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Page 1
NATIONAL TALENT SEARCH EXAMINATION, 2015 - 16
(STATE LEVEL)
(FOR STUDENTS STUDYING IN CLASS X)
SAT – ANSWER KEY
1 C 11 A 21 A 31 B 41 B
2 C 12 D 22 C 32 C 42 D
3 B 13 B 23 D 33 C 43 B
4 D 14 A 24 A 34 B 44 C
5 D 15 C 25 C 35 C 45 A
6 A 16 C 26 A 36 D 46 C
7 D 17 C 27 B 37 D 47 C
8 B 18 A 28 C 38 D 48 D
9 B 19 B 29 B 39 D 49 D
10 D 20 D 30 D 40 B 50 D
51 B 61 C 71 B 81 D 91 B
52 C 62 A/B 72 A 82 A 92 D
53 B 63 B 73 C 83 C 93 D
54 A 64 D 74 D 84 B 94 C
55 B 65 A 75 B 85 A 95 B
56 D 66 C 76 D 86 C 96 B
57 B 67 D 77 B 87 A 97 C
58 D 68 B 78 B 88 A 98 D
59 B 69 C 79 B 89 C 99 A
60 B 70 C 80 A 90 A 100 D
Page 2
NATIONAL TALENT SEARCH EXAMINATION, 2015 - 16
(STATE LEVEL)
(FOR STUDENTS STUDYING IN CLASS X)
SAT – ANSWER KEY
1 C 11 A 21 A 31 B 41 B
2 C 12 D 22 C 32 C 42 D
3 B 13 B 23 D 33 C 43 B
4 D 14 A 24 A 34 B 44 C
5 D 15 C 25 C 35 C 45 A
6 A 16 C 26 A 36 D 46 C
7 D 17 C 27 B 37 D 47 C
8 B 18 A 28 C 38 D 48 D
9 B 19 B 29 B 39 D 49 D
10 D 20 D 30 D 40 B 50 D
51 B 61 C 71 B 81 D 91 B
52 C 62 A/B 72 A 82 A 92 D
53 B 63 B 73 C 83 C 93 D
54 A 64 D 74 D 84 B 94 C
55 B 65 A 75 B 85 A 95 B
56 D 66 C 76 D 86 C 96 B
57 B 67 D 77 B 87 A 97 C
58 D 68 B 78 B 88 A 98 D
59 B 69 C 79 B 89 C 99 A
60 B 70 C 80 A 90 A 100 D
NATIONAL TALENT SEARCH EXAMINATION, 2015-16
(STATE LEVEL)
(FOR STUDENTS STUDYING IN CLASS X)
SAT – SOLUTION
MATHEMATICS
1. Sol.
? ? ? ?
2
2
2
2
2
1 1 1
f 2x 4x 1
x4 x
11
2x 4 1
4x
11
2x
4x
1
f x x
4
? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
??
??
? ? ? ? ??
??
??
??
??
??
??
?? ??
??
??
??
??
?
2. Sol.
? ? ? ?
x 2 x 3
x 2 x 3 0
x 3 x 1 0
x 3, x 1
x9
??
? ? ?
? ? ?
??
? ? ?
??
??
3. Sol.
5 2 6 ?
=
? ? ? ?
22
3 2 2 6
32
??
??
4. Sol.
xy
ab
yx
x y x y
a 1 b 1
yx
11
1
a 1 1 b
??
??
? ? ? ?
??
??
5. Sol.
? ? ? ?
? ? ? ?
22
22
2 x 2x 1 1 3 y 6y 9 9 31
2 x 1 2 3 y 3 27 31
? ? ? ? ? ? ? ?
? ? ? ? ? ? ?
