MH SET 2017: 16 April, Paper III, Mathematical Sciences
Text of page 3
x2 y
f (x, y)
x2 y2
f ( x, y) x2 y 7x
( x, y ) (0, 0) f (0, 0) 0
3 4
,
5 5
12
5
f
x
13 f
5 y
13
5
Text of page 4
h (x) x2
h (x) 0
1
1
| | 1
1 2 0
2 1 0 f (x, y) xy (12 3 x 4 y)
2 3 1 4
,1
3
Text of page 5
u f (x 2 y) g(x 2 y)
f : R2 R3
2 2
u u
4 2
x y2
f (u , v ) (u 2 5 v , ve 2 u , 2 u log (1 v 2 ))
2 2
u u
4
x2 y2
g : R2 R2
2 2
u u
2
x2 y2 g (1, 2) (0, 0)
2
u 2
u 1 2
2 D ( f o g ) (1, 2)
x2 y2 3 4
f : R2 R3
f (u , v ) (u 2 5 v , ve 2 u , 2 u log (1 v 2 )) 15 20
4 6
0 1 2 2 4
5 1 0
15 20
5 5
3 4
1 1
2 4
2 0
0 5
15 4 2
0 1
20 6 4
2 0
0 1 5 15 4 2
1 1 0 20 6 4
Text of page 6
Z x
Z i
Z 3
Z 2
Zp x
Zp x
Zp x
f (x) Zp x
f( ) 0 Zp
Z 5
Zp x
Z i
Text of page 7
d 2
: R 2 [t ] R 2[ t ] zn
dt n 0
b1 (t ) t2 t 1, b2 (t ) t2 3t 2
b3 (t ) t2 2t 1
R 2[ t ]
1 1 1
{1}
0 1 2
0 0 1
lim z n 1 f ( zn )
n
1 1 0
{ }
1 3 2
0 4 2 1
f (z)
( z 1)5
0 1 0
sin ( z 1)
0 0 2 f (z)
( z 1)4
0 0 0
1
f (z) cos
1 2 3 z 1
1 3 2 2 1
f (z) e( z 1) cos ( z z3 )
1 1 1 z 1
Text of page 8
C {0}
D :| z z0 | r | f ( z )|
1
f (z)
z
f (z) | z| 1
f ( z) x2 xy y2, z D
z x iy
z D
1
if z 1,
f (z) z 1
1 if z 1.
E {0} {1 / n / n N}
F {1 / n / n N}
Text of page 9
1
f1 ( x ) sin ,x 0
x
f1 (0) 0
1
f 2 (x) x sin
x
f 2 (0) 0
A
Text of page 10
or der P
1
1
3 5
7 2 i
i
e
( 1) 2i
Text of page 11
4
2
1 i
7 9
3
2
2 3 5 i
7 x1 , x 2 , ......., x n Y
n
| ( y , x i )| 2 y 2
i 1
| ( y, x )
z X x Y
( z, x )| y z
E {x Y| ( y, x ) 0}
E {x Y| ( y, x ) 0}
Text of page 12
Y {y }
x 2 | ( x , y )| 2
f (x) f ( y)
x X
[Y] X x y
x, y X ( x, y)
(x, y ) ( y , y)
x !Y" x 0
x su p {| f ( x )| /
f X, f 1}
X M # M!
M M!!
M!
X M # M!
