KVPY SA Stream Solution 2012
May 13, 2018 | Author: Nilesh Gupta | Category: N/A
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KVPY SA Stream Solution 2012...
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HINTS & SOLUTIONS (YEAR-2012) ANSWER KEY Q ues .
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
A n s .
C
B
B
A
D
B
B
B
B
B
A
C
D
A
C
B
A
C
D
B
Q ues . 21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
A n s .
A
A
D
A
C
B
B
C
A
C
A
C
D
C
D
B
B
B
C
Q ues . 41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
A n s .
B
C
B
B
A
D
B
A
A
C
C
A
B
D
B
D
C
C
A
Q ues . 61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
A n s .
B
C
B
C
A
D
B
B
D
B
B
B
B
*
A
D
C
C
B
D
B
D
CAREER POINT : 128, Shakti Nagar, Kota-324009 (Raj.), Ph: 0744-2503892
Page # 138
PART-A (1 Mark) MATHEMATICS 1.
f(x) = ax2 + bx + c 10 = 4a+2b+c ......... (1) –2 = 4a – 2b + c .. ... ... (2) 12 = 4b b = 3
2.
(.75 )3 (1)3 (.75 )3 1 = = 4 1 (0 .75 ) . 25 square root = 2
3.
10, 10 +d , 10+2d , d I, d I 10+2d < 10+10+d d < 10
d = 1, 2, 3, ..... 9 9 triangles are possible 4.
a = 3k b=k c = 5k – 4k = k d = 6k – 5k = k a b 2c 3 d
5.
=
3k k 2k 3 k
=
1 2
2 2 ....... n 2 ] [12 3 2 5 2 ..... (2n 1)2 ] 2 2 [12
1 2 + 2 2 + 3 2 + ...... + (2n) 2 =
2n( 2n 1)( 4 n 1) 6
[1 2 + 3 2 ..... + (2n – 1)2 + 2 2 [1 2 + 2 n ......+ n 2] =
2n( 2n 1)( 4 n 1) 6
S+4
S+
n(n 1)( 2n 1) 6
=
2n( 2n 1)( 4 n 1) 6
–
2n(2n 1)( 4 n 1) 6 4 n(n 1)( 2n 1) 6
CAREER POINT : 128, Shakti Nagar, Kota-324009 (Raj.), Ph: 0744-2503892
Page # 139
2n 1 [ 4 n 1 2n 2 ] 6
= 2n
=
2 n(2n 1)(2 n 1) 6 4 n(n 1)(2n 1)
Ratio =
2n 2 2n 1
×
6
6 2n 2 = 2n( 2n 1)(2n 1) 2n 1
10 1
>
10 0
200n + 200 > 202n – 101 2n < 301 n<
6.
30 1 2
value = 15 0 maximum value
A AD B = 18 0 – 2 B C BFC = 180 – 2 B 18 0 – 18 0
A 2
– B + 180 –
C 2
– B = 180
A C + 2B 2
36 0 = A + C + 4B 36 0 = A + B + C + 3B
B = 60
IFD = IBD =
B = 30 2
7.
+
=
+
2 1 2
1
2
=
= 1
+
2 = 1
2 1
CAREER POINT : 128, Shakti Nagar, Kota-324009 (Raj.), Ph: 0744-2503892
Page # 140
8.
R
=
1 2
= 2R + R = r
Now Now 3R = r R = r/3.
9.
tan =
AB , AF
tan =
2 1
sin =
AX AF
2 5
x = 90
= A X ;
XF =
1 5
1 2 1 1 ( AX ) ( XF) Are a of AXF 1 2 2 5 5 = = = 1 1 Are a of AB F 5 ( AB AF ) 2 1 2 2 10.
RQP = 176º SPQ = 2º SQP = 89º (SP = PQ) SQR = 176 – 89 = 87º
11.
o
1 19 5 o = 90 + 15× = 2 2 = 360 –
19 5 2
Difference =
=
72 0 19 5 2
=
52 5 2
52 5 19 5 33 0 = = 165º 2 2
CAREER POINT : 128, Shakti Nagar, Kota-324009 (Raj.), Ph: 0744-2503892
Page # 141
12.
Let A take x
B take y has has together is hours =
1 1 in of work x y
Let time be t
1 x
t
1 + 8 = t 8 y x
t 8 = y x
1 x
t
1 t 4 . 5 = y y
4 .5 t = y x x 8 = ; y t 8 t
=
x t = y 4 .5
t 4 .5
t2 = 36 t = 6 hours. 13.
Let weight of bucket be and weight of water is
2a + b = 20 ............. (1) and 3a + 2b = 33 ............. (2)
= 7 = 6 total weight = + = 13 13 14.
mn = 144 (m, n) = total 15 positive ordered pairs and ne gative gative ordered pairs are poss ible
15.
0
5 , 1 0 , 1 5 , ... 4 0
1
2 , 7 , ... .. .. . .. . 3 6
3
3 , 8 , ... .. .. . .. . 3 8
4
4 , 9 , ... .. .. . .. . 3 9
PHYSICS 16.
Momentum conservation mv = (m + m)v v’ =
v 2 2
v K.E. = × 2m 2 m = mv 2 /4. 2 2 1
CAREER POINT : 128, Shakti Nagar, Kota-324009 (Raj.), Ph: 0744-2503892
Page # 142
17.
A ball ball falls vertically vertically downward downward and bounces off a horizontal floor. floor. The spe ed of the ball jus t before Down
:
m g – F – m a1
a1 = g –
Up :
F m
m g + F = m a2
a2 = g +
F m
a2 > a1 .
19.
= 30º + 90º = 120º .
22.
i=r=0 So,
= 0
No dispersion.
23.
CAREER POINT : 128, Shakti Nagar, Kota-324009 (Raj.), Ph: 0744-2503892
Page # 143
24.
25.
In
v2 3R
P=
In
Q =
In
R=
3v2 R v2 R 4v2
In
S=
So,
P
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