Least value = 2
Page 3
NATIONAL TALENT SEARCH EXAMINATION, 2015 - 16
(STATE LEVEL)
(FOR STUDENTS STUDYING IN CLASS X)
SAT – ANSWER KEY
1 C 11 A 21 A 31 B 41 B
2 C 12 D 22 C 32 C 42 D
3 B 13 B 23 D 33 C 43 B
4 D 14 A 24 A 34 B 44 C
5 D 15 C 25 C 35 C 45 A
6 A 16 C 26 A 36 D 46 C
7 D 17 C 27 B 37 D 47 C
8 B 18 A 28 C 38 D 48 D
9 B 19 B 29 B 39 D 49 D
10 D 20 D 30 D 40 B 50 D
51 B 61 C 71 B 81 D 91 B
52 C 62 A/B 72 A 82 A 92 D
53 B 63 B 73 C 83 C 93 D
54 A 64 D 74 D 84 B 94 C
55 B 65 A 75 B 85 A 95 B
56 D 66 C 76 D 86 C 96 B
57 B 67 D 77 B 87 A 97 C
58 D 68 B 78 B 88 A 98 D
59 B 69 C 79 B 89 C 99 A
60 B 70 C 80 A 90 A 100 D
NATIONAL TALENT SEARCH EXAMINATION, 2015-16
(STATE LEVEL)
(FOR STUDENTS STUDYING IN CLASS X)
SAT – SOLUTION
MATHEMATICS
1. Sol.
? ? ? ?
2
2
2
2
2
1 1 1
f 2x 4x 1
x4 x
11
2x 4 1
4x
11
2x
4x
1
f x x
4
? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
??
??
? ? ? ? ??
??
??
??
??
??
??
?? ??
??
??
??
??
?
2. Sol.
? ? ? ?
x 2 x 3
x 2 x 3 0
x 3 x 1 0
x 3, x 1
x9
??
? ? ?
? ? ?
??
? ? ?
??
??
3. Sol.
5 2 6 ?
=
? ? ? ?
22
3 2 2 6
32
??
??
4. Sol.
xy
ab
yx
x y x y
a 1 b 1
yx
11
1
a 1 1 b
??
??
? ? ? ?
??
??
5. Sol.
? ? ? ?
? ? ? ?
22
22
2 x 2x 1 1 3 y 6y 9 9 31
2 x 1 2 3 y 3 27 31
? ? ? ? ? ? ? ?
? ? ? ? ? ? ?
Least value = 2
6. Sol.
? ?
2
22
22
2
2r h r h
4r 4rh r
3r 4rh
r
4:3
h
? ? ?
??
?
?
7. Sol.
y = c (cy + bz) + az
(1 – c
2
)y = (bc + a) z ……….(1)
Z = b(cy + bz) + ay
(1 – b
2
) z = (bc + a) y ……….(2)
2
2
2 2 2 2
1 c bc a
bc a 1b
1 b c b c
??
?
? ?
? ? ?
22
bc ?
2
2 2 2
abc abc a
a b c 1 2abc
???
? ? ? ? ?
8. Sol.
x(x
3
– 1) < 0
x(x – 1) (x
2
+ x + 1) < 0
x
2
+ x + 1 > 0 because discriminant is – ve
x(x – 1) < 0 0 x 1 ? ? ?
9. Sol.
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
250 200 150 100
50 50 50 50
5 4 3 2
50 50 50 50
2 3 4 5
2 3 4 5
32 81 64 25
?
?
10. Sol.
4 *5 + 5 * 6
= (4 + 5 – 4 × 5) + (5 + 6 – 5 × 6)
= - 30
11. Sol.
Let principal amount is A. then
25
A1
A 10 1
2
1250 A 50,000
100 100
??
??
? ? ? ?
12. Sol.
Net cost price
198 198
10 10
11
100 100
??
??
10 10
198 400
11 9
Selling price 2 198 396
loss 400 396 4
4
%loss 100 1
400
??
? ? ?
??
??
? ? ?
? ? ?
? ? ?
13. Sol.
Let the price two years before be P.
So, current price will be
2
4
P1
100
??
??
??
??
