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Page 1
NTSE STAGE – I (DELHI STATE)
05 – A (2019 – 20)
(For Class – X)
MENTAL ABILITY TEST (MAT)
HINTS & SOLUTIONS
1. 2
1. Positive factors of 256 are
1, 2, 4, 8, 16, 32, 64, 128, 256
?
? ?
? ?
? ?
? ?
n 9
a r 1 1 2 1
sq
r 1 2 1
? ?
? ?
? ?
[where a = 1, and r = 2, and n = 9]
? Sq = 511
2. 4
2.
? ?
? ?
? ?
2
2
X X 1 1
X X 1 1
X1 X XX1 XX1
? ? ?
?
? ? ?
? ? ?
=
? ? ? ?
? ?
? ?
2 2 2
2X X 1
XX1 2X 1 2X 2X
XX 1 XX 1 X X 1
?
? ? ? ? ?
? ?
? ? ?
= 2
3. 1
3. 5 + 6 + 7 + … + 19
Here a = 5, d = 1 and n = 15
? S
n
= ? ?
n
2a n 1 d
2
? ? ? ?
? ?
? ?
15
15 15
S 10 14 1 24
2 2
? ? ? ? ?
= 15 x 12 = 180
4. 1
4.
1 2 3
: : 6:8:9
2 3 4
?
Let numbers be 6x, 8x and 9x
? 9x – 6x = 27
? x = 9
? Numbers are 54, 72, 81
5. 2 or 4
5.
? ?
25 26 27 28 25 0 1 2 3
3333 3 3 3 3 3 ??? ? ? ? ?
= ? ?
25
3 1 3 9 27 ? ? ?
=
25 23
3 40 3 958 ? ? ? ? ?
=
25 23
3 40 3 8 45 ? ? ? ?
6. 4
6. Rohan’s final score =
90 2 75 1
3
? ? ?
= 85
Page 2
NTSE STAGE – I (DELHI STATE)
05 – A (2019 – 20)
(For Class – X)
MENTAL ABILITY TEST (MAT)
HINTS & SOLUTIONS
1. 2
1. Positive factors of 256 are
1, 2, 4, 8, 16, 32, 64, 128, 256
?
? ?
? ?
? ?
? ?
n 9
a r 1 1 2 1
sq
r 1 2 1
? ?
? ?
? ?
[where a = 1, and r = 2, and n = 9]
? Sq = 511
2. 4
2.
? ?
? ?
? ?
2
2
X X 1 1
X X 1 1
X1 X XX1 XX1
? ? ?
?
? ? ?
? ? ?
=
? ? ? ?
? ?
? ?
2 2 2
2X X 1
XX1 2X 1 2X 2X
XX 1 XX 1 X X 1
?
? ? ? ? ?
? ?
? ? ?
= 2
3. 1
3. 5 + 6 + 7 + … + 19
Here a = 5, d = 1 and n = 15
? S
n
= ? ?
n
2a n 1 d
2
? ? ? ?
? ?
? ?
15
15 15
S 10 14 1 24
2 2
? ? ? ? ?
= 15 x 12 = 180
4. 1
4.
1 2 3
: : 6:8:9
2 3 4
?
Let numbers be 6x, 8x and 9x
? 9x – 6x = 27
? x = 9
? Numbers are 54, 72, 81
5. 2 or 4
5.
? ?
25 26 27 28 25 0 1 2 3
3333 3 3 3 3 3 ??? ? ? ? ?
= ? ?
25
3 1 3 9 27 ? ? ?
=
25 23
3 40 3 958 ? ? ? ? ?
=
25 23
3 40 3 8 45 ? ? ? ?
6. 4
6. Rohan’s final score =
90 2 75 1
3
? ? ?
= 85
7. 1
7. Let Grand mother = G, mother = M and daughter = D
? Possible ways = GMD
GDM
MGD
MDG
DGM
DMG
8. 2
8. Let at time of marriage man’s age = x years
And man’s wife’s age = y years
? x = y + 6 ….(1)
And ? ? ? ?