Text of page 13
Z Y X
Text of page 14
P:X Y
d1 d2
Text of page 15
z f (x 2 y2 z2)
p( y zp ) q( x zq )
px ( y zq ) qy ( x zp )
px ( y zp ) qy ( x zq )
p( y zq ) q( x zp )
yp xq xyz x
(x 2 z2 ) p xy q pq
z z
n 1
p ,q
m 2 x y
2n 1 m
Text of page 16
d2y
ex y 0
dx2
z( x y) c(3 z 1)
x2 y2 1, z 1
$( x ) Ck xk
x2 y2 2 z3 z2 2 k 0
x y z 2
$(0) 1 $ '(0) 0
2 2 2
x y z 4
x2 y2 z2 2 z3
1
2
dx dy
y x
dt dt
1
2
1
2
1
2
Text of page 17
µ(d )
d| 1000
2x 3 % 0 (m od 101)
3x 4 % 0 (m od 123)
4x 5 % 0 (m od 67)
5x 6 % 0 (m od 12)
1
m (r 2 r 2 &2 )
2
1
m (r 2 r &2 )
2
1
m (r 2 r 2 &2 )
2
1
m (r 2 & &2 )
2
Text of page 18
&
1 1
L( x , x ) m x2 k x2
2 2
1
m l 2 &2 m gl (1 cos &)
2 w h er e
1
m l 2 &2 m gl (1 cos &)
2 ' k /m
1
m l 2 &2 m gl (1 cos &)
2
1
m l 2 &2 m gl (1 cos &)
2
x (t ) C 1 e' t C 2 e 't
x (t ) C1 C2 t
x (t ) C1 cos 't C 2 sin 't
x (t ) C1 cos ' 2 t C 2 sin ' 2 t
Text of page 19
: (0, 1) R3
: ( 1, 1) R3
(t ) (t , t 2 , t 3 )
"( s ) 0 s (0, 1)
t h e cu r vat u r e
s (0, 1)
2
t ' (s ) (s 1) n ( s )
b ' (s ) 2 n (s ) v
0 u 2
x (u , v )
t ' (s ) 2 n (s )
x (u , v ) (v cos u , v sin u , au )
n ' (s ) 2 t (s) ( s 1) b ( s )
t ' (s ) 2 n (s )
n ' (s ) (s 1) t (s ) 2 b (s )
b ' (s ) ( s 1) n ( s )
n ' (s ) (s 1) t ( s ) 2 b (s )
Text of page 20
/4
I( y ( x )) (0 ( y ")2 y2 x2 dx
y (0) 0 y '(0) 1
x2 1
I( y ( x )) (x 1
f ( x , y, y ', y ") d x y
4
y'
4 2
y 1 cos x
y tan x
y cos x
y sin x
2 2
u u
I(u ( x, y )) (( )) x y
* d xd y
*
0
f d f
y" dx y"
f d f 2 2
u u
y' dx y" 0
x2 y2
2 2
u u
f d f 0
x2 y2
y' dx y'
2
u u
0
x2 y
f d f
2
y" dx y' u u
0
x x2
Text of page 21
t
x (t ) 1 t2 4 ( (t s ) x (s ) d s
0
y" y x , y (0) 1 y (1) 0
1
u (x) 2x 1 ( k1 ( x, t ) u (t ) d t
0
t (1 x ), 0 t x
k1 ( x , t )
x (1 t ), x t 1
1
u (x) 2x 1 ( k 2 ( x , t ) u (t ) d t
0
(1 x ), 0 t x
k2 (x, t )
(1 t ), x t 1
1
u (x) 2x 1 ( k 3 ( x , t ) u (t ) d t
0
t, 0 t x
k3 ( x , t )
x, x t 1
1
u (x) 2x 1 ( k 4 ( x , t ) u (t ) d t
0
xt (1 x ), 0 t x
k4 ( x , t )
x 2 (1 t ), x t 1
Text of page 22
t ( a , f ( a ))
(e
t2 t2 s2
x (t ) e x (s ) ds
0
(b, f (b))
x b x a
f (a ) f ( b)
a b b a
2 x b x a
et f (a ) f ( b)
a b a b
2
et t
x b x a
2
f (b) f (a )
e t a b b a
2
et t
x b x a
f (b) f (a )
a b a b
E 1 +
+ ,E y' 1 y y (0) 0
, 1 E 1
E + ,
+
,
Text of page 23
1
t
x
( J 0 ( - ) J 0 ( t -) d -
0
ab cd
abcd
1
abcd
1
abcd
ac bd
abcd
L{f (t )} F (s )
L{e at f (t )}
e | s| a
2 a
2
(t a2 )
2 a
F (s a) 2
(t a2 )
F (s a) 2 a
(t a)
as
e F (s )
2 a
as
e F (s a) (t a)
Text of page 24
d (A, B) µ(A + B), A, B R
µ * (E ) in f ) µ(E n ) : E n R,
n 1
n 1, 2,....., E / En*
n 1
A, B, C R
fn : X [0, ]
0
lim inf ( f n d µ
( lim in f n d µ
f, g LP (X, µ) P 1
f n (x) .
