Page 1
WEST BENGAL NTSE STAGE 1 2020-21 _MAT
Direction : Read the following questions 1-15 carefully and give answer by filling the circle of the
letter denoting your select answer on the OMR answer Sheet :
1. If there is a common roots of the equation
2
0 x ax b + + = and
2
0 x bx a + + = then the value of ab + is
(A) 1 (B) –1 (C) 0 (D)
1
2
2. A principle becomes twice of its amount in 10 years at a certain rate of simple interest, At the same rate of
simple interest, that principle becomes thrice of its amount in
(A) 15 years (B) 20 years (B) 25 years (D) 30 years
3. The length of each of two parallel chords AB and CD is 12 cm , then the distance between two chords is
(A) 12 cm (B) 14 cm (D) 16 cm (D) 18 cm
4. The ratio of the volumes of two cubes is 1 : 27, the ration of total surface areas of wo cubes is
(A) 1 : 6 (B) 1 : 8 (C) 1 : 9 (D) 1 : 18
5. A box has 210 coins of denomination one – rupee and fifty paise only. The ratio of their respective values is
13 : 11. The number of one-rupee is
(A) 75 (B) 76 (C) 78 (D) 87
6. If the volume of two solid right circular cylinders are same and their height are in the ratio 1:3, then the ratio of
length of radii is
(A) 3 : 1 (B) 1: 3 (C) 1:3 (D) 3:1
7. The product of
( ) ( ) ( ) ( )
2 3 2 5 4 2 3 5 2 - + + - is
(A) 1 (B) 2 (C) 3 (D) 4
8. If
1 1 1
,, x y y z z x
z x y
- ? - ? - ? then sum of three variation constant is
(A) –1 (B) 0 (C) 1 (D) 1 ? .
9. Keeping the radius of a right circular cone. Same. If the height of its increased thrice, the volume of it will be
increased by
(A) 100 % (B) 200 % (C) 300 % (D) 400 %
10. In ABC ? and PQR ? , if 50 AQ ? = ? = ?, AB ; : QP AC QR = and 60 R ? = ? , then B ? is
(A) 50° (B) 60° (C) 70° (D) 80°
11. If the measure of two angles of a triangle are 65°20’3” and 54°37’57”, then the circular value of third angle is
(A)
c
? (B)
2
c
?
(C)
3
c
?
(D)
2
3
c
?
Page 2
WEST BENGAL NTSE STAGE 1 2020-21 _MAT
Direction : Read the following questions 1-15 carefully and give answer by filling the circle of the
letter denoting your select answer on the OMR answer Sheet :
1. If there is a common roots of the equation
2
0 x ax b + + = and
2
0 x bx a + + = then the value of ab + is
(A) 1 (B) –1 (C) 0 (D)
1
2
2. A principle becomes twice of its amount in 10 years at a certain rate of simple interest, At the same rate of
simple interest, that principle becomes thrice of its amount in
(A) 15 years (B) 20 years (B) 25 years (D) 30 years
3. The length of each of two parallel chords AB and CD is 12 cm , then the distance between two chords is
(A) 12 cm (B) 14 cm (D) 16 cm (D) 18 cm
4. The ratio of the volumes of two cubes is 1 : 27, the ration of total surface areas of wo cubes is
(A) 1 : 6 (B) 1 : 8 (C) 1 : 9 (D) 1 : 18
5. A box has 210 coins of denomination one – rupee and fifty paise only. The ratio of their respective values is
13 : 11. The number of one-rupee is
(A) 75 (B) 76 (C) 78 (D) 87
6. If the volume of two solid right circular cylinders are same and their height are in the ratio 1:3, then the ratio of
length of radii is
(A) 3 : 1 (B) 1: 3 (C) 1:3 (D) 3:1
7. The product of
( ) ( ) ( ) ( )
2 3 2 5 4 2 3 5 2 - + + - is
(A) 1 (B) 2 (C) 3 (D) 4
8. If
1 1 1
,, x y y z z x
z x y
- ? - ? - ? then sum of three variation constant is
(A) –1 (B) 0 (C) 1 (D) 1 ? .
9. Keeping the radius of a right circular cone. Same. If the height of its increased thrice, the volume of it will be
increased by
(A) 100 % (B) 200 % (C) 300 % (D) 400 %
10. In ABC ? and PQR ? , if 50 AQ ? = ? = ?, AB ; : QP AC QR = and 60 R ? = ? , then B ? is
(A) 50° (B) 60° (C) 70° (D) 80°
11. If the measure of two angles of a triangle are 65°20’3” and 54°37’57”, then the circular value of third angle is
(A)
c
? (B)
2
c
?
(C)
3
c
?
(D)
2
3
c
?
WEST BENGAL NTSE 2021
12. Three squares are based on the sides of a right triangle. The area of the two smaller ones are 225 sq. cm and
400 sq.cm. What is the area of the third one?
