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 Page 1


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


 
  
 
 
 
NTSE STAGE – I (HARYANA STATE) 
 (2020 – 21)  
 (For Class – X) 
SCHOLASTIC APTITUDE TEST 
ANSWER KEYS 
 1. 4 2. 4 3. 1 4. 3 
 5 2 6. 4 7. 3 8. 2 
 9. 2 10. 2 11. 4 12. 1 
 13. 1 14. 3 15. 3 16. 4 
 17. 3 18. 3 19. 2 20. 3 
 21. 4 22. 4 23. 2 24. 1 
 25. 4 26. 1 27. 1 28. 2 
 29. 4 30. 1 31. 4 32. 4 
 33. 3 34. 2 35. 4 36. 4 
 37. 3 38. 2 39. 4 40. 2 
 41. 3 42. 2 43. 1 44. 2 
 45. 2 46. 4 47. 2 48. 3 
 49. 1 50. 2 51. 4 52. 3 
 53. 3 54. 3 55. 3 56. 2 
 57. 4 58. 1 59. 1 60. 4 
 61. 4 62. 2 63. 4 64. 2 
 65. 3 66. 1 67. 2 68. 3 
 69. 2 70. 1 71. 3 72. 1 
 73. 2 74. 4 75. 4 76. 2 
 77. 2 78. 1 79. 3 80. 3 
 81. 4 82. 3 83. 3 84. 1 
 85. 2 86. 3 87. 3 88. 3 
 89. 2 90. 2 91. 4 92. 3 
 93. 3 94. 1 95. 4 96. 3 
 97. 3 98. 4 99. 3 100. 1 
 
 
 
 
  
 
 
 
 
NTSE STAGE – I (HARYANA STATE) 
 (2020 – 21)  
 (For Class – X) 
SCHOLASTIC APTITUDE TEST 
 
HINTS & SOLUTIONS 
 
1. 4 
Sol.  A 
B 
C 
S K R 
Q 
P 
M 
N 
x 
2x 
x 
 
 AB = 10 
 AC = 10 
 P, Q are mid points of AB & AC 
 ? AP = PB = 5 
 AQ = QC = 5 
 BC = 12 
 ? x + 2x + x = 12 ? x = 3 
 ? BS = 3, SR = 6, RC = 3 
  ?ABC is isosceles 
 AK ? BC and BK = KC 
 ? BS = SK = KR = RC = 3 
  PQ || BC 
 ? ABK ? 
BS BP
SP || AK PSB AKB
SK PA
= ? ? ? ? 
 ? PS ? BC and 
PS 1
AK 2
= 
 
1
PS AK
2
= 
 Similarly, QR ? BC 
 
22
ACK AK 10 6 8 ? ? = - = 
 
1
PS AK PS 4
2
= ? = 
 and similarly QR = 4 
Page 3


 
  
 
 
 
NTSE STAGE – I (HARYANA STATE) 
 (2020 – 21)  
 (For Class – X) 
SCHOLASTIC APTITUDE TEST 
ANSWER KEYS 
 1. 4 2. 4 3. 1 4. 3 
 5 2 6. 4 7. 3 8. 2 
 9. 2 10. 2 11. 4 12. 1 
 13. 1 14. 3 15. 3 16. 4 
 17. 3 18. 3 19. 2 20. 3 
 21. 4 22. 4 23. 2 24. 1 
 25. 4 26. 1 27. 1 28. 2 
 29. 4 30. 1 31. 4 32. 4 
 33. 3 34. 2 35. 4 36. 4 
 37. 3 38. 2 39. 4 40. 2 
 41. 3 42. 2 43. 1 44. 2 
 45. 2 46. 4 47. 2 48. 3 
 49. 1 50. 2 51. 4 52. 3 
 53. 3 54. 3 55. 3 56. 2 
 57. 4 58. 1 59. 1 60. 4 
 61. 4 62. 2 63. 4 64. 2 
 65. 3 66. 1 67. 2 68. 3 
 69. 2 70. 1 71. 3 72. 1 
 73. 2 74. 4 75. 4 76. 2 
 77. 2 78. 1 79. 3 80. 3 
 81. 4 82. 3 83. 3 84. 1 
 85. 2 86. 3 87. 3 88. 3 
 89. 2 90. 2 91. 4 92. 3 
 93. 3 94. 1 95. 4 96. 3 
 97. 3 98. 4 99. 3 100. 1 
 
