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Page 1
NTSE STAGE – I
(2016- 17 )
02/2016-17
MENTAL ABILITY TEST
SOLUTIONS
1. z + y +z = 0
?
? ? ? ? ? ? x y y z z x
11
xyz
? ? ?
?
=
z x y
11
xyz
? ?? ??
?
= – 1 + 11 = 10
2. sin A + cos A = 2 cos A
sin A =
? ?
2 1 cosA ?
tan A = 2 1 ?
? ?
2 1 tan A 1 ? ?
3. ? ? ? ? ? ? ? ?
2 2 2 2
k 5 2 2 k 1 2 2 ? ?? ? ? ??
? ? ? ? ?
2 2
k 5 k 1 0 ? ? ? ?
? ? ? ? ?
2 2
k 5 k 1 ? ? ?
? k – 5 = k – 1
? k – 5 = – k + 1
? k = ?3
? k
2
+ 7 = 16
4. s = x ? SA = 6x
2
s
1
= 1.4x ? SA
1
= 6 (1.4x)
2
= 6 (1.96x
2
)
? increase % =
? ?
2
2
6x 1.96 1
100
6x
?
?
= 96%
5. 6 ? ? ? ?
2 2
10 ? ? ? ?
? ? ? ?
2
2
2
2
? ?? ? ? ??
?? ?
=
36 10
2
?
= 13
p = 13
Page 2
NTSE STAGE – I
(2016- 17 )
02/2016-17
MENTAL ABILITY TEST
SOLUTIONS
1. z + y +z = 0
?
? ? ? ? ? ? x y y z z x
11
xyz
? ? ?
?
=
z x y
11
xyz
? ?? ??
?
= – 1 + 11 = 10
2. sin A + cos A = 2 cos A
sin A =
? ?
2 1 cosA ?
tan A = 2 1 ?
? ?
2 1 tan A 1 ? ?
3. ? ? ? ? ? ? ? ?
2 2 2 2
k 5 2 2 k 1 2 2 ? ?? ? ? ??
? ? ? ? ?
2 2
k 5 k 1 0 ? ? ? ?
? ? ? ? ?
2 2
k 5 k 1 ? ? ?
? k – 5 = k – 1
? k – 5 = – k + 1
? k = ?3
? k
2
+ 7 = 16
4. s = x ? SA = 6x
2
s
1
= 1.4x ? SA
1
= 6 (1.4x)
2
= 6 (1.96x
2
)
? increase % =
? ?
2
2
6x 1.96 1
100
6x
?
?
= 96%
5. 6 ? ? ? ?
2 2
10 ? ? ? ?
? ? ? ?
2
2
2
2
? ?? ? ? ??
?? ?
=
36 10
2
?
= 13
p = 13
6. 54 km/hr =
5
54 m/s 15m/s
18
? ?
? ?
? ?
? ?
? Length of train = ? ? 15 12 m ?
= 180 m
7. x + y = 9
(10 x+y) - (10 y + x) = 45
9 (x – y) = 45
x – y = 5
? x = 7, y = 2
? 72 is the number
8. All multiples of 8 from 16 to 88.
? Total 10 numbers
9. 3 =
1
x
1
1
1
5
3
?
?
?
? 3 =
1
x
3
1
16
?
?
? 3 =
16
x
19
?
? x =
16
3
19
?
? x =
41
19
10.
? ?
2
2
2x 2
x 1 x 1
x 1 x 1 x 1
?
? ?
? ?
? ? ?
=
? ? ? ? ? ? ? ? ? ?
? ? ? ?
2
2 2
2 2 2
2 2
x 1 x 1 x 1 x 1 2 x 1
x 1 x 1
? ? ? ? ? ? ?
? ?
=
? ? ? ? ? ?
? ? ? ?
? ? ? ?
2
2 2
2 2
2 2
x 1 x 1 x 1 2 x 1
x 1 x 1
? ? ? ? ? ?
? ?
=
? ? ? ? ? ?
? ? ? ?
2
2 2 2
2 2
x 1 2x 2 2 x 1
x 1 x 1
? ? ? ?
? ?
=
? ? ? ?
? ?
? ? ? ?
2 2
2 2
2 2
2 x 1 x 1
x 1 x 1
? ? ?
? ?
=
? ?
2
4
2 2x 2
x 1
? ?
