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NTSE STAGE – I (DELHI STATE)  
003 –A (2020 – 21)  
 (For Class – X) 
MENTAL ABILITY TEST (MAT) 
 
FIITJEE ANSWER KEYS 
 1. Bonus  2. 1  3. 3  4. 2 
 5. 3  6. 4  7. 1  8. 2 
 9. 4  10. 2  11. 2  12. 4 
 13. 1  14. 4  15. 1  16. 3 
 17. 4  18. 2  19. 4  20. 1 
 21. 4  22. 3  23. 4  24. 4 
 25. 3  26. 2  27. 1  28. 1 
 29. 3  30. 4   31. 4  32. 2 
 33. 1  34. 3  35. 2  36.  1   
 37. 3  38. 4  39. 1  40. 3 
 41. 1  42. 4  43. 1  44. 2 
 45. 3  46. 2  47. Bonus  48. 4 
 49. 3  50. 2  51. 4  52. 3 
 53. 2  54. 2  55. 3  56. 1 
 57. 2  58. 4  59. 2  60. 4 
 61. 1  62. 1  63. 2  64. 4 
 65. 3  66. 2  67. 3  68. 1 
 69. 3  70. 2  71. 4  72. 1 
 73. 3  74. 4  75. 3  76. 1 
 77. Bonus  78. 2  79. 4  80. 4 
 81. 3  82. 3  83. 4  84. 4 
 85. 2  86. 3  87. 3  88. 2   
 89. 3  90. 3  91. 1  92. 4   
 93. 4  94. 3  95. 2  96. 2   
 97. 3  98. 4  99. 2  100. 4 
 
Page 2


 
  
 
 
 
 
NTSE STAGE – I (DELHI STATE)  
003 –A (2020 – 21)  
 (For Class – X) 
MENTAL ABILITY TEST (MAT) 
 
FIITJEE ANSWER KEYS 
 1. Bonus  2. 1  3. 3  4. 2 
 5. 3  6. 4  7. 1  8. 2 
 9. 4  10. 2  11. 2  12. 4 
 13. 1  14. 4  15. 1  16. 3 
 17. 4  18. 2  19. 4  20. 1 
 21. 4  22. 3  23. 4  24. 4 
 25. 3  26. 2  27. 1  28. 1 
 29. 3  30. 4   31. 4  32. 2 
 33. 1  34. 3  35. 2  36.  1   
 37. 3  38. 4  39. 1  40. 3 
 41. 1  42. 4  43. 1  44. 2 
 45. 3  46. 2  47. Bonus  48. 4 
 49. 3  50. 2  51. 4  52. 3 
 53. 2  54. 2  55. 3  56. 1 
 57. 2  58. 4  59. 2  60. 4 
 61. 1  62. 1  63. 2  64. 4 
 65. 3  66. 2  67. 3  68. 1 
 69. 3  70. 2  71. 4  72. 1 
 73. 3  74. 4  75. 3  76. 1 
 77. Bonus  78. 2  79. 4  80. 4 
 81. 3  82. 3  83. 4  84. 4 
 85. 2  86. 3  87. 3  88. 2   
 89. 3  90. 3  91. 1  92. 4   
 93. 4  94. 3  95. 2  96. 2   
 97. 3  98. 4  99. 2  100. 4 
 
 
  
 
 
 
 
NTSE STAGE – I (DELHI STATE) 
003 –A (2020 – 21)  
(For Class – X) 
MENTAL ABILITY TEST (MAT) 
 
SOLUTIONS 
 
1. Bonus 
 
2. 1  
2. 20% of x = y 
 
20
xy
100
??
=
??
??
 
 y % of 20 
 
y 20 1
20 x 20
100 100 100
??
? = ? ?
??
??
 
