MH SET 2016: 29 May, Paper II, Mathematical Sciences
Text of page 3
x [0, 1], n 1, 2, ............
1
3 11
3 13
2
2
3 13
3 11
x (0, )
( 1) m 3m
m
x
m 0 8
1
2
1
8
Text of page 5
P (A| B) = P (A| B)
11. L et X be a r v w i t h N (1, 1). D efi n e
t h e ev en t s :
A
Text of page 6
1 1
m, n N
2m 2n
Text of page 7
d ( x , y) | x y|
| x y|
d ( x, y )
1 | x y|
d ( x, y) 1 if x y
= 0 if x y
d ( x, y) x2 y2
Text of page 10
f ( z) z 3 sin z
cos 2 z
dz
| z| 1
(2 z 1) ( z 3)
f :
2 i
2 i
7
2 i
5
i
5
Text of page 11
p (n x)
P (X = x 1) q( x 1) P (X = x )
n
X= X i /n
i 1
n
x
f :
3z 2 z
f (z) | z | x 2
y 2 dz
C
z2 1
Text of page 12
L et X
n
Sn Xi .
i 1
sin z
f (z) ,
z
z
Text of page 13
5 1
. , a x b
6 b a
f ( x , a , b)
0, ot h erwise
n
1
3 (X i X)2
6 i 1
a X ,
n
n
3 (X i X)2
i 1
b X
n
1
p n
6 3 (X i X)2
i 1
a X ,
n
n
3 (X i X)2
i 1
b X
n
n
a X ,
3 (X i X)2
n
b X
3 (X i X)2
n
a X n
,
2
3 (X i X)
i 1
n
b X
3 (X i X)2
Text of page 14
! !
E (Tn ) ! n 1
T1 2X T2 X(n ) .
n
Va r (Tn ) 0
! !
!
Text of page 15
Z[ 2 ] = {a 2b | a , b Z}
(Z p , + p , × p )
Z"Z
! !
u ( x )/v (!) if a (!) # x # b(!)
f X ( x , !)
0 ot h er wise
n
ai X i !
i 1
a (!) !
!
1
ai
n
n
ai 1
i 1
n n
ai 1, ai2 1
i 1 i 1
n 1
ai
n
Text of page 16
1
| A|
! ! %
$ (!)
Va r(T)
P (| T !| & C)
C2
2 $( ) e3 .
d
$(!)
d! T(X) = ( 2) X .
Va r (T)
I X (!)
Va r (T)
P (Sup| T $(!)| > C)
C2
$
2
d $ (!)
d! $
Va r (T) '
I X (!)
$
Text of page 17
M {[ a ij ]m . n | a ij }
(1 0 0)
* +
*0 1 0 ++
*
* +
*,0 0 1 +-
(0 1 0)
* +
n * 1 0 0 ++
T= (X 15) *
5 * +
*, 0 0 1 +-
n
T= (X 10)
5
( 1 0 0)
* +
n (X 10) *0 1 0 ++
T= , *
5 s * +
*, 0 0 1+-
2
(X i X)
s
n 1
( 1 0 0)
* +
X 10 *0 1 0 ++
T= *
(n 1)s * +
*, 0 0 1 +-
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( 1 4 0)
* +
*0 3 0 ++
*
/ 12 * +
*, 0 0 5 +-
/ 22 /12 /22
(2 1 0)
* +
*0 2 0 ++
*
* +
*,0 0 3 +-
(2 0 0)
* +
*0 5 0 ++
*
* +
*,0 1 3 +-
(1 4 5)
* +
* +
*0 2 6+
* +
*,0 0 3+-
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! ! ! !
f ( x , !), ! . 0 1
! 0 {!0 } 1 {!1 }.
f ( x , !0 )
( x)
f ( x , !1 )
f ( x , !0 )
(x)
m a x {f ( x , !1 ), f ( x , !0 )
f ( x , !0 )
(x)
m in {f ( x , !0 ), f ( x , !1 )
f ( x , !1 )
( x)
f ( x , !0 )
p 3x 2 q2 y
2
z ax 2 x3 (a y )3/ 2 b
3 y px p3
2
z ax x3 (a y )3 / 2 b
3 4 y3 27 x 2 0
2 4 y2 27 x 3 0
z ax x2 (a y )3/ 2 b
3
4x3 27 y 2 0
2
z ax 2 x (a y )3/ 2 b
3 4 y2 27 y 0
Text of page 20
(0xy 3 y cos x ) d x (x 2 y2
a
1 sin x )d y 0
3
0 ,1 1
2
2
0 ,1 1
3
3
0 1, 1
2
2
0 1, 1
3
L
Ch nh ,
h 1
Yst
L
wh sh
nh 2 h 1
Ch
w h sh
nh 2
Ch
N h sh
nh 2
Ch
n sh
nh 2
Ch
Text of page 21
$
33 3
2 2 dy
(x y ) 2 xy 0
dx
dy
(x 2 y2 ) 2 xy 0
dx
3 $ $3
2 2 dy
(x y ) 2 xy 0
dx
dy
(x 2 y2 ) 2 xy 0
dx
s 2y
Text of page 22
a ccu r a cy (
2
p (1 p ) z0 / 2
d
2
z0 / 2
d
p (1 p ) z0 / 2
d
( p (1 p ) z 0 / 2 )2
d
Text of page 23
0 4
/
v
ai 4 i
i 1
ai 0
ni
ai ,i 1, 2, ......., v,
n
v
ni n
i 1
ai 1
ni
n
Text of page 24
Yij 0 4i 1j ij , i 1, 2, ...........,
j 1, 2, ........., b
3 4
/
y i2. y..2 b
, yi . y ij ,
b vb d 1