6
x12 y12
5
? ? ?
= 5x + 60 = 6y + 72
= 5x – 6y = 12 …(2)
Solving both equations we got x = 24 and y = 18
9. 3
9. P (number is even) =
1
2
P (number is less than 4) =
1
2
P (number is even and less than 4) =
1
6
?
? ?
? ?
P number is even and less than 4
number is less than 4
P
number is even P number is even
? ?
?
? ?
? ?
=
1
1
6
1
3
2
?
10. 2
10. 10 balls ? 5B and 5W
After removing 1 B balls, total balls left = 9 and
Total black balls left = 4
? P (B ball after removing 1
st
B ball) =
4
9
11. 2
11. 10 – 3 = 12 ? 10 – 3 + 5 = 12
12 – 4 = 13 ? 12 – 4 + 5 = 13
14 – 5 = 14 ? 14 – 5 + 5 = 14
16 – 6 = ? ? 16 – 6 + 5 = 15
12. 2
12. If bus does not stops, then it will travel 9 km more with 54 kmph
? It will stop for
9 9
hr 60
54 54
? ? min
= 10 min
13. 4
Page 3
NTSE STAGE – I (DELHI STATE)
05 – A (2019 – 20)
(For Class – X)
MENTAL ABILITY TEST (MAT)
HINTS & SOLUTIONS
1. 2
1. Positive factors of 256 are
1, 2, 4, 8, 16, 32, 64, 128, 256
?
? ?
? ?
? ?
? ?
n 9
a r 1 1 2 1
sq
r 1 2 1
? ?
? ?
? ?
[where a = 1, and r = 2, and n = 9]
? Sq = 511
2. 4
2.
? ?
? ?
? ?
2
2
X X 1 1
X X 1 1
X1 X XX1 XX1
? ? ?
?
? ? ?
? ? ?
=
? ? ? ?
? ?
? ?
2 2 2
2X X 1
XX1 2X 1 2X 2X
XX 1 XX 1 X X 1
?
? ? ? ? ?
? ?
? ? ?
= 2
3. 1
3. 5 + 6 + 7 + … + 19
Here a = 5, d = 1 and n = 15
? S
n
= ? ?
n
2a n 1 d
2
? ? ? ?
? ?
? ?
15
15 15
S 10 14 1 24
2 2
? ? ? ? ?
= 15 x 12 = 180
4. 1
4.
1 2 3
: : 6:8:9
2 3 4
?
Let numbers be 6x, 8x and 9x
? 9x – 6x = 27
? x = 9
? Numbers are 54, 72, 81
5. 2 or 4
5.
? ?
25 26 27 28 25 0 1 2 3
3333 3 3 3 3 3 ??? ? ? ? ?
= ? ?
25
3 1 3 9 27 ? ? ?
=
25 23
3 40 3 958 ? ? ? ? ?
=
25 23
3 40 3 8 45 ? ? ? ?
6. 4
6. Rohan’s final score =
90 2 75 1
3
? ? ?
= 85
7. 1
7. Let Grand mother = G, mother = M and daughter = D
? Possible ways = GMD
GDM
MGD
MDG
DGM
DMG
8. 2
8. Let at time of marriage man’s age = x years
And man’s wife’s age = y years
? x = y + 6 ….(1)
And ? ? ? ?
6
x12 y12
5
? ? ?
= 5x + 60 = 6y + 72
= 5x – 6y = 12 …(2)
Solving both equations we got x = 24 and y = 18
9. 3
9. P (number is even) =
1
2
P (number is less than 4) =
1
2
P (number is even and less than 4) =
1
6
?
? ?
? ?
P number is even and less than 4
number is less than 4
P
number is even P number is even
? ?
?
? ?
? ?
=
1
1
6
1
3
2
?