 = 
4x
4% of x
100
= 
 
3. 3 
3. 
nn
a 3 4 =+ 
 Put n = 1, 1, 3 [series will be 7, 10, 13, …] 
 a = 7, d = 2, n = 12 
 ( )
12
n
s 2a n 1 d
2
?? = + -
??
 
 = ( ) ( )
12
2 7 12 1 3
2
?? +-
??
 
 
 = ( ) 6 14 39 282 += 
 
4. 2 
4. Time taken by slower train to pass the driver ? distance would be 500 m. 
 Time = 
500 18
24 sec
45 30 5
?=
+
 
 
5. 3 
5. 18, 50, 98,... 
 3 2,5 2,7 2 9 2 162 ?= 
 
6. 4 
6. 
pq
am
+
= 
pq
an
-
= 
 ( ) a p q 1 d m + + - =   ( ) a p q 1 d n + - - =  
 Add both equations  
 ( ) 2a 2 p 1 d m n + - = + 
 P
th
 term ( )
mn
a p 1 d
2
+
+ - = 
 
Page 3


 
  
 
 
 
 
NTSE STAGE – I (DELHI STATE)  
003 –A (2020 – 21)  
 (For Class – X) 
MENTAL ABILITY TEST (MAT) 
 
FIITJEE ANSWER KEYS 
 1. Bonus  2. 1  3. 3  4. 2 
 5. 3  6. 4  7. 1  8. 2 
 9. 4  10. 2  11. 2  12. 4 
 13. 1  14. 4  15. 1  16. 3 
 17. 4  18. 2  19. 4  20. 1 
 21. 4  22. 3  23. 4  24. 4 
 25. 3  26. 2  27. 1  28. 1 
 29. 3  30. 4   31. 4  32. 2 
 33. 1  34. 3  35. 2  36.  1   
 37. 3  38. 4  39. 1  40. 3 
 41. 1  42. 4  43. 1  44. 2 
 45. 3  46. 2  47. Bonus  48. 4 
 49. 3  50. 2  51. 4  52. 3 
 53. 2  54. 2  55. 3  56. 1 
 57. 2  58. 4  59. 2  60. 4 
 61. 1  62. 1  63. 2  64. 4 
 65. 3  66. 2  67. 3  68. 1 
 69. 3  70. 2  71. 4  72. 1 
 73. 3  74. 4  75. 3  76. 1 
 77. Bonus  78. 2  79. 4  80. 4 
 81. 3  82. 3  83. 4  84. 4 
 85. 2  86. 3  87. 3  88. 2   
 89. 3  90. 3  91. 1  92. 4   
 93. 4  94. 3  95. 2  96. 2   
 97. 3  98. 4  99. 2  100. 4 
 
 
  
 
 
 
 
NTSE STAGE – I (DELHI STATE) 
003 –A (2020 – 21)  
(For Class – X) 
MENTAL ABILITY TEST (MAT) 
 
SOLUTIONS 
 
1. Bonus 
 
2. 1  
2. 20% of x = y 
 
20
xy
100
??
=
??
??
 
 y % of 20 
 
y 20 1
20 x 20
100 100 100
??
? = ? ?
??
??
 
 = 
4x
4% of x
100
= 
 
3. 3 
3. 
nn
a 3 4 =+ 
 Put n = 1, 1, 3 [series will be 7, 10, 13, …] 
 a = 7, d = 2, n = 12 
 ( )
12
n
s 2a n 1 d
2
?? = + -
??
 
 = ( ) ( )
12
2 7 12 1 3
2
?? +-
??
 
