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Page 1
101.
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1
4
1
1/4
1
95
4
99
3
Ans(2)
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102.
? ?
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2
m n P
m n 2 mn p
m n p 2 mn
m n p 4mn
Ans(4)
??
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? ? ? ?
? ? ?
103.
2
2
3
3
1
x 14
x
1
x4
x
1
x 4 ( 13)
x
52
Ans( 1)
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??
??
?
104.
27a 36 9 4 27 12 a
26a 15 41
26
a
26
a1
Ans( 1)
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??
?
?
??
105.
A
B
C
O
Page 2
101.
? ?
1
4
1
1/4
1
95
4
99
3
Ans(2)
?
?? ??
?
?? ??
?? ??
??
?
102.
? ?
? ?
2
m n P
m n 2 mn p
m n p 2 mn
m n p 4mn
Ans(4)
??
? ? ?
? ? ? ?
? ? ?
103.
2
2
3
3
1
x 14
x
1
x4
x
1
x 4 ( 13)
x
52
Ans( 1)
??
??
??
?
104.
27a 36 9 4 27 12 a
26a 15 41
26
a
26
a1
Ans( 1)
? ? ? ? ? ?
??
?
?
??
105.
A
B
C
O
BC
BOC 180
2
180 60
120
Ans(4)
? ? ?
??
? ? ? ?
??
??
? ? ? ?
??
106.
A
B
C
30°+
B
2
?
E
D
60°
B/2
B/2
30°+
B
2
?
BB
30 C E 180
22
30 120 E 180
E 30
Ans(2)
??
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ?
? ? ?
107.
A
B
C
D
90°-a
a
2a
a
90°-a
BCD 90
Ans(4)
? ? ?
108.
Sm = n Sn = m
? ?
2n
2a m 1 n
m
? ? ? ?
? ?
? ?
? ?
22
2m
2a n 1 n
n
nm
m n n 2
mn
nm
n2
mn
2n m n
2a m 1 2
m mn
? ? ? ?
?? ?
??
??
??
?
??
??
??
??
?
??
? ? ?
??
??
Page 3
101.
? ?
1
4
1
1/4
1
95
4
99
3
Ans(2)
?
?? ??
?
?? ??
?? ??
??
?
102.
? ?
? ?
2
m n P
m n 2 mn p
m n p 2 mn
m n p 4mn
Ans(4)
??
? ? ?
? ? ? ?
? ? ?
103.
2
2
3
3
1
x 14
x
1
x4
x
1
x 4 ( 13)
x
52
Ans( 1)
??
??
??
?
104.
27a 36 9 4 27 12 a
26a 15 41
26
a
26
a1
Ans( 1)
? ? ? ? ? ?
??
?
?
??
105.
A
B
C
O
BC
BOC 180
2
180 60
120
Ans(4)
? ? ?
??
? ? ? ?
??
??
? ? ? ?
??
106.
A
B
C
30°+
B
2
?
E
D
60°
B/2
B/2
30°+
B
2
?
BB
30 C E 180
22
30 120 E 180
E 30
Ans(2)
??
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ?
? ? ?
107.
A
B
C
D
90°-a
a
2a
a
90°-a
BCD 90
Ans(4)
? ? ?
108.
Sm = n Sn = m
? ?
2n
2a m 1 n
m
? ? ? ?
? ?
? ?
? ?
22
2m
2a n 1 n
n
nm
m n n 2
mn
nm
n2
mn
2n m n
2a m 1 2
m mn
? ? ? ?
?? ?
??
??
??
?
??
??
??
??
?
??
? ? ?
??
??
? ? ? ?
? ? ? ? ? ? ? ?
? ?
2
2
2 2 2 2
2n 2 m 1 m n
2a
mn
2n 2 m 1 m n m n 1 m n 1 mn
Sm n 2
2 mn mn
mn
n m mn m n m mn mn n m n
mn
mn
? ? ?
?
?? ? ? ? ? ? ? ? ?
? ? ?
??
??
?
?? ? ? ? ? ? ? ? ? ? ? ?
??
? ? ?
109.
? ?
? ? ? ? ? ?