10. 2
10. 10 balls ? 5B and 5W
After removing 1 B balls, total balls left = 9 and
Total black balls left = 4
? P (B ball after removing 1
st
B ball) =
4
9
11. 2
11. 10 – 3 = 12 ? 10 – 3 + 5 = 12
12 – 4 = 13 ? 12 – 4 + 5 = 13
14 – 5 = 14 ? 14 – 5 + 5 = 14
16 – 6 = ? ? 16 – 6 + 5 = 15
12. 2
12. If bus does not stops, then it will travel 9 km more with 54 kmph
? It will stop for
9 9
hr 60
54 54
? ? min
= 10 min
13. 4
13.
40 1620 30 960 x 5200
100 100 100
? ? ?
? ?
?
40 1620 30 960
x
5200
? ? ?
?
? x = 18
14. 2
14. Between 1
st
and 25
th
tree there are 24 gap & let say each gap is of x m distance.
? 24 x = 30
30
x
24
?
Now between 3
rd
& 15
th
tree there are 12 gaps
? Distance between 3
rd
& 15
th
tree
30
12 15 m
24
? ? ?
15. 4
15. Time 8 8:30 9 9:30 10 10:30 11 11:30 12 12:30 1 1:30
Bell 3 1 1 1 3 3 1 1 1 1 1 3
? Bell rung 20 times.
16. 4
16.
80A 50B
100 100
?
or
B 8
A 5
?
Now
x A B
B x 100
100 A
?
? ? ? ?
8
x 100 160
5
? ? ? ?
17. 3
17. Let numbers = (x – 2), (x – 1), (x + 1), (x + 2)
? ? ? ? ? ? ? ? x2 x 1 x x 1 x2
7
5
? ?? ? ?? ??
? ?
5x
7
5
? ?
? x = 7
? highest number = 9
18. 2
18. ? ? ? ?
33 3 22 2
xy z 3xyz x y z xy z xy yz zx ?? ? ? ? ? ?? ???
Now we know that, ? ? ? ?
2
2 2 2
x yz x y z 2xy yzzx ? ? ??? ? ??
15 15 51
xy yz zx 87
2
? ?
? ? ? ? ?
? ?
333
x y z 3xyz 15 51 87 ? ? ? ? ? ?
= 15 × ( ?36)
= ?540
19. 4
19. Let sides = 3x, 4x & 5x cm
Page 4
NTSE STAGE – I (DELHI STATE)
05 – A (2019 – 20)
(For Class – X)
MENTAL ABILITY TEST (MAT)
HINTS & SOLUTIONS
1. 2
1. Positive factors of 256 are
1, 2, 4, 8, 16, 32, 64, 128, 256
?
? ?
? ?
? ?
? ?
n 9
a r 1 1 2 1
sq
r 1 2 1
? ?
? ?
? ?
[where a = 1, and r = 2, and n = 9]
? Sq = 511
2. 4
2.
? ?
? ?
? ?
2
2
X X 1 1
X X 1 1
X1 X XX1 XX1
? ? ?
?
? ? ?
? ? ?
=
? ? ? ?
? ?
? ?
2 2 2
2X X 1
XX1 2X 1 2X 2X
XX 1 XX 1 X X 1
?
? ? ? ? ?
? ?
? ? ?
= 2
3. 1
3. 5 + 6 + 7 + … + 19
Here a = 5, d = 1 and n = 15
? S
n
= ? ?
n
2a n 1 d
2
? ? ? ?
? ?
? ?
15
15 15
S 10 14 1 24
2 2
? ? ? ? ?
= 15 x 12 = 180
4. 1
4.
1 2 3
: : 6:8:9
2 3 4
?
Let numbers be 6x, 8x and 9x
? 9x – 6x = 27
? x = 9
? Numbers are 54, 72, 81
5. 2 or 4
5.
? ?
25 26 27 28 25 0 1 2 3
3333 3 3 3 3 3 ??? ? ? ? ?
= ? ?
25
3 1 3 9 27 ? ? ?
=
25 23
3 40 3 958 ? ? ? ? ?
=
25 23
3 40 3 8 45 ? ? ? ?
6. 4
6. Rohan’s final score =
90 2 75 1
3
? ? ?