 
 = ( ) 6 14 39 282 += 
 
4. 2 
4. Time taken by slower train to pass the driver ? distance would be 500 m. 
 Time = 
500 18
24 sec
45 30 5
?=
+
 
 
5. 3 
5. 18, 50, 98,... 
 3 2,5 2,7 2 9 2 162 ?= 
 
6. 4 
6. 
pq
am
+
= 
pq
an
-
= 
 ( ) a p q 1 d m + + - =   ( ) a p q 1 d n + - - =  
 Add both equations  
 ( ) 2a 2 p 1 d m n + - = + 
 P
th
 term ( )
mn
a p 1 d
2
+
+ - = 
 
 
  
 
 
 
 
7. 1 
7. Speed equation  
 
600 600
400
1
t
t
2
-=
+
 
 By hit and trial method  
 T = 1 hour  
 
8. 2 
8. Horizontal and vertical distance are same. 
 
perpendicular
tan 1
base
? = = 
 ? = 45
0
 
 
9. 4 
9. Girls (those who wear spectacles) 
 = 
25 5
1400 250
100 7
? ? = 
 
10. 2 
10. P Q R 
 65x6 :  84x5  : 100x3 
 13     : 14     : 10 
 
 P takes 5% i.e., 
5
7400 370
100
?= 
 Balance = 7400 – 370 = 7030 
 Q’s share = 
14
7030 2660
37
?= 
 
11. 2 
11. Distance = ( )
Pr oduct of speed
Diff. between arrival time
Diff. of speed
? 
 = 
10 15 12
6 km
5 60
?
?= 
 
12. 4 
12. 
24 7
tan cos
7 25
? = ? = 
 14tan 75cos 7sec ? - ? - ? 
 = 
24 7 25
14 75 7
7 25 7
? - ? - ? 
 = 48 – 21 – 25 = 2  
 
13. 1 
13. 
2
2
1
x 2 98 2
x
??
+ + = +
??
??
 
 
1
x 10
x
+= 
Page 4


 
  
 
 
 
 
NTSE STAGE – I (DELHI STATE)  
003 –A (2020 – 21)  
 (For Class – X) 
MENTAL ABILITY TEST (MAT) 
 
FIITJEE ANSWER KEYS 
 1. Bonus  2. 1  3. 3  4. 2 
 5. 3  6. 4  7. 1  8. 2 
 9. 4  10. 2  11. 2  12. 4 
 13. 1  14. 4  15. 1  16. 3 
 17. 4  18. 2  19. 4  20. 1 
 21. 4  22. 3  23. 4  24. 4 
 25. 3  26. 2  27. 1  28. 1 
 29. 3  30. 4   31. 4  32. 2 
 33. 1  34. 3  35. 2  36.  1   
 37. 3  38. 4  39. 1  40. 3 
 41. 1  42. 4  43. 1  44. 2 
 45. 3  46. 2  47. Bonus  48. 4 
 49. 3  50. 2  51. 4  52. 3 
 53. 2  54. 2  55. 3  56. 1 
 57. 2  58. 4  59. 2  60. 4 
 61. 1  62. 1  63. 2  64. 4 
 65. 3  66. 2  67. 3  68. 1 
 69. 3  70. 2  71. 4  72. 1 
 73. 3  74. 4  75. 3  76. 1 
 77. Bonus  78. 2  79. 4  80. 4 
 81. 3  82. 3  83. 4  84. 4 
 85. 2  86. 3  87. 3  88. 2   
 89. 3  90. 3  91. 1  92. 4   
 93. 4  94. 3  95. 2  96. 2   
 97. 3  98. 4  99. 2  100. 4 
 
 
  
 
 
 
 
NTSE STAGE – I (DELHI STATE) 
003 –A (2020 – 21)  
(For Class – X) 
MENTAL ABILITY TEST (MAT) 
 
SOLUTIONS 
 
1. Bonus 
 
2. 1  
2. 20% of x = y 
 
20
xy
100
??
=
??
??
 
 y % of 20 
 
y 20 1
20 x 20
100 100 100
??
? = ? ?
??
??
 
 = 
4x
4% of x
100
= 
 
3. 3 
3. 
nn
a 3 4 =+ 
 Put n = 1, 1, 3 [series will be 7, 10, 13, …] 
 a = 7, d = 2, n = 12 
 ( )
12
n
s 2a n 1 d
2
?? = + -
??
 