? ?
?
=
2
4
8x
x 1 ?
11. c + h = 29
4c + 2h = 92
? 2c = 34
c = 17
Page 3
NTSE STAGE – I
(2016- 17 )
02/2016-17
MENTAL ABILITY TEST
SOLUTIONS
1. z + y +z = 0
?
? ? ? ? ? ? x y y z z x
11
xyz
? ? ?
?
=
z x y
11
xyz
? ?? ??
?
= – 1 + 11 = 10
2. sin A + cos A = 2 cos A
sin A =
? ?
2 1 cosA ?
tan A = 2 1 ?
? ?
2 1 tan A 1 ? ?
3. ? ? ? ? ? ? ? ?
2 2 2 2
k 5 2 2 k 1 2 2 ? ?? ? ? ??
? ? ? ? ?
2 2
k 5 k 1 0 ? ? ? ?
? ? ? ? ?
2 2
k 5 k 1 ? ? ?
? k – 5 = k – 1
? k – 5 = – k + 1
? k = ?3
? k
2
+ 7 = 16
4. s = x ? SA = 6x
2
s
1
= 1.4x ? SA
1
= 6 (1.4x)
2
= 6 (1.96x
2
)
? increase % =
? ?
2
2
6x 1.96 1
100
6x
?
?
= 96%
5. 6 ? ? ? ?
2 2
10 ? ? ? ?
? ? ? ?
2
2
2
2
? ?? ? ? ??
?? ?
=
36 10
2
?
= 13
p = 13
6. 54 km/hr =
5
54 m/s 15m/s
18
? ?
? ?
? ?
? ?
? Length of train = ? ? 15 12 m ?
= 180 m
7. x + y = 9
(10 x+y) - (10 y + x) = 45
9 (x – y) = 45
x – y = 5
? x = 7, y = 2
? 72 is the number
8. All multiples of 8 from 16 to 88.
? Total 10 numbers
9. 3 =
1
x
1
1
1
5
3
?
?
?
? 3 =
1
x
3
1
16
?
?
? 3 =
16
x
19
?
? x =
16
3
19
?
? x =
41
19
10.
? ?
2
2
2x 2
x 1 x 1
x 1 x 1 x 1
?
? ?
? ?
? ? ?
=
? ? ? ? ? ? ? ? ? ?
? ? ? ?
2
2 2
2 2 2
2 2
x 1 x 1 x 1 x 1 2 x 1
x 1 x 1
? ? ? ? ? ? ?
? ?
=
? ? ? ? ? ?
? ? ? ?
? ? ? ?
2
2 2
2 2
2 2
x 1 x 1 x 1 2 x 1
x 1 x 1
? ? ? ? ? ?
? ?
=
? ? ? ? ? ?
? ? ? ?
2
2 2 2
2 2
x 1 2x 2 2 x 1
x 1 x 1
? ? ? ?
? ?
=
? ? ? ?
? ?
? ? ? ?
2 2
2 2
2 2
2 x 1 x 1
x 1 x 1
? ? ?
? ?
=
? ?
2
4
2 2x 2
x 1
? ?
? ?
?
=
2
4
8x
x 1 ?
11. c + h = 29
4c + 2h = 92
? 2c = 34
c = 17
h = 12
12.
16 8
6 8x 4y 3
d u
? ? ? ? ?
6 24
6 4x y 1
u d
? ? ? ? ?
1 1
x, y
d u
? ?
? ?
? ?
? ?
Solving, we get, y = ½, x = 1/8
? b + s = 8 {b represents Parth’s speed}
b – s = 2 {s represents speed of stream}
? b = 5 km/hr
13.
75 25 32
log log log
16 81 243
? ?
=
75 32 81
log
16 243 25
? ?
? ?
? ?
? ?
= log 2
14. At 4:15, angle between hands = ? ? ? ? 4 30 5.5 15 ? ? ?
= 120 82.5 ?
= 37.5
0
15. 35 55 17.88 ? ?
8 5 17.88 ?
5 2.235 ?
80 6 5 10 5 22.35 ? ? ?
16. LCM of 30 sec, 1 min , 45 sec and 75 sec = 15 min
? at 9:15 AM, they will simultaneously change again.
17.
A A B C 222 2
D B C D 3 4 5 15
? ? ? ? ? ? ?
18.