= 85
7. 1
7. Let Grand mother = G, mother = M and daughter = D
? Possible ways = GMD
GDM
MGD
MDG
DGM
DMG
8. 2
8. Let at time of marriage man’s age = x years
And man’s wife’s age = y years
? x = y + 6 ….(1)
And ? ? ? ?
6
x12 y12
5
? ? ?
= 5x + 60 = 6y + 72
= 5x – 6y = 12 …(2)
Solving both equations we got x = 24 and y = 18
9. 3
9. P (number is even) =
1
2
P (number is less than 4) =
1
2
P (number is even and less than 4) =
1
6
?
? ?
? ?
P number is even and less than 4
number is less than 4
P
number is even P number is even
? ?
?
? ?
? ?
=
1
1
6
1
3
2
?
10. 2
10. 10 balls ? 5B and 5W
After removing 1 B balls, total balls left = 9 and
Total black balls left = 4
? P (B ball after removing 1
st
B ball) =
4
9
11. 2
11. 10 – 3 = 12 ? 10 – 3 + 5 = 12
12 – 4 = 13 ? 12 – 4 + 5 = 13
14 – 5 = 14 ? 14 – 5 + 5 = 14
16 – 6 = ? ? 16 – 6 + 5 = 15
12. 2
12. If bus does not stops, then it will travel 9 km more with 54 kmph
? It will stop for
9 9
hr 60
54 54
? ? min
= 10 min
13. 4
13.
40 1620 30 960 x 5200
100 100 100
? ? ?
? ?
?
40 1620 30 960
x
5200
? ? ?
?
? x = 18
14. 2
14. Between 1
st
and 25
th
tree there are 24 gap & let say each gap is of x m distance.
? 24 x = 30
30
x
24
?
Now between 3
rd
& 15
th
tree there are 12 gaps
? Distance between 3
rd
& 15
th
tree
30
12 15 m
24
? ? ?
15. 4
15. Time 8 8:30 9 9:30 10 10:30 11 11:30 12 12:30 1 1:30
Bell 3 1 1 1 3 3 1 1 1 1 1 3
? Bell rung 20 times.
16. 4
16.
80A 50B
100 100
?
or
B 8
A 5
?
Now
x A B
B x 100
100 A
?
? ? ? ?
8
x 100 160
5
? ? ? ?
17. 3
17. Let numbers = (x – 2), (x – 1), (x + 1), (x + 2)
? ? ? ? ? ? ? ? x2 x 1 x x 1 x2
7
5
? ?? ? ?? ??
? ?
5x
7
5
? ?
? x = 7
? highest number = 9
18. 2
18. ? ? ? ?
33 3 22 2
xy z 3xyz x y z xy z xy yz zx ?? ? ? ? ? ?? ???
Now we know that, ? ? ? ?
2
2 2 2
x yz x y z 2xy yzzx ? ? ??? ? ??
15 15 51
xy yz zx 87
2
? ?
? ? ? ? ?
? ?
333
x y z 3xyz 15 51 87 ? ? ? ? ? ?
= 15 × ( ?36)
= ?540
19. 4
19. Let sides = 3x, 4x & 5x cm
3x 4x 5x
S 6 x
2
? ?
? ? ?
? ? ? ? ? ? Area S S a S b S c ? ? ???
384 6x 3x 2x x ? ???
384 = 6x
2
? x = 8
? P = 12 x = 12 × 8 = 96 cm
20. 3
20. (1)
1 1 17
1 16
66
3 3
17
17
16
? ?
? ?
(2)
1 1 1 17
1 1 60
60
3 3
1 17
17
1
9
9
8
? ? ?
? ?
?
(3)
1 1 1 13
1 1 48
48
3 3
1 13
13
1
9
9
4
? ? ?
? ?
?
(4)
1 1 8
1 35
35
3
9
8
8
? ?
?
21. 3
21. a $ b = a × (a + b)
? (2 $ 0) $ 1 = [2 × (2 + 0)] $ 1
= 4 $ 1
= 4 × (4 + 1)
= 20
22. 2
22.