Page 4
NATIONAL TALENT SEARCH EXAMINATION, 2015 - 16
(STATE LEVEL)
(FOR STUDENTS STUDYING IN CLASS X)
SAT – ANSWER KEY
1 C 11 A 21 A 31 B 41 B
2 C 12 D 22 C 32 C 42 D
3 B 13 B 23 D 33 C 43 B
4 D 14 A 24 A 34 B 44 C
5 D 15 C 25 C 35 C 45 A
6 A 16 C 26 A 36 D 46 C
7 D 17 C 27 B 37 D 47 C
8 B 18 A 28 C 38 D 48 D
9 B 19 B 29 B 39 D 49 D
10 D 20 D 30 D 40 B 50 D
51 B 61 C 71 B 81 D 91 B
52 C 62 A/B 72 A 82 A 92 D
53 B 63 B 73 C 83 C 93 D
54 A 64 D 74 D 84 B 94 C
55 B 65 A 75 B 85 A 95 B
56 D 66 C 76 D 86 C 96 B
57 B 67 D 77 B 87 A 97 C
58 D 68 B 78 B 88 A 98 D
59 B 69 C 79 B 89 C 99 A
60 B 70 C 80 A 90 A 100 D
NATIONAL TALENT SEARCH EXAMINATION, 2015-16
(STATE LEVEL)
(FOR STUDENTS STUDYING IN CLASS X)
SAT – SOLUTION
MATHEMATICS
1. Sol.
? ? ? ?
2
2
2
2
2
1 1 1
f 2x 4x 1
x4 x
11
2x 4 1
4x
11
2x
4x
1
f x x
4
? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
??
??
? ? ? ? ??
??
??
??
??
??
??
?? ??
??
??
??
??
?
2. Sol.
? ? ? ?
x 2 x 3
x 2 x 3 0
x 3 x 1 0
x 3, x 1
x9
??
? ? ?
? ? ?
??
? ? ?
??
??
3. Sol.
5 2 6 ?
=
? ? ? ?
22
3 2 2 6
32
??
??
4. Sol.
xy
ab
yx
x y x y
a 1 b 1
yx
11
1
a 1 1 b
??
??
? ? ? ?
??
??
5. Sol.
? ? ? ?
? ? ? ?
22
22
2 x 2x 1 1 3 y 6y 9 9 31
2 x 1 2 3 y 3 27 31
? ? ? ? ? ? ? ?
? ? ? ? ? ? ?
Least value = 2
6. Sol.
? ?
2
22
22
2
2r h r h
4r 4rh r
3r 4rh
r
4:3
h
? ? ?
??
?
?
7. Sol.
y = c (cy + bz) + az
(1 – c
2
)y = (bc + a) z ……….(1)
Z = b(cy + bz) + ay
(1 – b
2
) z = (bc + a) y ……….(2)
2
2
2 2 2 2
1 c bc a
bc a 1b
1 b c b c
??
?
? ?
? ? ?
22
bc ?
2
2 2 2
abc abc a
a b c 1 2abc
???
? ? ? ? ?
8. Sol.
x(x
3
– 1) < 0
x(x – 1) (x
2
+ x + 1) < 0
x
2
+ x + 1 > 0 because discriminant is – ve
x(x – 1) < 0 0 x 1 ? ? ?
9. Sol.
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
250 200 150 100
50 50 50 50
5 4 3 2
50 50 50 50
2 3 4 5
2 3 4 5
32 81 64 25
?
?
10. Sol.
4 *5 + 5 * 6
= (4 + 5 – 4 × 5) + (5 + 6 – 5 × 6)
= - 30
11. Sol.
Let principal amount is A. then
25
A1
A 10 1
2
1250 A 50,000
100 100
??
??
? ? ? ?
12. Sol.
Net cost price
198 198
10 10
11
100 100
??
??
10 10
198 400
11 9
Selling price 2 198 396
loss 400 396 4
4
%loss 100 1
400
??
? ? ?
??
??
? ? ?
? ? ?
? ? ?
13. Sol.
Let the price two years before be P.
So, current price will be
2
4
P1
100
??
??
??
??
2
4
P 1 6,76,000
100
??
? ? ? ?
??
??
14. Sol.
OP
2
= x
2
+ y
2
OR
2
= (x – a)
2
+ (y – b)
2
OQ
2
= (x – a)
2
+ y
2
OS
2
= x
2
+ (y – b)
2
2 2 2 2
OP OR OQ OS ? ? ? ?
? ? O x, y
? ? P o,o
? ? Q a ,o
? ? R a,b ? ? S o,b
15. Sol.
?