 = ( ) ( )
12
2 7 12 1 3
2
?? +-
??
 
 
 = ( ) 6 14 39 282 += 
 
4. 2 
4. Time taken by slower train to pass the driver ? distance would be 500 m. 
 Time = 
500 18
24 sec
45 30 5
?=
+
 
 
5. 3 
5. 18, 50, 98,... 
 3 2,5 2,7 2 9 2 162 ?= 
 
6. 4 
6. 
pq
am
+
= 
pq
an
-
= 
 ( ) a p q 1 d m + + - =   ( ) a p q 1 d n + - - =  
 Add both equations  
 ( ) 2a 2 p 1 d m n + - = + 
 P
th
 term ( )
mn
a p 1 d
2
+
+ - = 
 
 
  
 
 
 
 
7. 1 
7. Speed equation  
 
600 600
400
1
t
t
2
-=
+
 
 By hit and trial method  
 T = 1 hour  
 
8. 2 
8. Horizontal and vertical distance are same. 
 
perpendicular
tan 1
base
? = = 
 ? = 45
0
 
 
9. 4 
9. Girls (those who wear spectacles) 
 = 
25 5
1400 250
100 7
? ? = 
 
10. 2 
10. P Q R 
 65x6 :  84x5  : 100x3 
 13     : 14     : 10 
 
 P takes 5% i.e., 
5
7400 370
100
?= 
 Balance = 7400 – 370 = 7030 
 Q’s share = 
14
7030 2660
37
?= 
 
11. 2 
11. Distance = ( )
Pr oduct of speed
Diff. between arrival time
Diff. of speed
? 
 = 
10 15 12
6 km
5 60
?
?= 
 
12. 4 
12. 
24 7
tan cos
7 25
? = ? = 
 14tan 75cos 7sec ? - ? - ? 
 = 
24 7 25
14 75 7
7 25 7
? - ? - ? 
 = 48 – 21 – 25 = 2  
 
13. 1 
13. 
2
2
1
x 2 98 2
x
??
+ + = +
??
??
 
 
1
x 10
x
+= 
 
  
 
 
 
 
 
3
3
3
1 1 1
x x 3 x
x x x
? ? ? ?
+ = + - +
? ? ? ?
? ? ? ?
 
 = 
3
10 3 10 -? 
 = 1000 – 30 = 970  
 
14. 4 
14. d. maximum  
 b. minimum 
 b. monk 
 a. music 
 
 option (4) d, c, b, a 
15. 1 
15. Let present age of father and son be 7x and 3x. 
 After 10 years it will be  
 (7x + 10) and (3x + 10) 
 
 According to question  
 
7x 10 2
3x 10 1
+
=
+
 
 
 7x + 10 = 6x + 20  
 x = 10 
 ? present age of father is 7x i.e., 7 x 10 = 70 years  
 
16. 3 
16. Sum of students in 2017 
 = 32 + 24 + 17 + 24 + 23 = 120 
 Sum of students in 2018 
 = 18 + 16 + 29 + 11 + 21 = 95 
 Difference = 120 – 95 = 25  
 
17. 4 
17. Sum of students in class III. 
 = 39 + 33 + 52 + 17 + 29 = 170 
 Sum of students in class I. 
 = 22 + 28 + 26 + 32 + 18 = 126 
 Require answer = 
170
100 134.92
126
?= 
 Approx = 135 
 
18. 2 
18. Sum of students in 2018 
 = 18 + 16 + 29 + 11 + 21 = 95 
 Square = (95)
2
 = 9025 
 
 
19. 4 
19. Student in class I in 2017 = 32 
 Student in class II in 2017 = 24 
 Require answer = 
32 24
100
24
-
? 
 = 
8
100 33.33%
24
?= 
Page 5


 
  
 
 
 
 