B C
E
D
A
8
8
10
12
6
Construction: Draw DE ? BC
? Area of ABCD = Area of rec ABED + Area of ?DEC
1
b b h
2
?? ? ?? ?
1
8 12 6 8
2
? ? ? ? ?
= 96 + 24 = 120 m
2
23. 3
Page 5
NTSE STAGE – I (DELHI STATE)
05 – A (2019 – 20)
(For Class – X)
MENTAL ABILITY TEST (MAT)
HINTS & SOLUTIONS
1. 2
1. Positive factors of 256 are
1, 2, 4, 8, 16, 32, 64, 128, 256
?
? ?
? ?
? ?
? ?
n 9
a r 1 1 2 1
sq
r 1 2 1
? ?
? ?
? ?
[where a = 1, and r = 2, and n = 9]
? Sq = 511
2. 4
2.
? ?
? ?
? ?
2
2
X X 1 1
X X 1 1
X1 X XX1 XX1
? ? ?
?
? ? ?
? ? ?
=
? ? ? ?
? ?
? ?
2 2 2
2X X 1
XX1 2X 1 2X 2X
XX 1 XX 1 X X 1
?
? ? ? ? ?
? ?
? ? ?
= 2
3. 1
3. 5 + 6 + 7 + … + 19
Here a = 5, d = 1 and n = 15
? S
n
= ? ?
n
2a n 1 d
2
? ? ? ?
? ?
? ?
15
15 15
S 10 14 1 24
2 2
? ? ? ? ?
= 15 x 12 = 180
4. 1
4.
1 2 3
: : 6:8:9
2 3 4
?
Let numbers be 6x, 8x and 9x
? 9x – 6x = 27
? x = 9
? Numbers are 54, 72, 81
5. 2 or 4
5.
? ?
25 26 27 28 25 0 1 2 3
3333 3 3 3 3 3 ??? ? ? ? ?
= ? ?
25
3 1 3 9 27 ? ? ?
=
25 23
3 40 3 958 ? ? ? ? ?
=
25 23
3 40 3 8 45 ? ? ? ?
6. 4
6. Rohan’s final score =
90 2 75 1
3
? ? ?
= 85
7. 1
7. Let Grand mother = G, mother = M and daughter = D
? Possible ways = GMD
GDM
MGD
MDG
DGM
DMG
8. 2
8. Let at time of marriage man’s age = x years
And man’s wife’s age = y years
? x = y + 6 ….(1)
And ? ? ? ?
6
x12 y12
5
? ? ?
= 5x + 60 = 6y + 72
= 5x – 6y = 12 …(2)
Solving both equations we got x = 24 and y = 18
9. 3
9. P (number is even) =
1
2
P (number is less than 4) =
1
2
P (number is even and less than 4) =
1
6
?
? ?
? ?
P number is even and less than 4
number is less than 4
P
number is even P number is even
? ?
?
? ?
? ?
=
1
1
6
1
3
2
?
10. 2
10. 10 balls ? 5B and 5W
After removing 1 B balls, total balls left = 9 and
Total black balls left = 4
? P (B ball after removing 1
st
B ball) =
4
9
11. 2
11. 10 – 3 = 12 ? 10 – 3 + 5 = 12
12 – 4 = 13 ? 12 – 4 + 5 = 13
14 – 5 = 14 ? 14 – 5 + 5 = 14
16 – 6 = ? ? 16 – 6 + 5 = 15
12. 2
12. If bus does not stops, then it will travel 9 km more with 54 kmph
? It will stop for
9 9
hr 60
54 54
? ? min
= 10 min
13. 4
13.
40 1620 30 960 x 5200
100 100 100
? ? ?
? ?
?
40 1620 30 960
x
5200
? ? ?
?
? x = 18
14. 2
14. Between 1
st
and 25
th
tree there are 24 gap & let say each gap is of x m distance.
? 24 x = 30
30
x
24
?