( lim f n d µ lim ( f n d µ
f g P f P g P
f g P f P g P
f g P f P g P
f g P f P g P
Text of page 25
Z 10 x1 25 x 2 10 x12 x 22 4 x1 x 2
x1 2 x2 x3 10
x1 x2 x4 9
x1 , x 2 , x 3 , x 4 0
Text of page 26
$ (t )
$ (t )
$ (t )
aX b
$( at )
Xi
zj cj 0
i 1, 2, ......, n
W h i ch of t h e above i s
n
E e it
Xi [ $(t )]n
1
Text of page 27
$ (t )
Xn y1 y2 y3 ..... y n $( t 2 ) $( t )
| $(t )| 1
Fn 0 {y1 , y 2 , ....., yn }
$( t ) $ (t )
E (X n 1 / F n )
d
$ n (t ) $(t ) 2 X n 33 X
$n $
X
X if | X|
Y
(1, F , P ) X if | X| 4
0
Xn E (Z| F n ) E (X n 1 | F n )
E (X n 1 ) Xn P (Y B) P (X B)
P (Y B) P (X B)
P (Y B) 4 P (X B)
P (Y B) 0
Text of page 28
0 n
X1 X2 ..... Xn
P m /2
n
Text of page 29
0 if x 0
x 1
F (x) if 0 x 1
3
1 if x 1
Text of page 30
X (X1 , X 2 , ......, X k )
(x y) 0 x 1, 0 y 1
f ( x, y )
0 ot h er wise
k
n , p1 , p2 , ......, p k pi 1
i 1
&
p1 p2 , .....
pk 1/k
Text of page 31
X1 , X 2 , ......, X n
f ( x / µ)
P[X x]
exp [ ( x µ)] ; x µ, µ R
f ( x / µ)
0 ; ot herwise
t 1
x
n 1
t x
;
x n n
x 0, 1, 2 .... t
t 1
x
n 1
t x
n ;
2 2 x n n
s (X i X)
1
x 0, 1, 2 .... n
t 1
x 1
n 1
t x 1
;
x 1 n n
n
[(X (i ) X (1) )] x 1, 2 .... n
i 1
t 1 1
x
n 1
t 1 x
;
x n n
X (1) Min X i
X ( n ) Ma x X i x 1, 2 .... t
Text of page 32
f (x / )
f (x / ) 1
; x 4 0, 40 U (0, &i )
(1 x )
T H 0 : &1 &2
n 1
T H 1 : &1 &2
n
n
T
1 ; x (2) &1 ½
or x(2) 4 &1
$( x )
n 1 0 ; ot h er wise
T
n
T Yi Yi log 1 X i 1 ; x(2) &1 or x(2) 4 &1 ½
i 1 $( x )
0 ; ot h erwise
U (&, 2 &)
&
X (n )
2 1 ; X (2) 4 &1 (1 )½
$(X)
0 ; ot h er wise
X (1) + X ( n )
2
X (1) Min X i X (2) Ma x (X 1 , X 2 )
X (n ) Ma x X i
i
Text of page 33
N (&, 1)
C a u ch y d i st r i b u t i on C ( &
H0 : & 0
H1 : & 4 0
n
1 ; yi 4 n z
$(X) i 1
0 ; ot h erwise
n
n
1 ; yi 4 .z
H0 : & &0 H1 : & &0 $(X) i 1 8
0 ; ot h erwise
n
z
1 ; yi
$(X) i 1 n
0 ; ot herwise
n
8
1 ; (X 1 X2 ) 2 &0 2 z /2 1 ; yi 4 .z
$(X) $(X) i 1 n
0 ; ot h er wise
0 ; ot h erwise
Xi
Yi
1 ; (X1 X2 ) 2 &0 2 z /2 or 1 X 2i
$(X) X1 X 2 4 2 &0 2 z /2
0 ; ot h er wise B(n , p ); 0 p 1
X 1
n (1 n) 1 n
1 ; (X1 X 2 ) 4 2 &0 2 z /2
$(X)
0 ; ot h er wise X 1
n 1 2( n 1)
X 1
n 2(1 n)
X 1