NTSE STAGE – I (DELHI STATE)  
003 –A (2020 – 21)  
 (For Class – X) 
MENTAL ABILITY TEST (MAT) 
 
FIITJEE ANSWER KEYS 
 1. Bonus  2. 1  3. 3  4. 2 
 5. 3  6. 4  7. 1  8. 2 
 9. 4  10. 2  11. 2  12. 4 
 13. 1  14. 4  15. 1  16. 3 
 17. 4  18. 2  19. 4  20. 1 
 21. 4  22. 3  23. 4  24. 4 
 25. 3  26. 2  27. 1  28. 1 
 29. 3  30. 4   31. 4  32. 2 
 33. 1  34. 3  35. 2  36.  1   
 37. 3  38. 4  39. 1  40. 3 
 41. 1  42. 4  43. 1  44. 2 
 45. 3  46. 2  47. Bonus  48. 4 
 49. 3  50. 2  51. 4  52. 3 
 53. 2  54. 2  55. 3  56. 1 
 57. 2  58. 4  59. 2  60. 4 
 61. 1  62. 1  63. 2  64. 4 
 65. 3  66. 2  67. 3  68. 1 
 69. 3  70. 2  71. 4  72. 1 
 73. 3  74. 4  75. 3  76. 1 
 77. Bonus  78. 2  79. 4  80. 4 
 81. 3  82. 3  83. 4  84. 4 
 85. 2  86. 3  87. 3  88. 2   
 89. 3  90. 3  91. 1  92. 4   
 93. 4  94. 3  95. 2  96. 2   
 97. 3  98. 4  99. 2  100. 4 
 
 
  
 
 
 
 
NTSE STAGE – I (DELHI STATE) 
003 –A (2020 – 21)  
(For Class – X) 
MENTAL ABILITY TEST (MAT) 
 
SOLUTIONS 
 
1. Bonus 
 
2. 1  
2. 20% of x = y 
 
20
xy
100
??
=
??
??
 
 y % of 20 
 
y 20 1
20 x 20
100 100 100
??
? = ? ?
??
??
 
 = 
4x
4% of x
100
= 
 
3. 3 
3. 
nn
a 3 4 =+ 
 Put n = 1, 1, 3 [series will be 7, 10, 13, …] 
 a = 7, d = 2, n = 12 
 ( )
12
n
s 2a n 1 d
2
?? = + -
??
 
 = ( ) ( )
12
2 7 12 1 3
2
?? +-
??
 
 
 = ( ) 6 14 39 282 += 
 
4. 2 
4. Time taken by slower train to pass the driver ? distance would be 500 m. 
 Time = 
500 18
24 sec
45 30 5
?=
+
 
 
5. 3 
5. 18, 50, 98,... 
 3 2,5 2,7 2 9 2 162 ?= 
 
6. 4 
6. 
pq
am
+
= 
pq
an
-
= 
 ( ) a p q 1 d m + + - =   ( ) a p q 1 d n + - - =  
 Add both equations  
 ( ) 2a 2 p 1 d m n + - = + 
 P
th
 term ( )
mn
a p 1 d
2
+
+ - = 
 
 
  
 
 
 
 
7. 1 
7. Speed equation  
 
600 600
400
1
t
t
2
-=
+
 
 By hit and trial method  
 T = 1 hour  
 
8. 2 
8. Horizontal and vertical distance are same. 
 
perpendicular
tan 1
base
? = = 
 ? = 45
0
 
 
9. 4 
9. Girls (those who wear spectacles) 
 = 
25 5
1400 250
100 7
? ? = 
 
10. 2 
10. P Q R 
 65x6 :  84x5  : 100x3 
 13     : 14     : 10 
 
 P takes 5% i.e., 
5
7400 370
100
?= 
 Balance = 7400 – 370 = 7030 
 Q’s share = 
14
7030 2660
37
?= 
 
11. 2 
11. Distance = ( )
Pr oduct of speed
Diff. between arrival time
Diff. of speed
? 
 = 
10 15 12
6 km
5 60
?
?= 
 
12. 4 
12. 
24 7
tan cos
7 25
? = ? = 
 14tan 75cos 7sec ? - ? - ? 
 = 
24 7 25
14 75 7
7 25 7
? - ? - ? 
 = 48 – 21 – 25 = 2  
 
13. 1 
13. 
2
2
1
x 2 98 2
x
??
+ + = +
??
??
 