Now between 3
rd
& 15
th
tree there are 12 gaps
? Distance between 3
rd
& 15
th
tree
30
12 15 m
24
? ? ?
15. 4
15. Time 8 8:30 9 9:30 10 10:30 11 11:30 12 12:30 1 1:30
Bell 3 1 1 1 3 3 1 1 1 1 1 3
? Bell rung 20 times.
16. 4
16.
80A 50B
100 100
?
or
B 8
A 5
?
Now
x A B
B x 100
100 A
?
? ? ? ?
8
x 100 160
5
? ? ? ?
17. 3
17. Let numbers = (x – 2), (x – 1), (x + 1), (x + 2)
? ? ? ? ? ? ? ? x2 x 1 x x 1 x2
7
5
? ?? ? ?? ??
? ?
5x
7
5
? ?
? x = 7
? highest number = 9
18. 2
18. ? ? ? ?
33 3 22 2
xy z 3xyz x y z xy z xy yz zx ?? ? ? ? ? ?? ???
Now we know that, ? ? ? ?
2
2 2 2
x yz x y z 2xy yzzx ? ? ??? ? ??
15 15 51
xy yz zx 87
2
? ?
? ? ? ? ?
? ?
333
x y z 3xyz 15 51 87 ? ? ? ? ? ?
= 15 × ( ?36)
= ?540
19. 4
19. Let sides = 3x, 4x & 5x cm
3x 4x 5x
S 6 x
2
? ?
? ? ?
? ? ? ? ? ? Area S S a S b S c ? ? ???
384 6x 3x 2x x ? ???
384 = 6x
2
? x = 8
? P = 12 x = 12 × 8 = 96 cm
20. 3
20. (1)
1 1 17
1 16
66
3 3
17
17
16
? ?
? ?
(2)
1 1 1 17
1 1 60
60
3 3
1 17
17
1
9
9
8
? ? ?
? ?
?
(3)
1 1 1 13
1 1 48
48
3 3
1 13
13
1
9
9
4
? ? ?
? ?
?
(4)
1 1 8
1 35
35
3
9
8
8
? ?
?
21. 3
21. a $ b = a × (a + b)
? (2 $ 0) $ 1 = [2 × (2 + 0)] $ 1
= 4 $ 1
= 4 × (4 + 1)
= 20
22. 2
22.
B C
E
D
A
8
8
10
12
6
Construction: Draw DE ? BC
? Area of ABCD = Area of rec ABED + Area of ?DEC
1
b b h
2
?? ? ?? ?
1
8 12 6 8
2
? ? ? ? ?
= 96 + 24 = 120 m
2
23. 3
23. 4, 8, 28, 80, 244
× 3 – 4 × 3 + 4 × 3 – 4 × 3 + 4
24. 2
24. 4, 7, 12, 19, 28,
+3 +5 +7 +9
39 52
+11 +13
25. 4
25. 10080, 1680, 336, 84, 28,
? 6 ? 5 ? 4 ? 3
14
? 2
26. 2
26.
n
r
CI P 1 1
100
? ?
? ?
? ? ? ? ?
? ?
? ?
? ?
? ?
n
7
4347 30000 1 1
100
? ?
? ?
? ? ? ? ?
? ?
? ?
? ?
? ?
n
11490 107
10000 100
? ?
? ?
? ?
? ?
2 n
107 107
100 100
?? ??
? ?
?? ??
?? ??
? n = 2
27. 2
27.
1 1 1 1
3 5 2 4
2,9,16 ,32
=
1 1
3 2
2,9,2
1
, 2
1
6 6
6 6
3 2
2 ,9 ,2 ,2 ?
= 2
3
, 9
2
, 2
6
, 2
6
28. 3
28.
1
x 2
x
? ?
? x
2
+ 1 – 2x = 0
? (x - 1)
2
= 0
? x = 1
17 17
19 19
1 1
x 1 2
x 1
? ? ? ? ?
29. 3
29. Let runs required = x
? 15 ? 6 + x ? 5 = 7.2 ? 20
? x = 54
? required run rate =
54
10.8
5
?
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