n (1 n) 2(1 n)
Text of page 34
Xn
sam pl e of si ze
T1 Xn
N (&, 1)
Xn
&
Xn
&56
&
Xn
&
n (X m ed &) &
L et X
U (0, &)
&
3 n (2X &)2
&
&
Text of page 35
N (&, 1)
n X2
2
n, & R
2
1, & 0
2
1, & 0
N(&2 , 1), & R
U ( &, &)
&
&
&
&
Text of page 36
A ~ W p (n 1, ) X ~ N p (µ, )
| | 40 U 1
Y = (X µ)' (X µ)
(1 2 t ) p / 2
u' 1 U 1
µ't t' t
u'A 1 u e 2
1
µ't t' t
2 e 2
p
(1 2 t ) p /2
2
n
2
n p 1 X2 Xy
) 1.60 Y2 *
1 0.72 4 2
f ( x, y) e
2.4
A ~ W p (n 1, ) 7
l ' A l, l 4 1.60
) *
)1.60 1 *
1 1.60
2 ) *
n 1
)1.60 4 *
2
n n 1 1 0
) *
)0 1*
1.6 0
2 0 1.6
(l ' l) n 1
Text of page 37
X ~ N p (µ, ) X
Yi 8X i :i i 1, 2, ..., n
X (1)
:i ~ iid (0, 0 2 )
(2)
X
X (1) X (2) ; ; ; ; ;
Yi 8 Xi ,8
;
ei Yi Yi
n
X (1) X (2)
ei X i 0
i 1
n ;
X (1) ei Y i 0
i 1
n ; n
X (2)
X (1) Yi Yi
i 1 i 1
1
11 12 22 21 ; n
V (8) 02 / Xi2
i 1
yi 8x i 9zi :i 1 i n
Yi 8X i :i i 1, 2, ...., n
:i ~ (0, 02 )
1
; ; ; : i ~ f (: i ) e :i ' :i & 1 , :i 4 0
8 1.5, se (8) 0.75, 9 4, (&)
;
se ( 9 ) 0.75
; ;
cov (8, 9 ) 0.2
; ; ˆ OLS
se (8, 9 )
8
8ˆ OLS 8̂OLS
8
6 86
Text of page 38
8 0 8̂OLS
{Y, X8, 0 I }
2
R8 9 8<6
8̂OLS
8̂OLS
8̂ RLS
8̂OLS
V 8ˆ OLS 0 2 (X ' X) 1
8
8̂OLS
8̂ RLS
{Y, X8, 1}
8
8ˆ GLS (X1 1 1 X) 1 X1 1 1 Y
V (8ˆ RLS ) V (8ˆ OLS )
8ˆ GLS (X1 1 X) 1 X1 1 Y
V 8ˆ GLS (X1 1 1 X) 1
V (8ˆ RLS ) 0 2 (X' X) 1
E 8ˆ GLS 8
Text of page 39
; i ij
yk
( y)
CV ( x )
=
CV( y )
i (n 1)
i
CV ( x )
= n (n 1)
2 CV( y ) i
i
CV ( x ) (n 1)
= i
i
2 CV( y )
i n
CV ( x ) i
=4
2 CV( y )
0 = 1
= 0
1 = 0
= 1
Text of page 40
-i Qi
Qi
-i
>
Qi >
-i E
rE kr
1 / N Cn Qi >
-i E
E kr
yijk i -j 8k :ijk ,
i, j , k 1, 2, ..... p
yijk µ i -j : ijk ,
i, j , k 1, 2, ..... p
yijk µ i -j 8k : ijk ,
i, j , k 1, 2, ..... p
yijk µ ij 8k : ijk ,
i, j , k 1, 2, ..... p
Text of page 41
0 2: b 0 2-8
rb 82j
0 :2 b 0 2-8
a 1
rb 82j
0 :2 b 0 2-8
a 1
rb 82j
0 :2 b 0 2-8
a 1
Text of page 42
Xt $
Xt µ $ Xt 1 Zt
Xt 1 $2 Xt 2 Zt Z i ~ iid
Z t ~ iid N (0, 0 2 )
$1 $2 1, $1 $2 1,
1 $1 1
0 an d t h at X
$1 $ 2 4 1, $2 $1 1,
1 $2 1
$1 $2 1, $2 $1 1,
1 $2 1
$1 $2 4 1, $1 $2 1,
1 $t t
Xt µ+ $t j Z j
1 $ j 1
1 $1 1
Xt Zt & Zt 1
E(X t ) µ Yt Zt 1 / & Zt 1
1
V(X t )
1 $2
&
Text of page 43
?