22
22
2
2
2
2 2 2 2 2
2 2 2 2 2 2 2 2 2 4 2 2
2 2 2 4
A a b
B 2b a c
C b c
B 4AC 0
B 4AC
4b a c 4 a b b c
4b a 4b c 8b ac 4a b 4a c 4b 4b c
8b ac 4a c 4b
??
? ? ?
??
??
?
? ? ? ?
? ? ? ? ? ?
??
? ?
4 2 2 2
2
2
by 4
b a c 2b ac 0
b ac 0
?
? ? ?
??
2
b ac
Ans(3)
?
110.
A
B
C
p
q
? ? ? ?
2 2 2
2 2 2
2
p q AB
AB p q
p q p q
pq
AB 2q 1
AB 2q 1
Ans(2)
??
??
? ? ?
??
??
??
Page 4
101.
? ?
1
4
1
1/4
1
95
4
99
3
Ans(2)
?
?? ??
?
?? ??
?? ??
??
?
102.
? ?
? ?
2
m n P
m n 2 mn p
m n p 2 mn
m n p 4mn
Ans(4)
??
? ? ?
? ? ? ?
? ? ?
103.
2
2
3
3
1
x 14
x
1
x4
x
1
x 4 ( 13)
x
52
Ans( 1)
??
??
??
?
104.
27a 36 9 4 27 12 a
26a 15 41
26
a
26
a1
Ans( 1)
? ? ? ? ? ?
??
?
?
??
105.
A
B
C
O
BC
BOC 180
2
180 60
120
Ans(4)
? ? ?
??
? ? ? ?
??
??
? ? ? ?
??
106.
A
B
C
30°+
B
2
?
E
D
60°
B/2
B/2
30°+
B
2
?
BB
30 C E 180
22
30 120 E 180
E 30
Ans(2)
??
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ?
? ? ?
107.
A
B
C
D
90°-a
a
2a
a
90°-a
BCD 90
Ans(4)
? ? ?
108.
Sm = n Sn = m
? ?
2n
2a m 1 n
m
? ? ? ?
? ?
? ?
? ?
22
2m
2a n 1 n
n
nm
m n n 2
mn
nm
n2
mn
2n m n
2a m 1 2
m mn
? ? ? ?
?? ?
??
??
??
?
??
??
??
??
?
??
? ? ?
??
??
? ? ? ?
? ? ? ? ? ? ? ?
? ?
2
2
2 2 2 2
2n 2 m 1 m n
2a
mn
2n 2 m 1 m n m n 1 m n 1 mn
Sm n 2
2 mn mn
mn
n m mn m n m mn mn n m n
mn
mn
? ? ?
?
?? ? ? ? ? ? ? ? ?
? ? ?
??
??
?
?? ? ? ? ? ? ? ? ? ? ? ?
??
? ? ?
109.
? ?
? ? ? ? ? ?
22
22
2
2
2
2 2 2 2 2
2 2 2 2 2 2 2 2 2 4 2 2
2 2 2 4
A a b
B 2b a c
C b c
B 4AC 0
B 4AC
4b a c 4 a b b c
4b a 4b c 8b ac 4a b 4a c 4b 4b c
8b ac 4a c 4b
??
? ? ?
??
??
?
? ? ? ?
? ? ? ? ? ?
??
? ?
4 2 2 2
2
2
by 4
b a c 2b ac 0
b ac 0
?
? ? ?
??
2
b ac
Ans(3)
?
110.
A
B
C
p
q
? ? ? ?
2 2 2
2 2 2
2
p q AB
AB p q
p q p q
pq
AB 2q 1
AB 2q 1
Ans(2)
??
??
? ? ?
??
??
??
111.
d 25 16 4
45
35
Ans(3)
? ? ?
?
?
112.
32
4
r 4 r
3
r3
2 r 6
Ans(3)
? ? ?
?
? ? ?
113.
A B
C
10
8
6
4+r
6-r
6-r
8-r
r
r
8 r 4 r
2r 4
r 2cm
Ans( 1)
? ? ?
?
?
114.
1
( Direct ans)
6
Ans(4)
115.
11
6
3
Ans(3)
? ? ? ? ? ? ? ? ?
