
0 0 0 1 0 0
0 0 0 0 2 0
!0 0 0 0 0 3 "
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k
2
%
n
&X
i 1
i
S 2n %
%
% %
Sn
F
Sn
%
Sn
F
Sn
'%
'%
'%
'%
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1
n2
1
n2
r
$$
a. s .
$$$
p
$$
d
$$
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1 (
) n N*
n +
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1
243
10
243
233
243
11
243
,, ,,
,, ,,%
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-
1 -
2
-
-
-
-
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- -
-̂ -
1
-̂ V -ˆ
100
10
-̂ V -ˆ
100 %#
10 %#
-̂ V -ˆ
100
%#
1
-̂ V -ˆ
100 %#
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.
.
.%
.
.
.
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-
Tn2
-
Tn2
-
Tn2
-
Tn2
-
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R : |
-
-
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.
x y
z 0
y x
l 2 2
. /y /y
T = dx
. . 2
0 ! /x /t "
l 2
. /y
T = dx
2 /x
0
l
. /2 y
T = dx
2 /x 2
0
l 2
. /y
T = dx
2 /t
0
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Z1 Z22
1 3
0 0
2 2
1
112 4, 1 22 9 %.
2
3
2
1
1 1 1 1
5 2 2 3 2
1
3
1
3
1
6
1
2
1
2
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2
3.0 0.5 0.6
2 0.5 2.0 0.6
!0.6 0.6 4.0 "
2
2
9
4
9
3
9
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t
ha
kg
ha
t
ha
kg
ha
t
ha
kg
ha
&
d /108
d
t
ha
t
ha
kg
ha
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/L
qj
/q j
/L d /L
0
/q j dt /q j
/L /L
& q /q
d
L j 0
/t dt j
j
/L /L
& q /q
d
L j 0
/q j dt j
j
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cos - sin - 0
A = sin - cos - 0
0 0 1
1 0 0
0 cos - sin -
0 sin - cos -
0 0 1
cos - sin - 0
sin - cos - 0
cos - sin - 0
sin - cos - 0
0 0 1
cos - 0 sin -
sin - 0 cos -
0 1 0
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x2 y2
4
z
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#
4 3
# s cos s , 1 sin s , cos s
5 5
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# 3
/f d /f
k
/y d x dy
/2 f
k
/y 2
/f
f y k
/y
/f
y k
/y
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4
2
1 2
y dx
2
0
x2
4
x2
4
x2
4
x2
4
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0 -
x2
f x , y, y dx
x1
1
12
0 1 2
/f d /f
0
/y dx dy
0
1
/f
f y 0
/y
12
2
1
/f d /f
0
/y d x /y
0
1 -
/f
0
/y 2
x x1 1 2 -
2
12
1 -
/f d /f
0 0
/y d x /y
1
/f /f 1 2 - -2
0, 0 12
/y x x1
/y x x2 2
1
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-
dr
I = r2 r 2 d- r1 t
d- t s
-0
e
0
Zt if t is even
Xt
Z2t 1 1 / 2 if t is odd
.
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X 0
1
3 1
0
4 4
0 1 1 1
P =
4 2 4
Xt t0
3 1
t 0
! 4 4"
1
3
/4
x s ds
0
3
16
4
3
3 6 64
3
6 4
1
3 4
4
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t
1 t
x s ds
t s et s x s d s
0
0
1
t
1
t2
1
t
E
!
& X
"
n 1
n
mn
1 m
m
1 m
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5% 6
6 5
% 5% 6
0 0
0 0 1 0
1 0 0 0
P =
0.3 0.7 0 0
!0.6 0.2 0.2 0 "
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-
-
1 2
!3 4"
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t
F t s G s t ds
0
t
F s G t s ds
0
321
400
t
719 F s G s ds
720 0
719
919 t
F s G t s ds
321 0
523
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1
e t e t
e p 1 1
p
.