? ?
Triangle 1
?
? ?
Triangle 2
So, both the triangles are similar and in case of similar triangles, area of triangles are in ratio of
square of their heights
2
11
2
2 2
hh 93
16 h 4 h
? ? ? ?
16. Sol.
Volume of tetrahedron =
3
a
62
where
a length of edge ?
17. Sol.
Volume of parallelopide = Number of coins × Volume of single coin
2
11 9 6 n 1.5 0.25 ? ? ? ? ? ? ? ?
18. Sol.
sin
4
A = cos
2
A
tan
2
A – tan
4
A
24
24
22
44
sin A sin A
cos A cos A
sin A cos A
sin A cos A
??
??
22
22
22
cosec A sec A
cos A sin A
sin Acos A
??
?
4 2 2 2
2 2 2 2
sin A sin A sin A cos A
sin Acos A sin Acos A
1
??
??
??
19. Sol.
22
sin x cos x
22 ?
=
2
2
sin x
sin x
2
2
2
?
Applying A.M G.M ?
Page 5
NATIONAL TALENT SEARCH EXAMINATION, 2015 - 16
(STATE LEVEL)
(FOR STUDENTS STUDYING IN CLASS X)
SAT – ANSWER KEY
1 C 11 A 21 A 31 B 41 B
2 C 12 D 22 C 32 C 42 D
3 B 13 B 23 D 33 C 43 B
4 D 14 A 24 A 34 B 44 C
5 D 15 C 25 C 35 C 45 A
6 A 16 C 26 A 36 D 46 C
7 D 17 C 27 B 37 D 47 C
8 B 18 A 28 C 38 D 48 D
9 B 19 B 29 B 39 D 49 D
10 D 20 D 30 D 40 B 50 D
51 B 61 C 71 B 81 D 91 B
52 C 62 A/B 72 A 82 A 92 D
53 B 63 B 73 C 83 C 93 D
54 A 64 D 74 D 84 B 94 C
55 B 65 A 75 B 85 A 95 B
56 D 66 C 76 D 86 C 96 B
57 B 67 D 77 B 87 A 97 C
58 D 68 B 78 B 88 A 98 D
59 B 69 C 79 B 89 C 99 A
60 B 70 C 80 A 90 A 100 D
NATIONAL TALENT SEARCH EXAMINATION, 2015-16
(STATE LEVEL)
(FOR STUDENTS STUDYING IN CLASS X)
SAT – SOLUTION
MATHEMATICS
1. Sol.
? ? ? ?
2
2
2
2
2
1 1 1
f 2x 4x 1
x4 x
11
2x 4 1
4x
11
2x
4x
1
f x x
4
? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
??
??
? ? ? ? ??
??
??
??
??
??
??
?? ??
??
??
??
??
?
2. Sol.
? ? ? ?
x 2 x 3
x 2 x 3 0
x 3 x 1 0
x 3, x 1
x9
??
? ? ?
? ? ?
??
? ? ?
??
??
3. Sol.
5 2 6 ?
=
? ? ? ?
22
3 2 2 6
32
??
??
4. Sol.
xy
ab
yx
x y x y
a 1 b 1
yx
11
1
a 1 1 b
??
??
? ? ? ?
??
??
5. Sol.
? ? ? ?
? ? ? ?
22
22
2 x 2x 1 1 3 y 6y 9 9 31
2 x 1 2 3 y 3 27 31
? ? ? ? ? ? ? ?
? ? ? ? ? ? ?
Least value = 2
6. Sol.
? ?
2
22
22
2
2r h r h
4r 4rh r
3r 4rh
r
4:3
h
? ? ?
??
?
?
7. Sol.
y = c (cy + bz) + az
(1 – c
2
)y = (bc + a) z ……….(1)
Z = b(cy + bz) + ay
(1 – b
2
) z = (bc + a) y ……….(2)
2
2
2 2 2 2
1 c bc a
bc a 1b
1 b c b c
??
?
? ?
? ? ?
22
bc ?
2
2 2 2
abc abc a
a b c 1 2abc
???
? ? ? ? ?