 
 
 
  
 
 
 
 
NTSE STAGE – I (HARYANA STATE) 
 (2020 – 21)  
 (For Class – X) 
SCHOLASTIC APTITUDE TEST 
 
HINTS & SOLUTIONS 
 
1. 4 
Sol.  A 
B 
C 
S K R 
Q 
P 
M 
N 
x 
2x 
x 
 
 AB = 10 
 AC = 10 
 P, Q are mid points of AB & AC 
 ? AP = PB = 5 
 AQ = QC = 5 
 BC = 12 
 ? x + 2x + x = 12 ? x = 3 
 ? BS = 3, SR = 6, RC = 3 
  ?ABC is isosceles 
 AK ? BC and BK = KC 
 ? BS = SK = KR = RC = 3 
  PQ || BC 
 ? ABK ? 
BS BP
SP || AK PSB AKB
SK PA
= ? ? ? ? 
 ? PS ? BC and 
PS 1
AK 2
= 
 
1
PS AK
2
= 
 Similarly, QR ? BC 
 
22
ACK AK 10 6 8 ? ? = - = 
 
1
PS AK PS 4
2
= ? = 
 and similarly QR = 4 
 
  
 
 
 Now in ?QRS ? ?QRS = 90° 
 
2 2 2 2
SQ SR RQ 6 4 2 13 ? = + = + = 
 ? PQRS will be a rectangle 
 [PQRS] = 6 × 4 = 24 
 ? [PQS] = [SRQ] = 12 
 Now [PSQ] 
1
SQ PM 12
2
= ? ? = 
 
1
2 13 PM 12
2
? ? = 
 
12
PM
13
= 
 Similarly, 
12
RN
13
= 
 Now, In right angle triangle ?PSM 
 
2
2 2 2
12 8
SM PS PM 4
13 13
??
= - = - =
??
??
 
 Similarly, 
8
QN
13
= 
 Now, MN = SQ – SM – QN 
 
8 8 26 16 10
2 13
13 13 13 13
-
= - - = = 
 
4. 3 
Sol. Thyroxin regulates carbohydrate, protein and fat metabolism in the body so as to provide the 
best balance for growth. 
 
6. 4 
Sol. Fertilisation takes place in fallopian tube.  
  
8. 2 
Sol. Hibiscus and mustard are bisexual flowers. 
 
9. 2 
Sol. 
 
A 
E 
D 
B 
F 
x 15 
9 15 
C 
O 
 
 
22
AB 15 9 12 cm BD AC CE = - = = = = 
 Let OF = x cm then 
2
DE 2 225 x =- 
 Using 
abc
R
4
=
?
 
 
( )
( )
2
2
24 24 2 225 x
15
1
4 15 x 2 225 x
2
? ? -
=
? ? + -
 
Page 4


 
  
 
 
 
NTSE STAGE – I (HARYANA STATE) 
 (2020 – 21)  
 (For Class – X) 
SCHOLASTIC APTITUDE TEST 
ANSWER KEYS 
 1. 4 2. 4 3. 1 4. 3 
 5 2 6. 4 7. 3 8. 2 
 9. 2 10. 2 11. 4 12. 1 
 13. 1 14. 3 15. 3 16. 4 
 17. 3 18. 3 19. 2 20. 3 
 21. 4 22. 4 23. 2 24. 1 
 25. 4 26. 1 27. 1 28. 2 
 29. 4 30. 1 31. 4 32. 4 
 33. 3 34. 2 35. 4 36. 4 
 37. 3 38. 2 39. 4 40. 2 
 41. 3 42. 2 43. 1 44. 2 
 45. 2 46. 4 47. 2 48. 3 
 49. 1 50. 2 51. 4 52. 3 
 53. 3 54. 3 55. 3 56. 2 
 57. 4 58. 1 59. 1 60. 4 
 61. 4 62. 2 63. 4 64. 2 
 65. 3 66. 1 67. 2 68. 3 
 69. 2 70. 1 71. 3 72. 1 
 73. 2 74. 4 75. 4 76. 2 
 77. 2 78. 1 79. 3 80. 3 
 81. 4 82. 3 83. 3 84. 1 
 85. 2 86. 3 87. 3 88. 3 
 89. 2 90. 2 91. 4 92. 3 
 93. 3 94. 1 95. 4 96. 3 
 97. 3 98. 4 99. 3 100. 1 
 
