MH SET 2017: 16 April, Paper II, Mathematical Sciences
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1
f 2 3i
1
2
1 i
6
1 i
6
2 3i
13
1 n
n 3 z 1 dz
| z| 2
z
3
2
3
2
3
2
1
2
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3 1 1
0 1 2
X2 X3 Xn
X1 ....... .
2 3 n
n
1
i 1 i t
n
i
i 1 i t
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0 ; Z1 = X1
1 ; Z1 = X 2
1
2 2
1 2
2Z1
1 2 1 2
1 2 2Z1
1 2 1 2
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x1 , x 2 : x12 x 22 4 F F
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0 1 0
0 0 1
0 0 0
z2 z4
1 ........
2! 4!
z2 z4
1 ........ 0 1 1
2! 4!
0 0 1
z3 z5
z ........
3! 5! 0 0 0
z3 z5
z ........
3! 5!
1 1 0
1 3 2 0 1 1
0 4 2 0 0 1
0 3 1
0 1 0
0 0 0
0 0 0
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nx
1 n2 x2
x
1 n x2
2n 1
2
n
2
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The complex function
x2 x3
1 x .........
2! 3!
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z 3
f z e1 /( z 2) ?
z1 z3 z2 z4 z 1
·
z2 z3 z1 z4
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a b
0 d
!
!
!
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" "
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1 0 0 0 0 1 0 0 0 0 2 1 0 0 0 2 1 1 0 0 0 1 0 0 0 0 2 1 0 0 0 2 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 2 0 0 0 0 2
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x
x y
T y
2x y z
z
1 2
1 1
0 1
1 1 0
2 1 1
2 1 1
1 1 0
2 1
1 1
1 0
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i s h yper bol i c on
$ $
$ $
## ## ## ##
## ## ## ##
51
2
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x x
x
1 ey dx ey 1 dy 0
y
%2 z %z
0
x
%x 2 %y
x ey c
%2 z %2 z
0
x
%y 2 %x 2
x ye y c
%2 z %z
0
%y 2 %x
x
y ey c
%2 z %z
0
%y 2 %y
x
y xe y c
T h e fu n ct i on
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ac
X Y
cb d ad b
1 ac 1 ac
d d
&& &&
d d
&& &&
d d
&& &&
d d
&& &&
d
&&
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1 n p fX x fX x 2
'
n i 1
j X j && E X1
fX x fX x 2 x
n
1 p
n n 1
' j X j &&
2
j 1 fX x
E X1
2 fX x 1
n
1 p
n 1
' j X j && 0
j 1
n
1 p
n n 1
' X j && E X1
j 1
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( )
2 1
X ( 1 x
)
m
x n
' pi q n i
i 0 i
m
x 1 n
' pi q n i
i 0 i
m 1
x n
m ' pi q n i
i 0 i
m 1
x 1 n
m ' pi q n i
i 0 i
m 2
x 2 n
m · ' pi q n i
i 0 i
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n
' log X i
i 1
)
)
X * K) n
X2
X2
)
X2
)2
X2
n
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n
' Xi
i 1
n
' Xi
i 1
(" +
) )
" + )
" +
' X 2i , K
) )
) )
) )
) )
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$
$
$
$
"
e 1 1
,
e e2
1 e 1
,
e e2
e 1 1
,
e2 e
1 e 1
,
e2 e
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+ -
ˆ- Y X+ˆ
ˆ--.
ˆ
n K
ˆ-. ˆ-
n K
ˆ-. ˆ-
n
ˆ--.