A
B
B
C
2
1 22
2B C 7
4 7
? ? ? ?
=
77
2
B + C =
2
1 49
7
2 2
? ?
? B =
28
14
2
? ? Shaded area = 28 cm
2
Page 4
NTSE STAGE – I
(2016- 17 )
02/2016-17
MENTAL ABILITY TEST
SOLUTIONS
1. z + y +z = 0
?
? ? ? ? ? ? x y y z z x
11
xyz
? ? ?
?
=
z x y
11
xyz
? ?? ??
?
= – 1 + 11 = 10
2. sin A + cos A = 2 cos A
sin A =
? ?
2 1 cosA ?
tan A = 2 1 ?
? ?
2 1 tan A 1 ? ?
3. ? ? ? ? ? ? ? ?
2 2 2 2
k 5 2 2 k 1 2 2 ? ?? ? ? ??
? ? ? ? ?
2 2
k 5 k 1 0 ? ? ? ?
? ? ? ? ?
2 2
k 5 k 1 ? ? ?
? k – 5 = k – 1
? k – 5 = – k + 1
? k = ?3
? k
2
+ 7 = 16
4. s = x ? SA = 6x
2
s
1
= 1.4x ? SA
1
= 6 (1.4x)
2
= 6 (1.96x
2
)
? increase % =
? ?
2
2
6x 1.96 1
100
6x
?
?
= 96%
5. 6 ? ? ? ?
2 2
10 ? ? ? ?
? ? ? ?
2
2
2
2
? ?? ? ? ??
?? ?
=
36 10
2
?
= 13
p = 13
6. 54 km/hr =
5
54 m/s 15m/s
18
? ?
? ?
? ?
? ?
? Length of train = ? ? 15 12 m ?
= 180 m
7. x + y = 9
(10 x+y) - (10 y + x) = 45
9 (x – y) = 45
x – y = 5
? x = 7, y = 2
? 72 is the number
8. All multiples of 8 from 16 to 88.
? Total 10 numbers
9. 3 =
1
x
1
1
1
5
3
?
?
?
? 3 =
1
x
3
1
16
?
?
? 3 =
16
x
19
?
? x =
16
3
19
?
? x =
41
19
10.
? ?
2
2
2x 2
x 1 x 1
x 1 x 1 x 1
?
? ?
? ?
? ? ?
=
? ? ? ? ? ? ? ? ? ?
? ? ? ?
2
2 2
2 2 2
2 2
x 1 x 1 x 1 x 1 2 x 1
x 1 x 1
? ? ? ? ? ? ?
? ?
=
? ? ? ? ? ?
? ? ? ?
? ? ? ?
2
2 2
2 2
2 2
x 1 x 1 x 1 2 x 1
x 1 x 1
? ? ? ? ? ?
? ?
=
? ? ? ? ? ?
? ? ? ?
2
2 2 2
2 2
x 1 2x 2 2 x 1
x 1 x 1
? ? ? ?
? ?
=
? ? ? ?
? ?
? ? ? ?
2 2
2 2
2 2
2 x 1 x 1
x 1 x 1
? ? ?
? ?
=
? ?
2
4
2 2x 2
x 1
? ?
? ?
?
=
2
4
8x
x 1 ?
11. c + h = 29
4c + 2h = 92
? 2c = 34
c = 17
h = 12
12.
16 8
6 8x 4y 3
d u
? ? ? ? ?
6 24
6 4x y 1
u d
? ? ? ? ?
1 1
x, y
d u
? ?
? ?
? ?
? ?
Solving, we get, y = ½, x = 1/8
? b + s = 8 {b represents Parth’s speed}
b – s = 2 {s represents speed of stream}
? b = 5 km/hr
13.
75 25 32
log log log
16 81 243
? ?
=
75 32 81
log
16 243 25
? ?
? ?
? ?
? ?
= log 2
14. At 4:15, angle between hands = ? ? ? ? 4 30 5.5 15 ? ? ?
= 120 82.5 ?
= 37.5
0
15. 35 55 17.88 ? ?
8 5 17.88 ?
5 2.235 ?
80 6 5 10 5 22.35 ? ? ?
16. LCM of 30 sec, 1 min , 45 sec and 75 sec = 15 min
? at 9:15 AM, they will simultaneously change again.
17.
A A B C 222 2
D B C D 3 4 5 15
? ? ? ? ? ? ?