 
 
 
  
 
 
 
 
NTSE STAGE – I (HARYANA STATE) 
 (2020 – 21)  
 (For Class – X) 
SCHOLASTIC APTITUDE TEST 
 
HINTS & SOLUTIONS 
 
1. 4 
Sol.  A 
B 
C 
S K R 
Q 
P 
M 
N 
x 
2x 
x 
 
 AB = 10 
 AC = 10 
 P, Q are mid points of AB & AC 
 ? AP = PB = 5 
 AQ = QC = 5 
 BC = 12 
 ? x + 2x + x = 12 ? x = 3 
 ? BS = 3, SR = 6, RC = 3 
  ?ABC is isosceles 
 AK ? BC and BK = KC 
 ? BS = SK = KR = RC = 3 
  PQ || BC 
 ? ABK ? 
BS BP
SP || AK PSB AKB
SK PA
= ? ? ? ? 
 ? PS ? BC and 
PS 1
AK 2
= 
 
1
PS AK
2
= 
 Similarly, QR ? BC 
 
22
ACK AK 10 6 8 ? ? = - = 
 
1
PS AK PS 4
2
= ? = 
 and similarly QR = 4 
 
  
 
 
 Now in ?QRS ? ?QRS = 90° 
 
2 2 2 2
SQ SR RQ 6 4 2 13 ? = + = + = 
 ? PQRS will be a rectangle 
 [PQRS] = 6 × 4 = 24 
 ? [PQS] = [SRQ] = 12 
 Now [PSQ] 
1
SQ PM 12
2
= ? ? = 
 
1
2 13 PM 12
2
? ? = 
 
12
PM
13
= 
 Similarly, 
12
RN
13
= 
 Now, In right angle triangle ?PSM 
 
2
2 2 2
12 8
SM PS PM 4
13 13
??
= - = - =
??
??
 
 Similarly, 
8
QN
13
= 
 Now, MN = SQ – SM – QN 
 
8 8 26 16 10
2 13
13 13 13 13
-
= - - = = 
 
4. 3 
Sol. Thyroxin regulates carbohydrate, protein and fat metabolism in the body so as to provide the 
best balance for growth. 
 
6. 4 
Sol. Fertilisation takes place in fallopian tube.  
  
8. 2 
Sol. Hibiscus and mustard are bisexual flowers. 
 
9. 2 
Sol. 
 
A 
E 
D 
B 
F 
x 15 
9 15 
C 
O 
 
 
22
AB 15 9 12 cm BD AC CE = - = = = = 
 Let OF = x cm then 
2
DE 2 225 x =- 
 Using 
abc
R
4
=
?
 
 
( )
( )
2
2
24 24 2 225 x
15
1
4 15 x 2 225 x
2
? ? -
=
? ? + -
 
 
  
 
 
 x 4.2 cm ?= 
 
12. 1 
Sol.  
C 
B 
A 
X 
Z 
Y 
Q 
R 
P 
 
 By using Menalau’s theorem 
 CR : RQ : QX = BP : PR : RZ = AQ : QP : PY = 3 : 3 : 1 
 Now, AX : XB = 1 : 2 
 ? ? ? ? ?=
2
BXC ABC
3
 
 CR : RX = 3 : 4 
 ? ? ? ? ? ? ? = =
48
BRX BXC ABC
7 21
 
 Join P to X,  Since RP : PB = 1:1 
 ? ? ? ? ? ?
14
XPR BRX ABC
2 21
? = = 
 RQ : QX = 3 : 1 
 ? ? ? ? ? ?
31
PQR XPR ABC
47
? = = 
 ( )
2
13
ar PQR 14 14 7 3 cm
74
? = ? ? ? = 
 
15. 3 
Sol. Arteries always carry blood away from heart, while veins always carry blood towards the 
heart. 
 