? ? ? ?
??
Page 5
101.
? ?
1
4
1
1/4
1
95
4
99
3
Ans(2)
?
?? ??
?
?? ??
?? ??
??
?
102.
? ?
? ?
2
m n P
m n 2 mn p
m n p 2 mn
m n p 4mn
Ans(4)
??
? ? ?
? ? ? ?
? ? ?
103.
2
2
3
3
1
x 14
x
1
x4
x
1
x 4 ( 13)
x
52
Ans( 1)
??
??
??
?
104.
27a 36 9 4 27 12 a
26a 15 41
26
a
26
a1
Ans( 1)
? ? ? ? ? ?
??
?
?
??
105.
A
B
C
O
BC
BOC 180
2
180 60
120
Ans(4)
? ? ?
??
? ? ? ?
??
??
? ? ? ?
??
106.
A
B
C
30°+
B
2
?
E
D
60°
B/2
B/2
30°+
B
2
?
BB
30 C E 180
22
30 120 E 180
E 30
Ans(2)
??
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ?
? ? ?
107.
A
B
C
D
90°-a
a
2a
a
90°-a
BCD 90
Ans(4)
? ? ?
108.
Sm = n Sn = m
? ?
2n
2a m 1 n
m
? ? ? ?
? ?
? ?
? ?
22
2m
2a n 1 n
n
nm
m n n 2
mn
nm
n2
mn
2n m n
2a m 1 2
m mn
? ? ? ?
?? ?
??
??
??
?
??
??
??
??
?
??
? ? ?
??
??
? ? ? ?
? ? ? ? ? ? ? ?
? ?
2
2
2 2 2 2
2n 2 m 1 m n
2a
mn
2n 2 m 1 m n m n 1 m n 1 mn
Sm n 2
2 mn mn
mn
n m mn m n m mn mn n m n
mn
mn
? ? ?
?
?? ? ? ? ? ? ? ? ?
? ? ?
??
??
?
?? ? ? ? ? ? ? ? ? ? ? ?
??
? ? ?
109.
? ?
? ? ? ? ? ?
22
22
2
2
2
2 2 2 2 2
2 2 2 2 2 2 2 2 2 4 2 2
2 2 2 4
A a b
B 2b a c
C b c
B 4AC 0
B 4AC
4b a c 4 a b b c
4b a 4b c 8b ac 4a b 4a c 4b 4b c
8b ac 4a c 4b
??
? ? ?
??
??
?
? ? ? ?
? ? ? ? ? ?
??
? ?
4 2 2 2
2
2
by 4
b a c 2b ac 0
b ac 0
?
? ? ?
??
2
b ac
Ans(3)
?
110.
A
B
C
p
q
? ? ? ?
2 2 2
2 2 2
2
p q AB
AB p q
p q p q
pq
AB 2q 1
AB 2q 1
Ans(2)
??
??
? ? ?
??
??
??
111.
d 25 16 4
45
35
Ans(3)
? ? ?
?
?
112.
32
4
r 4 r
3
r3
2 r 6
Ans(3)
? ? ?
?
? ? ?
113.
A B
C
10
8
6
4+r
6-r
6-r
8-r
r
r
8 r 4 r
2r 4
r 2cm
Ans( 1)
? ? ?
?
?
114.
1
( Direct ans)
6
Ans(4)
115.
11
6
3
Ans(3)
? ? ? ? ? ? ? ? ?
? ? ? ?
??
116.
11 55m 44
55m 55
m1
Ans(2)
??
?
?
117.
x y 1
2x 2y 2
??
??
Both lines coincide. Thus there will be infinite number of solution
Ans (3)
118.
A
B
C
22
ax ?
x
a
?
22
x
cos
ax
Ans( 1)
??
?
119.
? ? ? ?
n
x n x 1 q x r
1 n r
Ans( 3)
? ? ? ?
??
120.
Ans (2) Direct answer
121. Ans: C
Solution:-
12
avg
12
2 V V
V
VV
2 60 40
100
48 KMPH
?
?
??
?
?
122. Ans:
if
p mv, p 4mv
p 4mv mv
3mv
% of change 300%
??
? ? ?
?
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