18.
A
B
B
C
2
1 22
2B C 7
4 7
? ? ? ?
=
77
2
B + C =
2
1 49
7
2 2
? ?
? B =
28
14
2
? ? Shaded area = 28 cm
2
19. ? = x
h =
3
x
2
w =
1 3
. x
2 2
=
3
x
4
? Area of floor =
2
3
x
4
2
3
4 x 432
4
? ?
2
x 144 ?
x = 12
? height =
3
x
2
= 18
20.
15 16 17
333 ? ?
= ? ?
15
3 1 3 9 ? ?
=
15
13 3 ? ? Divisible by 13
21. CI =
2
5
6000 1 6000
100
? ?
? ?
? ?
? ?
=
441
6000 6000
400
? ?
= 615
SI =
6000 5 2
600
100
? ?
?
? difference = Rs 15
22. ? ? ? ?
3 3
3.5 2.5 27.25 ? ?
23. 13 x 10 8 5 ? ? ?
? 13 x 10 8 5 2 8 5 ? ? ? ?
? x 10 4 10 ? ?
? x = – 4
24.
3
3
6
6 4
4
? BC = 10 cm (Tangents from a point to the circle are of equal length)
25. SP of 5 = CP of 3
Let CP of 1 be Re 1
SP of 5 = 3
Page 5
NTSE STAGE – I
(2016- 17 )
02/2016-17
MENTAL ABILITY TEST
SOLUTIONS
1. z + y +z = 0
?
? ? ? ? ? ? x y y z z x
11
xyz
? ? ?
?
=
z x y
11
xyz
? ?? ??
?
= – 1 + 11 = 10
2. sin A + cos A = 2 cos A
sin A =
? ?
2 1 cosA ?
tan A = 2 1 ?
? ?
2 1 tan A 1 ? ?
3. ? ? ? ? ? ? ? ?
2 2 2 2
k 5 2 2 k 1 2 2 ? ?? ? ? ??
? ? ? ? ?
2 2
k 5 k 1 0 ? ? ? ?
? ? ? ? ?
2 2
k 5 k 1 ? ? ?
? k – 5 = k – 1
? k – 5 = – k + 1
? k = ?3
? k
2
+ 7 = 16
4. s = x ? SA = 6x
2
s
1
= 1.4x ? SA
1
= 6 (1.4x)
2
= 6 (1.96x
2
)
? increase % =
? ?
2
2
6x 1.96 1
100
6x
?
?
= 96%
5. 6 ? ? ? ?
2 2
10 ? ? ? ?
? ? ? ?
2
2
2
2
? ?? ? ? ??
?? ?
=
36 10
2
?
= 13
p = 13
6. 54 km/hr =
5
54 m/s 15m/s
18
? ?
? ?
? ?
? ?
? Length of train = ? ? 15 12 m ?
= 180 m
7. x + y = 9
(10 x+y) - (10 y + x) = 45
9 (x – y) = 45
x – y = 5
? x = 7, y = 2
? 72 is the number
8. All multiples of 8 from 16 to 88.
? Total 10 numbers
9. 3 =
1
x
1
1
1
5
3
?
?
?
? 3 =
1
x
3
1
16
?
?
? 3 =
16
x
19
?
? x =
16
3
19
?
? x =
41
19
10.
? ?
2
2
2x 2
x 1 x 1
x 1 x 1 x 1
?
? ?
? ?
? ? ?
=
? ? ? ? ? ? ? ? ? ?
? ? ? ?
2
2 2
2 2 2
2 2
x 1 x 1 x 1 x 1 2 x 1
x 1 x 1
? ? ? ? ? ? ?
? ?
=
? ? ? ? ? ?
? ? ? ?
? ? ? ?
2
2 2
2 2
2 2
x 1 x 1 x 1 2 x 1
x 1 x 1
? ? ? ? ? ?
? ?
=
? ? ? ? ? ?
? ? ? ?
2
2 2 2
2 2
x 1 2x 2 2 x 1
x 1 x 1
? ? ? ?
? ?
=
? ? ? ?
? ?
? ? ? ?
2 2
2 2
2 2
2 x 1 x 1
x 1 x 1
? ? ?
? ?
=
? ?
2
4
2 2x 2
x 1
? ?
? ?
?
=
2
4
8x
x 1 ?