v b
y.. yij
i 1 j 1
yi2. y..2
v vb
y.2j y..2 v
, y y ij
b vb . j i 1
y.2j y..2
v vb
Text of page 25
0
4 0
4
/
v b
4i 1j
i 1 j 1
v b
4i 1j 0
i 1 j 1
v b
4i 1j 0 0
i 1 j 1
v b
4i 1j 0
i 1 j 1
Text of page 26
(8 3)
* +
* +
, 3 1-
17
5
8
15
7
15
1
15
Text of page 1
MAHARASHTRA STATE ELIGIBILITY TEST - 29TH MAY, 2016
ANSWER KEY UPDATED AFTER EVALUATION OF GRIEVANCES FOR PAPER - II
SUBJECT: MATHEMATICAL SCIENCE (SET A) (SUBJECT CODE 30)
1 C 31 C 61 B
2 B 32 C 62 B
3 C 33 C 63 B
4 C 34 C 64 B
5 A 35 C 65 C
6 B 36 C 66 C
7 D 37 D 67 B
8 C 38 D 68 B
9 D 39 A 69 C
10 C 40 A 70 C
11 A 41 A 71 A
12 C 42 A 72 9
13 A 43 B 73 A
14 B 44 B 74 A
15 B 45 A 75 A
16 B 46 A 76 A
17 A 47 A 77 D
18 A 48 A 78 D
19 D 49 A 79 D
20 D 50 A 80 D
21 B 51 D 81 B
22 B 52 D 82 B
23 A 53 D 83 D
24 A 54 D 84 D
25 D 55 D
26 D 56 D
27 D 57 B
28 D 58 B
29 D 59 C
30 D 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
Text of page 2
MAHARASHTRA STATE ELIGIBILITY TEST - 29TH MAY, 2016
ANSWER KEY UPDATED AFTER EVALUATION OF GRIEVANCES FOR PAPER - II
SUBJECT: MATHEMATICAL SCIENCE (SET B) (SUBJECT CODE 30)
1 B 31 A 61 A
2 D 32 A 62 A
3 C 33 A 63 D
4 D 34 A 64 D
5 C 35 A 65 D
6 A 36 A 66 D
7 C 37 D 67 B
8 A 38 D 68 B
9 B 39 D 69 D
10 B 40 D 70 D
11 B 41 D 71 A
12 C 42 D 72 A
13 B 43 B 73 D
14 C 44 B 74 D
15 C 45 C 75 B
16 A 46 C 76 B
17 C 47 B 77 A
18 C 48 B 78 A
19 C 49 B 79 D
20 C 50 B 80 D
21 C 51 C 81 D
22 C 52 C 82 D
23 D 53 B 83 D
24 D 54 B 84 D
25 A 55 C
26 A 56 C
27 A 57 A
28 A 58 9
29 B 59 A
30 B 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
Text of page 3
MAHARASHTRA STATE ELIGIBILITY TEST - 29TH MAY, 2016
ANSWER KEY UPDATED AFTER EVALUATION OF GRIEVANCES FOR PAPER - II
SUBJECT: MATHEMATICAL SCIENCE (SET C) (SUBJECT CODE 30)
1 A 31 C 61 B
2 C 32 C 62 B
3 A 33 B 63 A
4 B 34 B 64 A
5 B 35 B 65 D
6 B 36 B 66 D
7 C 37 C 67 D
8 B 38 C 68 D
9 C 39 B 69 D
10 C 40 B 70 D
11 A 41 C 71 C
12 B 42 C 72 C
13 D 43 A 73 C
14 C 44 9 74 C
15 D 45 A 75 C
16 C 46 A 76 C
17 A 47 A 77 D
18 A 48 A 78 D
19 A 49 D 79 A
20 A 50 D 80 A
21 A 51 D 81 A
22 A 52 D 82 A
23 D 53 B 83 B
24 D 54 B 84 B
25 D 55 D
26 D 56 D
27 D 57 A
28 D 58 A
29 B 59 D
30 B 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
Text of page 4
MAHARASHTRA STATE ELIGIBILITY TEST - 29TH MAY, 2016
ANSWER KEY UPDATED AFTER EVALUATION OF GRIEVANCES FOR PAPER - II
SUBJECT: MATHEMATICAL SCIENCE (SET D) (SUBJECT CODE 30)
1 B 31 A 61 C
2 B 32 A 62 C
3 B 33 A 63 D
4 C 34 A 64 D
5 B 35 D 65 A
6 C 36 D 66 A
7 C 37 D 67 A
8 A 38 D 68 A
9 B 39 B 69 B
10 D 40 B 70 B
11 C 41 D 71 A
12 D 42 D 72 A
13 C 43 A 73 A
14 A 44 A 74 A
15 C 45 D 75 A
16 A 46 D 76 A
17 C 47 B 77 D
18 C 48 B 78 D
19 B 49 A 79 D
20 B 50 A 80 D
21 B 51 D 81 D
22 B 52 D 82 D
23 C 53 D 83 B
24 C 54 D 84 B
25 B 55 D
26 B 56 D
27 C 57 C
28 C 58 C
29 A 59 C
30 9 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 DPage 1 of 28
Source: Savitribai Phule Pune University. Question paper published by Savitribai Phule Pune University.