{X n , n 0}
?
?
3/4 1/4 0
p 1/4 1/2 1/4
?
0 3/4 1/4
?
1
p(X 0 i)
3
p (X 2 2| x1 1)
Text of page 44
{X n }0
p [X n 1 1| X n 1] p1
p [X n 1 0| X n 1]
p [X n 1 1| X n 0] p0
p [X n 1 0| X n 0]
p [X1 1] 1 1 p (X1 0)
1 p0
1 p1
p1 p0
1
2
1 1/2
Text of page 46
6
Text of page 1
MAHARASHTRA STATE ELIGIBILITY TEST - 16TH APRIL,2017
ANSWER KEY UPDATED AFTER EVALUATION OF GRIEVANCES FOR PAPER-III
SUBJECT: MATHEMATICAL SCIENCE (SET A) (SUBJECT CODE 30)
1 C 31 A 61 A 91 C 121 D
2 D 32 C 62 A 92 9 122 D
3 C 33 D 63 A 93 C 123 A
4 C 34 D 64 B 94 C 124 C
5 D 35 9 65 D 95 A 125 C
6 B 36 D 66 A 96 D 126 A
7 A 37 9 67 C 97 B 127 D
8 C 38 9 68 B 98 A 128 C
9 B 39 B 69 A 99 B 129 C
10 D 40 A 70 C 100 B 130 C
11 C 41 D 71 A 101 D 131 A
12 D 42 B 72 A/C 102 A 132 A
13 A 43 C 73 A 103 B 133 A
14 B 44 D 74 B 104 B 134 A
15 B 45 B 75 C 105 B 135 D
16 C 46 A 76 B 106 B 136 B
17 A 47 D 77 B 107 A 137 D
18 C 48 C 78 A 108 C 138 C
19 C 49 B 79 B 109 D 139 C
20 A 50 D 80 A 110 A 140 B
21 C 51 C 81 B 111 A 141 A
22 A 52 C 82 C 112 A 142 C
23 A 53 A 83 C 113 D 143 B
24 D 54 B 84 B 114 D 144 C
25 B 55 C 85 B 115 C 145 B
26 9 56 B 86 C 116 A
27 D 57 C 87 D 117 A
28 A 58 D 88 C 118 B
29 A 59 B 89 D 119 D
30 C 60 D 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
Text of page 2
MAHARASHTRA STATE ELIGIBILITY TEST - 16TH APRIL,2017 ANSWER KEY UPDATED AFTER EVALUATION OF GRIEVANCES FOR PAPER-III SUBJECT: MATHEMATICAL SCIENCE (SET B) (SUBJECT CODE 30) 1 D 31 A 61 B 91 A 121 A 2 C 32 D 62 A 92 A 122 C 3 C 33 C 63 C 93 D 123 B 4 D 34 B 64 B 94 D 124 C 5 C 35 D 65 D 95 C 125 B 6 C 36 C 66 C 96 A 126 B 7 A 37 C 67 D 97 A 127 B 8 A 38 A 68 A 98 B 128 A 9 D 39 B 69 B 99 D 129 B 10 B 40 C 70 B 100 B 130 A 11 9 41 B 71 C 101 D 131 B 12 D 42 C 72 A 102 D 132 C 13 A 43 D 73 C 103 A 133 C 14 A 44 B 74 C 104 C 134 B 15 C 45 D 75 A 105 C 135 B 16 A 46 A 76 D 106 A 136 C 17 C 47 A 77 B 107 D 137 D 18 D 48 A 78 A 108 C 138 C 19 D 49 B 79 B 109 C 139 D 20 9 50 D 80 B 110 C 140 B 21 D 51 A 81 D 111 A 141 C 22 9 52 C 82 A 112 A 142 9 23 9 53 B 83 B 113 A 143 C 24 B 54 A 84 B 114 A 144 C 25 A 55 C 85 B 115 D 145 A 26 D 56 A 86 B 116 B 27 B 57 A/C 87 A 117 D 28 C 58 A 88 C 118 C 29 D 59 B 89 D 119 C 30 B 60 C 90 A 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