11. c + h = 29
4c + 2h = 92
? 2c = 34
c = 17
h = 12
12.
16 8
6 8x 4y 3
d u
? ? ? ? ?
6 24
6 4x y 1
u d
? ? ? ? ?
1 1
x, y
d u
? ?
? ?
? ?
? ?
Solving, we get, y = ½, x = 1/8
? b + s = 8 {b represents Parth’s speed}
b – s = 2 {s represents speed of stream}
? b = 5 km/hr
13.
75 25 32
log log log
16 81 243
? ?
=
75 32 81
log
16 243 25
? ?
? ?
? ?
? ?
= log 2
14. At 4:15, angle between hands = ? ? ? ? 4 30 5.5 15 ? ? ?
= 120 82.5 ?
= 37.5
0
15. 35 55 17.88 ? ?
8 5 17.88 ?
5 2.235 ?
80 6 5 10 5 22.35 ? ? ?
16. LCM of 30 sec, 1 min , 45 sec and 75 sec = 15 min
? at 9:15 AM, they will simultaneously change again.
17.
A A B C 222 2
D B C D 3 4 5 15
? ? ? ? ? ? ?
18.
A
B
B
C
2
1 22
2B C 7
4 7
? ? ? ?
=
77
2
B + C =
2
1 49
7
2 2
? ?
? B =
28
14
2
? ? Shaded area = 28 cm
2
19. ? = x
h =
3
x
2
w =
1 3
. x
2 2
=
3
x
4
? Area of floor =
2
3
x
4
2
3
4 x 432
4
? ?
2
x 144 ?
x = 12
? height =
3
x
2
= 18
20.
15 16 17
333 ? ?
= ? ?
15
3 1 3 9 ? ?
=
15
13 3 ? ? Divisible by 13
21. CI =
2
5
6000 1 6000
100
? ?
? ?
? ?
? ?
=
441
6000 6000
400
? ?
= 615
SI =
6000 5 2
600
100
? ?
?
? difference = Rs 15
22. ? ? ? ?
3 3
3.5 2.5 27.25 ? ?
23. 13 x 10 8 5 ? ? ?
? 13 x 10 8 5 2 8 5 ? ? ? ?
? x 10 4 10 ? ?
? x = – 4
24.
3
3
6
6 4
4
? BC = 10 cm (Tangents from a point to the circle are of equal length)
25. SP of 5 = CP of 3
Let CP of 1 be Re 1
SP of 5 = 3
CP of 5 = 5
? Loss of 5 = 2
? Loss % =
2
100 40% loss
5
? ?
26. The required sequence is:
M L K J I H G F E D C B A Z Y X W V U T S R Q P O N
27. THREAT ? RHTTAE
? PEARLY ? AEPYLR
Logic : First half is reversed, then second half of reversed.
28. The pattern is: 2 2,32,42,52 ? ?? ?? ?? ?
So, next term is 308 x 6 – 2 = 1846
29. The arrangement is:
Kamal, Rashi, Vinita, Preeti, Leela
? 3
rd
in order of height is Vinita.
30. Figure (1) is the best illustration.
31. From Venn Diagram
32. From Venn Diagram
33. From Venn Diagram
34. 1. 7 7 7 7 0 ? ? ? ? ?
2. ? ? 7 7 7 7 7 1 ? ? ? ? ?
3. 7 7 7 7 7 7 ? ? ? ? ?
4. ? ? 7 7 7 7 7 7 ? ? ? ? ? ?
35.
The triangles are represented by C, D, E, H, K, M, AC, CD, BD, CF, DG, KM, EGK, CFK,
DGM, MGH, ABCD, CDFG, ACFKE, EFKGHM and DGMBH.
So, 21 triangles.
Total number of triangles = 21
36. Lateral inversion.
37. 20 10 2 ? ? [T is 20, J is 10]
? 24 ? 8 = 3 [X is 24, H is 8]
38.
15 6 4
36
10
? ?
?
6 7 5
21
10
? ?
?
50 10 10
500
10
? ?
?
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Delhi: State Level Solutions (MAT) - 2016-17 Notes
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Delhi: State Level Solutions (MAT) - 2016-17 Class 10 Questions
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The content of Delhi: State Level Solutions (MAT) - 2016-17 is prepared as per the latest Class 10 syllabus.
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