8. Sol.
x(x
3
– 1) < 0
x(x – 1) (x
2
+ x + 1) < 0
x
2
+ x + 1 > 0 because discriminant is – ve
x(x – 1) < 0 0 x 1 ? ? ?
9. Sol.
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
250 200 150 100
50 50 50 50
5 4 3 2
50 50 50 50
2 3 4 5
2 3 4 5
32 81 64 25
?
?
10. Sol.
4 *5 + 5 * 6
= (4 + 5 – 4 × 5) + (5 + 6 – 5 × 6)
= - 30
11. Sol.
Let principal amount is A. then
25
A1
A 10 1
2
1250 A 50,000
100 100
??
??
? ? ? ?
12. Sol.
Net cost price
198 198
10 10
11
100 100
??
??
10 10
198 400
11 9
Selling price 2 198 396
loss 400 396 4
4
%loss 100 1
400
??
? ? ?
??
??
? ? ?
? ? ?
? ? ?
13. Sol.
Let the price two years before be P.
So, current price will be
2
4
P1
100
??
??
??
??
2
4
P 1 6,76,000
100
??
? ? ? ?
??
??
14. Sol.
OP
2
= x
2
+ y
2
OR
2
= (x – a)
2
+ (y – b)
2
OQ
2
= (x – a)
2
+ y
2
OS
2
= x
2
+ (y – b)
2
2 2 2 2
OP OR OQ OS ? ? ? ?
? ? O x, y
? ? P o,o
? ? Q a ,o
? ? R a,b ? ? S o,b
15. Sol.
?
? ?
Triangle 1
?
? ?
Triangle 2
So, both the triangles are similar and in case of similar triangles, area of triangles are in ratio of
square of their heights
2
11
2
2 2
hh 93
16 h 4 h
? ? ? ?
16. Sol.
Volume of tetrahedron =
3
a
62
where
a length of edge ?
17. Sol.
Volume of parallelopide = Number of coins × Volume of single coin
2
11 9 6 n 1.5 0.25 ? ? ? ? ? ? ? ?
18. Sol.
sin
4
A = cos
2
A
tan
2
A – tan
4
A
24
24
22
44
sin A sin A
cos A cos A
sin A cos A
sin A cos A
??
??
22
22
22
cosec A sec A
cos A sin A
sin Acos A
??
?
4 2 2 2
2 2 2 2
sin A sin A sin A cos A
sin Acos A sin Acos A
1
??
??
??
19. Sol.
22
sin x cos x
22 ?
=
2
2
sin x
sin x
2
2
2
?
Applying A.M G.M ?
2
2
2
2
22
sin x
sin x
sin x
sin x
sin x cos x
2
2
2
2
2.
2
2
2 2 2 2
?
?
??
Least value = 22
20. Sol.
AC ? ? ?
BD ? ? ?
L.H.S =
A C B D
tan tan tan tan
2 2 2 2
?
C C D D
tan tan tan tan
2 2 2 2 2 2
C C D D
C tan C tan
2 2 2 2
2
?? ? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
?
PHYSICS
21. Sol.
2
2
1
E mv
2
1P
E
2m
P 2mE
?
??
?
22. Sol.
21
21
12
Pv nRT
nR
vT
P
nR
tan
P
1
tan
P
tan tan
PP
??
?
??
??
? ? ?
? ? ?
??
2
?
1
?
1
P
2
P
V
T
23. Sol.
Harmonics are multiple of fundamental frequencies.
24. Sol.
2
2
1
E k A
2
EA
?
?
25. Sol.
Sinc =
1
?
C = 45
o
26. Sol.
In the absence of atmosphere, no scattering of light.
27. Sol.
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The "West Bengal: State Level Solutions (SAT) - 2015-16 Class 10 Questions" guide is a valuable resource for all aspiring students preparing for the
Class 10 exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study West Bengal: State Level Solutions (SAT) - 2015-16 on the App
Students of Class 10 can study West Bengal: State Level Solutions (SAT) - 2015-16 alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the West Bengal: State Level Solutions (SAT) - 2015-16,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of West Bengal: State Level Solutions (SAT) - 2015-16 is prepared as per the latest Class 10 syllabus.
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