Text of page 3
MAHARASHTRA STATE ELIGIBILITY TEST - 16TH APRIL,2017 ANSWER KEY UPDATED AFTER EVALUATION OF GRIEVANCES FOR PAPER-III SUBJECT: MATHEMATICAL SCIENCE (SET C) (SUBJECT CODE 30) 1 C 31 B 61 C 91 D 121 B 2 C 32 C 62 A 92 D 122 C 3 D 33 D 63 C 93 A 123 C 4 C 34 B 64 C 94 C 124 B 5 D 35 D 65 A 95 C 125 B 6 A 36 A 66 C 96 A 126 C 7 C 37 A 67 A 97 D 127 D 8 D 38 A 68 A 98 C 128 C 9 D 39 B 69 D 99 C 129 D 10 9 40 D 70 B 100 C 130 B 11 D 41 A 71 9 101 A 131 C 12 9 42 C 72 D 102 A 132 9 13 9 43 B 73 A 103 A 133 C 14 B 44 A 74 A 104 A 134 C 15 A 45 C 75 C 105 D 135 A 16 D 46 A 76 B 106 B 136 D 17 B 47 A/C 77 A 107 D 137 B 18 C 48 A 78 C 108 C 138 A 19 D 49 B 79 D 109 C 139 B 20 B 50 C 80 A 110 B 140 B 21 A 51 B 81 A 111 A 141 D 22 D 52 A 82 A 112 C 142 A 23 C 53 C 83 D 113 B 143 B 24 B 54 B 84 D 114 C 144 B 25 D 55 D 85 C 115 B 145 B 26 C 56 C 86 A 116 B 27 C 57 D 87 A 117 B 28 A 58 A 88 B 118 A 29 B 59 B 89 D 119 B 30 C 60 B 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
Text of page 4
MAHARASHTRA STATE ELIGIBILITY TEST - 16TH APRIL,2017 ANSWER KEY UPDATED AFTER EVALUATION OF GRIEVANCES FOR PAPER-III SUBJECT: MATHEMATICAL SCIENCE (SET D) (SUBJECT CODE 30) 1 C 31 A 61 9 91 A 121 C 2 D 32 C 62 D 92 A 122 9 3 C 33 B 63 A 93 A 123 C 4 D 34 A 64 A 94 A 124 C 5 C 35 C 65 C 95 D 125 A 6 D 36 A 66 A 96 B 126 D 7 B 37 A/C 67 C 97 D 127 B 8 C 38 A 68 D 98 C 128 A 9 D 39 B 69 D 99 C 129 B 10 B 40 C 70 9 100 B 130 B 11 A 41 B 71 D 101 A 131 D 12 D 42 A 72 9 102 C 132 A 13 C 43 C 73 9 103 B 133 B 14 B 44 B 74 B 104 C 134 B 15 D 45 D 75 A 105 B 135 B 16 C 46 C 76 A 106 B 136 B 17 C 47 D 77 A 107 B 137 A 18 A 48 A 78 B 108 A 138 C 19 B 49 B 79 D 109 B 139 D 20 C 50 B 80 B 110 A 140 A 21 B 51 C 81 D 111 B 141 A 22 C 52 A 82 D 112 C 142 A 23 D 53 C 83 A 113 C 143 D 24 B 54 C 84 C 114 B 144 D 25 D 55 A 85 C 115 B 145 C 26 A 56 C 86 A 116 C 27 A 57 A 87 D 117 D 28 A 58 A 88 C 118 C 29 B 59 D 89 C 119 D 30 D 60 B 90 C 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
Text of page 5
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.