!e 1" 2 2
1 e p 1
p
2 2 !e 1"
1 ep 1
p
2 2 !e 1"
1 ep 1
p
2 2 !e 1"
1
4
3
4
1
2
1
3
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u
1
u
4
u 2
u 3
3
4
t 1
R x dx 2
0 f
(
f i j
R t dt*
0 + f
(
r t d t* 4
0 + 3
5
3
R x dx
0
t
cos
0
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dz ez
dz
z2 1 z 1
3
C C
i
e
1 i
3 e2
ez
3
dz
z 1 z
C
1
2
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f 3
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fn d x %
0 f d0
lim
f d0
E
f n dx %
1
1
lim
fn d x
f d0
lim E
1
f n dx %
lim
f d0
E
5
q
5
q
5
5
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MAHARASHTRA STATE ELIGIBILITY TEST - 29TH MAY, 2016
ANSWER KEY UPDATED AFTER EVALUATION OF GRIEVANCES FOR PAPER - III
SUBJECT: MATHEMATICAL SCIENCE (SET A) (SUBJECT CODE 30)
1 A 31 A 61 D 91 A 121 B
2 A 32 9 62 e 92 A 122 B
3 A 33 B 63 C 93 D 123 D
4 B 34 B 64 C 94 D 124 D
5 C 35 C 65 A 95 C 125 C
6 C 36 C 66 A 96 C 126 C
7 D 37 A 67 B 97 B 127 D
8 D 38 A 68 B 98 9 128 D
9 A 39 A 69 B 99 C 129 D
10 A 40 A 70 B 100 C 130 D
11 D 41 C 71 D 101 B 131 A
12 D 42 C 72 D 102 B 132 A
13 D 43 D 73 D 103 D 133 C
14 D 44 D 74 D 104 D 134 C
15 D 45 C 75 C/A/B/D 105 B 135 B
16 D 46 C 76 C 106 B 136 B
17 A 47 B 77 A 107 A 137 C
18 A 48 C 78 A 108 A 138 C
19 D 49 D 79 A 109 A 139 D
20 D 50 D 80 A 110 A 140 D
21 D 51 A 81 C 111 D 141 C
22 D 52 A 82 9 112 D 142 C
23 C 53 C 83 C 113 D 143 A
24 C 54 C 84 C 114 D 144 A
25 D 55 D 85 D 115 C 145 C
26 D 56 D 86 D 116 C 146 C
27 D 57 B 87 C 117 C
28 D 58 B 88 C 118 C
29 C 59 A 89 B 119 A
30 C 60 A 90 B 120 A
9 = No option is correct or the question is wrong, a= A and B, b = A and C, c = A and D, d = A,B and C, e = A,B and
D,f = A,C and D, g = A,B,C and D, h = B and C, i = B and D, j = B,C and D, k = C and D
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MAHARASHTRA STATE ELIGIBILITY TEST - 29TH MAY, 2016 ANSWER KEY UPDATED AFTER EVALUATION OF GRIEVANCES FOR PAPER - III SUBJECT: MATHEMATICAL SCIENCE (SET B) (SUBJECT CODE 30) 1 A 31 B 61 A 91 A 121 C 2 A 32 C 62 A 92 A 122 C 3 A 33 D 63 A 93 A 123 D 4 B 34 D 64 A 94 A 124 D 5 D 35 A 65 C 95 D 125 C 6 D 36 A 66 9 96 D 126 C 7 C 37 C 67 C 97 D 127 A 8 C 38 C 68 C 98 D 128 A 9 D 39 D 69 D 99 C 129 C 10 D 40 D 70 D 100 C 130 C 11 D 41 B 71 C 101 C 131 C 12 D 42 B 72 C 102 C 132 C 13 C 43 A 73 B 103 A 133 D 14 C 44 A 74 B 104 A 134 D 15 A 45 D 75 A 105 B 135 A 16 9 46 e 76 A 106 B 136 A 17 B 47 C 77 D 107 D 137 D 18 B 48 C 78 D 108 D 138 D 19 C 49 A 79 C 109 C 139 D 20 C 50 A 80 C 110 C 140 D 21 A 51 B 81 B 111 D 141 D 22 A 52 B 82 9 112 D 142 D 23 A 53 B 83 C 113 D 143 A 24 A 54 B 84 C 114 D 144 A 25 C 55 D 85 B 115 A 145 D 26 C 56 D 86 B 116 A 146 D 27 D 57 D 87 D 117 C 28 D 58 D 88 D 118 C 29 C 59 C/A/B/D 89 B 119 B 30 C 60 C 90 B 120 B 9 = No option is correct or the question is wrong, a= A and B, b = A and C, c = A and D, d = A,B and C, e = A,B and D,f = A,C and D, g = A,B,C and D, h = B and C, i = B and D, j = B,C and D, k = C and D