16. 4 
Sol. 0.001 M NaOH ? [OH
–
] = 10
–3
 M 
 ? pOH = 3, so pH = 11 
 
17. 3 
Sol. Draw AQ ? ED 
 Then EQ = QD = 1 cm 
 Also, BP = PC = 1 cm 
 Join A to D and E 
 Now AP 3 cm, PQ 2cm == 
 
( )
AQ 3 2 cm ? = + 
 A 
E D 
C 
2 
2 
B 
1 1 
1 1 
P 
2 2 
Q 
 
 By Pythagoras theorem 
( )
2
AD AE 3 2 1 = = + + 
 Now, given circle is circumcircle of ?AED  
 
( ) ( ) ( )
( )
AE ED AD
Radius
4 ar AED
?=
?
 
 
( )
( )
( )
2
3 2 1 2
2 cm
1
4 2 3 2
2
??
++
??
??
==
? ? ? +
 
Page 5


 
  
 
 
 
NTSE STAGE – I (HARYANA STATE) 
 (2020 – 21)  
 (For Class – X) 
SCHOLASTIC APTITUDE TEST 
ANSWER KEYS 
 1. 4 2. 4 3. 1 4. 3 
 5 2 6. 4 7. 3 8. 2 
 9. 2 10. 2 11. 4 12. 1 
 13. 1 14. 3 15. 3 16. 4 
 17. 3 18. 3 19. 2 20. 3 
 21. 4 22. 4 23. 2 24. 1 
 25. 4 26. 1 27. 1 28. 2 
 29. 4 30. 1 31. 4 32. 4 
 33. 3 34. 2 35. 4 36. 4 
 37. 3 38. 2 39. 4 40. 2 
 41. 3 42. 2 43. 1 44. 2 
 45. 2 46. 4 47. 2 48. 3 
 49. 1 50. 2 51. 4 52. 3 
 53. 3 54. 3 55. 3 56. 2 
 57. 4 58. 1 59. 1 60. 4 
 61. 4 62. 2 63. 4 64. 2 
 65. 3 66. 1 67. 2 68. 3 
 69. 2 70. 1 71. 3 72. 1 
 73. 2 74. 4 75. 4 76. 2 
 77. 2 78. 1 79. 3 80. 3 
 81. 4 82. 3 83. 3 84. 1 
 85. 2 86. 3 87. 3 88. 3 
 89. 2 90. 2 91. 4 92. 3 
 93. 3 94. 1 95. 4 96. 3 
 97. 3 98. 4 99. 3 100. 1 
 
 
 
 
  
 
 
 
 
NTSE STAGE – I (HARYANA STATE) 
 (2020 – 21)  
 (For Class – X) 
SCHOLASTIC APTITUDE TEST 
 
HINTS & SOLUTIONS 
 
1. 4 
Sol.  A 
B 
C 
S K R 
Q 
P 
M 
N 
x 
2x 
x 
 
 AB = 10 
 AC = 10 
 P, Q are mid points of AB & AC 
 ? AP = PB = 5 
 AQ = QC = 5 
 BC = 12 
 ? x + 2x + x = 12 ? x = 3 
 ? BS = 3, SR = 6, RC = 3 
  ?ABC is isosceles 
 AK ? BC and BK = KC 
 ? BS = SK = KR = RC = 3 
  PQ || BC 
 ? ABK ? 
BS BP
SP || AK PSB AKB
SK PA
= ? ? ? ? 
 ? PS ? BC and 
PS 1
AK 2
= 
 
1
PS AK
2
= 
 Similarly, QR ? BC 
 
22
ACK AK 10 6 8 ? ? = - = 
 
1
PS AK PS 4
2
= ? = 
 and similarly QR = 4 
 
  
 
 
 Now in ?QRS ? ?QRS = 90° 
 
2 2 2 2
SQ SR RQ 6 4 2 13 ? = + = + = 
 ? PQRS will be a rectangle 
 [PQRS] = 6 × 4 = 24 
 ? [PQS] = [SRQ] = 12 
 Now [PSQ] 
1
SQ PM 12
2
= ? ? = 
 
1
2 13 PM 12
2
? ? = 
 
12
PM
13
= 
 Similarly, 
12
RN
13
= 
 Now, In right angle triangle ?PSM 
 
2
2 2 2
12 8
SM PS PM 4
13 13
??
= - = - =
??
??
 