 
1
x 10
x
+= 
 
  
 
 
 
 
 
3
3
3
1 1 1
x x 3 x
x x x
? ? ? ?
+ = + - +
? ? ? ?
? ? ? ?
 
 = 
3
10 3 10 -? 
 = 1000 – 30 = 970  
 
14. 4 
14. d. maximum  
 b. minimum 
 b. monk 
 a. music 
 
 option (4) d, c, b, a 
15. 1 
15. Let present age of father and son be 7x and 3x. 
 After 10 years it will be  
 (7x + 10) and (3x + 10) 
 
 According to question  
 
7x 10 2
3x 10 1
+
=
+
 
 
 7x + 10 = 6x + 20  
 x = 10 
 ? present age of father is 7x i.e., 7 x 10 = 70 years  
 
16. 3 
16. Sum of students in 2017 
 = 32 + 24 + 17 + 24 + 23 = 120 
 Sum of students in 2018 
 = 18 + 16 + 29 + 11 + 21 = 95 
 Difference = 120 – 95 = 25  
 
17. 4 
17. Sum of students in class III. 
 = 39 + 33 + 52 + 17 + 29 = 170 
 Sum of students in class I. 
 = 22 + 28 + 26 + 32 + 18 = 126 
 Require answer = 
170
100 134.92
126
?= 
 Approx = 135 
 
18. 2 
18. Sum of students in 2018 
 = 18 + 16 + 29 + 11 + 21 = 95 
 Square = (95)
2
 = 9025 
 
 
19. 4 
19. Student in class I in 2017 = 32 
 Student in class II in 2017 = 24 
 Require answer = 
32 24
100
24
-
? 
 = 
8
100 33.33%
24
?= 
 
  
 
 
 
 
 
20. 1 
20. Cube is 3 – d form of square similarly cuboid is 3 – d form of rectangle. 
 
21. 4 
21. 82 : 9 
 ? 
2
9 1 82 += 
 Similarly option (4) 
 
2
5 1 26 += 
 
22. 3 
22. A = 1 x 2 = 2 
 T = 20 x 2 = 40 
 1 and 20 are respective position of A and T is in alphabet. 
 Similarly ACT = 2 + 6 + 40 = 48 
 TAKE = 40 + 2 + 22 + 10 = 74  
 
23. 4 
23. 
 
126 98 70 41 
14 
42 
28 28 28 28 
 
 
24. 4 
24. 
 
1 3 7 15 
31 
63 
x2+1 
65 
127 
x2+1 x2+1 x2+1 x2+1 
x2+1 
 
 
25. 3 
25.    126  
7 28 63 124 215 344 
 ? ? ? ? ? ? 
 
3
21 - 
3
31 + 
3
41 - 
3
51 + 
3
61 - 
3
71 + 
 
26. 2 
26. 
 
A D E G I J M M 
Q P 
+4 
U P 
+4 +4 +4 +4 
+3 +3 +3 +3 +3 
U S 
 
 
27. 1 
27. 
 
Z8 W5 T2 Q8 N5 K3 
26 ? 2 + 6 = 8 20 ? 2 + 0 = 2 14 ? 1 + 4 = 5 
23 ? 2 + 3 = 5 17 ? 1 + 7 = 8 11 ? 1 + 1 = 2 
K2 
 
 
  
28. 1

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Delhi: State Level Answer Key (MAT) - 2020-21 Notes

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