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MAHARASHTRA STATE ELIGIBILITY TEST - 29TH MAY, 2016 ANSWER KEY UPDATED AFTER EVALUATION OF GRIEVANCES FOR PAPER - III SUBJECT: MATHEMATICAL SCIENCE (SET C) (SUBJECT CODE 30) 1 A 31 B 61 C 91 C 121 C 2 A 32 B 62 C 92 C 122 C 3 A 33 A 63 B 93 A 123 D 4 B 34 A 64 B 94 A 124 D 5 A 35 D 65 A 95 B 125 A 6 9 36 e 66 A 96 B 126 A 7 B 37 C 67 D 97 D 127 D 8 B 38 C 68 D 98 D 128 D 9 C 39 A 69 C 99 C 129 D 10 C 40 A 70 C 100 C 130 D 11 A 41 B 71 B 101 D 131 D 12 A 42 B 72 9 102 D 132 D 13 A 43 B 73 C 103 D 133 A 14 A 44 B 74 C 104 D 134 A 15 C 45 D 75 B 105 A 135 D 16 C 46 D 76 B 106 A 136 D 17 D 47 D 77 D 107 C 137 D 18 D 48 D 78 D 108 C 138 D 19 C 49 C/A/B/D 79 B 109 B 139 C 20 C 50 C 80 B 110 B 140 C 21 B 51 A 81 A 111 C 141 D 22 C 52 A 82 A 112 C 142 D 23 D 53 A 83 A 113 D 143 D 24 D 54 A 84 A 114 D 144 D 25 A 55 C 85 D 115 C 145 C 26 A 56 9 86 D 116 C 146 C 27 C 57 C 87 D 117 A 28 C 58 C 88 D 118 A 29 D 59 D 89 C 119 C 30 D 60 D 90 C 120 C 9 = No option is correct or the question is wrong, a= A and B, b = A and C, c = A and D, d = A,B and C, e = A,B and D,f = A,C and D, g = A,B,C and D, h = B and C, i = B and D, j = B,C and D, k = C and D
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MAHARASHTRA STATE ELIGIBILITY TEST - 29TH MAY, 2016 ANSWER KEY UPDATED AFTER EVALUATION OF GRIEVANCES FOR PAPER - III SUBJECT: MATHEMATICAL SCIENCE (SET D) (SUBJECT CODE 30) 1 A 31 B 61 B 91 D 121 D 2 A 32 B 62 9 92 D 122 D 3 A 33 B 63 C 93 D 123 A 4 B 34 B 64 C 94 D 124 A 5 C 35 D 65 B 95 A 125 D 6 C 36 D 66 B 96 A 126 D 7 D 37 D 67 D 97 C 127 D 8 D 38 D 68 D 98 C 128 D 9 C 39 C/A/B/D 69 B 99 B 129 C 10 C 40 C 70 B 100 B 130 C 11 B 41 A 71 A 101 C 131 D 12 C 42 A 72 A 102 C 132 D 13 D 43 A 73 A 103 D 133 D 14 D 44 A 74 A 104 D 134 D 15 A 45 C 75 D 105 C 135 C 16 A 46 9 76 D 106 C 136 C 17 C 47 C 77 D 107 A 137 A 18 C 48 C 78 D 108 A 138 9 19 D 49 D 79 C 109 C 139 B 20 D 50 D 80 C 110 C 140 B 21 B 51 C 81 C 111 C 141 C 22 B 52 C 82 C 112 C 142 C 23 A 53 B 83 A 113 D 143 A 24 A 54 B 84 A 114 D 144 A 25 D 55 A 85 B 115 A 145 A 26 e 56 A 86 B 116 A 146 A 27 C 57 D 87 D 117 D 28 C 58 D 88 D 118 D 29 A 59 C 89 C 119 D 30 A 60 C 90 C 120 D 9 = No option is correct or the question is wrong, a= A and B, b = A and C, c = A and D, d = A,B and C, e = A,B and D,f = A,C and D, g = A,B,C and D, h = B and C, i = B and D, j = B,C and D, k = C and D
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Source: Savitribai Phule Pune University. Question paper published by Savitribai Phule Pune University.