 Similarly, 
8
QN
13
= 
 Now, MN = SQ – SM – QN 
 
8 8 26 16 10
2 13
13 13 13 13
-
= - - = = 
 
4. 3 
Sol. Thyroxin regulates carbohydrate, protein and fat metabolism in the body so as to provide the 
best balance for growth. 
 
6. 4 
Sol. Fertilisation takes place in fallopian tube.  
  
8. 2 
Sol. Hibiscus and mustard are bisexual flowers. 
 
9. 2 
Sol. 
 
A 
E 
D 
B 
F 
x 15 
9 15 
C 
O 
 
 
22
AB 15 9 12 cm BD AC CE = - = = = = 
 Let OF = x cm then 
2
DE 2 225 x =- 
 Using 
abc
R
4
=
?
 
 
( )
( )
2
2
24 24 2 225 x
15
1
4 15 x 2 225 x
2
? ? -
=
? ? + -
 
 
  
 
 
 x 4.2 cm ?= 
 
12. 1 
Sol.  
C 
B 
A 
X 
Z 
Y 
Q 
R 
P 
 
 By using Menalau’s theorem 
 CR : RQ : QX = BP : PR : RZ = AQ : QP : PY = 3 : 3 : 1 
 Now, AX : XB = 1 : 2 
 ? ? ? ? ?=
2
BXC ABC
3
 
 CR : RX = 3 : 4 
 ? ? ? ? ? ? ? = =
48
BRX BXC ABC
7 21
 
 Join P to X,  Since RP : PB = 1:1 
 ? ? ? ? ? ?
14
XPR BRX ABC
2 21
? = = 
 RQ : QX = 3 : 1 
 ? ? ? ? ? ?
31
PQR XPR ABC
47
? = = 
 ( )
2
13
ar PQR 14 14 7 3 cm
74
? = ? ? ? = 
 
15. 3 
Sol. Arteries always carry blood away from heart, while veins always carry blood towards the 
heart. 
 
16. 4 
Sol. 0.001 M NaOH ? [OH
–
] = 10
–3
 M 
 ? pOH = 3, so pH = 11 
 
17. 3 
Sol. Draw AQ ? ED 
 Then EQ = QD = 1 cm 
 Also, BP = PC = 1 cm 
 Join A to D and E 
 Now AP 3 cm, PQ 2cm == 
 
( )
AQ 3 2 cm ? = + 
 A 
E D 
C 
2 
2 
B 
1 1 
1 1 
P 
2 2 
Q 
 
 By Pythagoras theorem 
( )
2
AD AE 3 2 1 = = + + 
 Now, given circle is circumcircle of ?AED  
 
( ) ( ) ( )
( )
AE ED AD
Radius
4 ar AED
?=
?
 
 
( )
( )
( )
2
3 2 1 2
2 cm
1
4 2 3 2
2
??
++
??
??
==
? ? ? +
 
 
  
 
 
 Circumference = 4 ? cm 
 
19. 2 
Sol. Tall dwarf 
  TT    tt 
  ? 
  Tt   ?   Tt F1 generation  
        ?  
  
TT 
Tt 
Tt 
tt 
T t 
T 
t 
 
  
 Homozygous tall  – 1 
 Heterozygous tall  – 2 
 Homozygous dwarf  – 1 
 
20. 3 
Sol. One mole SO 2 means 64 g of it = 6.022 ? 10
23
 molecules. 
 
21. 4 
Sol. Growing two or more crops but indefinite row pattern is known as mixed cropping. 
 
23. 2 
Sol.  
A 
P 
B 
D C 
Q 
x 
6-x 
r 
O 
r 
6cm 6cm 
4cm 4cm 
 
 Let radius of circle = r cm 
 and OQ = x cm then OP = (6 – x) cm 
 By Pythagoras theorem, 
 r
2
 = x
2
 + 36 and r
2
 = 16 + (6 – x)
2
 
 on solving both equations we get, 
 
2
4 340
x and r
39
== 
 Distance of chord EF from centre = - =
45
3 cm
33
 
 So, length of chord EF  
 
2
2
5
2r
3
??
=-
??
??
 
 
340 25
2 2 35
99
= - = 
 140 K 140 = ? =

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