ˆ
K
Dn
/0
D n2
1
1 1
1
1 1
1
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2 2
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1 1 1 1 , , , , 2 2 2 2 1 1 1 1 , , , , 2 2 2 2
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st at em en t s i s V1 1 V L2
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MAHARASHTRA STATE ELIGIBILITY TEST - 16TH APRIL, 2017
ANSWER KEY UPDATED AFTER EVALUATION OF GRIEVANCES FOR PAPER - II
SUBJECT: MATHEMATICAL SCIENCE (SET A) (SUBJECT CODE 30)
1 A 31 D 61 A
2 C 32 B 62 C
3 B 33 C 63 A
4 C 34 A 64 B
5 D 35 C 65 D
6 B 36 A 66 C
7 B 37 C 67 C
8 A 38 A 68 C
9 9 39 D 69 B
10 A 40 D 70 D
11 C 41 B 71 C
12 D 42 B 72 B
13 9 43 B 73 A
14 A 44 B 74 A
15 A 45 C 75 B
16 A 46 D 76 B
17 D 47 B 77 B
18 A 48 D 78 C
19 C 49 B 79 D
20 A 50 C 80 C
21 C 51 C/D 81 D
22 B 52 B 82 C
23 B 53 B 83 b
24 D/C 54 B 84 B
25 C 55 A
26 D 56 B
27 C 57 C
28 B 58 B
29 A 59 D
30 C 60 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 - 16TH APRIL, 2017
ANSWER KEY UPDATED AFTER EVALUATION OF GRIEVANCES FOR PAPER - II
SUBJECT: MATHEMATICAL SCIENCE (SET B) (SUBJECT CODE 30)
1 B 31 D 61 C
2 B 32 B 62 B
3 A 33 B 63 A
4 9 34 B 64 A
5 A 35 B 65 B
6 C 36 C 66 B
7 D 37 D 67 B
8 9 38 B 68 C
9 A 39 D 69 D
10 A 40 B 70 C
11 A 41 C 71 D
12 A 42 D 72 C
13 C 43 A 73 b
14 B 44 C 74 B
15 C 45 A 75 C/D
16 D 46 C 76 B
17 D 47 B 77 B
18 C 48 B 78 B
19 B 49 D/C 79 A
20 A 50 C 80 B
21 C 51 A 81 C
22 D 52 C 82 B
23 B 53 A 83 D
24 C 54 B 84 A
25 A 55 D
26 C 56 C
27 A 57 C
28 C 58 C
29 A 59 B
30 D 60 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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MAHARASHTRA STATE ELIGIBILITY TEST - 16TH APRIL, 2017
ANSWER KEY UPDATED AFTER EVALUATION OF GRIEVANCES FOR PAPER - II
SUBJECT: MATHEMATICAL SCIENCE (SET C) (SUBJECT CODE 30)
1 C 31 C 61 D
2 D 32 D 62 C
3 9 33 B 63 b
4 A 34 D 64 B
5 A 35 B 65 C/D
6 A 36 C 66 B
7 A 37 D 67 B
8 C 38 A 68 B
9 B 39 C 69 A
10 C 40 A 70 B
11 D 41 C 71 C
12 B 42 B 72 B
13 B 43 B 73 D
14 A 44 D/C 74 A
15 9 45 C 75 A
16 A 46 D 76 C
17 D 47 C 77 A
18 B 48 B 78 B
19 C 49 A 79 D
20 A 50 C 80 C
21 C 51 C 81 C
22 A 52 B 82 C
23 C 53 A 83 B
24 A 54 A 84 D
25 D 55 B
26 D 56 B
27 B 57 B
28 B 58 C
29 B 59 D
30 B 60 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 - 16TH APRIL, 2017
ANSWER KEY UPDATED AFTER EVALUATION OF GRIEVANCES FOR PAPER - II
SUBJECT: MATHEMATICAL SCIENCE (SET D) (SUBJECT CODE 30)
1 A 31 C 61 C
2 A 32 B 62 B
3 A 33 B 63 D
4 A 34 D/C 64 A
5 C 35 C 65 A
6 B 36 D 66 C
7 C 37 C 67 A
8 D 38 B 68 B
9 B 39 A 69 D
10 B 40 C 70 C
11 A 41 D 71 C
12 9 42 B 72 C
13 A 43 C 73 B
14 C 44 A 74 D
15 D 45 C 75 C
16 9 46 A 76 B
17 B 47 C 77 A
18 B 48 A 78 A
19 B 49 D 79 B
20 B 50 D 80 B
21 C 51 D 81 B
22 D 52 C 82 C
23 B 53 b 83 D
24 D 54 B 84 C
25 B 55 C/D
26 C 56 B
27 D 57 B
28 A 58 B
29 C 59 A
30 A 60 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 DPage 1 of 28
Source: Savitribai Phule Pune University. Question paper published by Savitribai Phule Pune University.