(A) 484 sq. cm (B) 259 sq.cm (C) 576 sq.cm (D) 625 sq. cm
13. If sin cos 0,0 90 ? - ? = ? ? ? ? ? and sec cosec x ? + ? = then x will be
(A) 1 (B) 2 (C) 22 (D) 2
14. If 32 is removed from the date 32, 25, 23, 21, 17, 15, 13, 12, 10 then median will be
(A) increased by 1. 5 (B) decreased by 1 (C) increase by 1 (D) Same
15. The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.7 m away from
the wall. The length of the ladder is
(A) 4.7 m (B) 9.4 m (C) 8.4 m (D) 9.7 m
Direction : In each question 16 to 25 there are two words separated by ‘:’ and other two separated from the
first two by the symbol ‘::’, find the relation between two sets of words and select one word from the right side
of ‘:’ which have the same relation as left set of word of ‘::’ . Fill the circle of the letter denoting yours selected
answer on the OMR answer sheet.
16. Lion : Roar :: Ass : ?
(A) Trumpet (B) Bray (C) Bark (D) Howl
17. Ocean ; Water :: Glacier : ?
(A) Mountain (B) Cave (C) Ice (D) Refrigerator
18. Arc : Circle :: Line segment : ?
(A) Sphere (B) Ellipse (C) Point (D) Square
19. Court : Justice :: School : ?
(A) Student (B) Teacher (C) Education (D) Building
20. Protein : Growth :: Carbohydrates : ?
(A) Immunity (B) Resistance (C) Diseases (D) Energy
21. USA : Congress :: Iran : ?
(A) Cortes (B) Althing (C) Majlis (D) Storting
22. Country : President :: State : ?
(A) Chief Minister (B) Minister of State (C) Speaker (D) Governor
23. AB : ZY :: CD : ?
A) UV (B) WX (C) VU (D) XW
24. 42 : 56 :: 110 : ?
(A) 148 (B) 132 (C) 132 (D) 124
Page 3
WEST BENGAL NTSE STAGE 1 2020-21 _MAT
Direction : Read the following questions 1-15 carefully and give answer by filling the circle of the
letter denoting your select answer on the OMR answer Sheet :
1. If there is a common roots of the equation
2
0 x ax b + + = and
2
0 x bx a + + = then the value of ab + is
(A) 1 (B) –1 (C) 0 (D)
1
2
2. A principle becomes twice of its amount in 10 years at a certain rate of simple interest, At the same rate of
simple interest, that principle becomes thrice of its amount in
(A) 15 years (B) 20 years (B) 25 years (D) 30 years
3. The length of each of two parallel chords AB and CD is 12 cm , then the distance between two chords is
(A) 12 cm (B) 14 cm (D) 16 cm (D) 18 cm
4. The ratio of the volumes of two cubes is 1 : 27, the ration of total surface areas of wo cubes is
(A) 1 : 6 (B) 1 : 8 (C) 1 : 9 (D) 1 : 18
5. A box has 210 coins of denomination one – rupee and fifty paise only. The ratio of their respective values is
13 : 11. The number of one-rupee is
(A) 75 (B) 76 (C) 78 (D) 87
6. If the volume of two solid right circular cylinders are same and their height are in the ratio 1:3, then the ratio of
length of radii is
(A) 3 : 1 (B) 1: 3 (C) 1:3 (D) 3:1
7. The product of
( ) ( ) ( ) ( )
2 3 2 5 4 2 3 5 2 - + + - is
(A) 1 (B) 2 (C) 3 (D) 4
8. If
1 1 1
,, x y y z z x
z x y
- ? - ? - ? then sum of three variation constant is
(A) –1 (B) 0 (C) 1 (D) 1 ? .
9. Keeping the radius of a right circular cone. Same. If the height of its increased thrice, the volume of it will be
increased by
(A) 100 % (B) 200 % (C) 300 % (D) 400 %
10. In ABC ? and PQR ? , if 50 AQ ? = ? = ?, AB ; : QP AC QR = and 60 R ? = ? , then B ? is
(A) 50° (B) 60° (C) 70° (D) 80°
11. If the measure of two angles of a triangle are 65°20’3” and 54°37’57”, then the circular value of third angle is
(A)
c
? (B)
2
c
?
(C)
3
c
?
(D)
2
3
c
?
WEST BENGAL NTSE 2021
12. Three squares are based on the sides of a right triangle. The area of the two smaller ones are 225 sq. cm and
400 sq.cm. What is the area of the third one?
(A) 484 sq. cm (B) 259 sq.cm (C) 576 sq.cm (D) 625 sq. cm
13. If sin cos 0,0 90 ? - ? = ? ? ? ? ? and sec cosec x ? + ? = then x will be
(A) 1 (B) 2 (C) 22 (D) 2
14. If 32 is removed from the date 32, 25, 23, 21, 17, 15, 13, 12, 10 then median will be
(A) increased by 1. 5 (B) decreased by 1 (C) increase by 1 (D) Same
15. The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.7 m away from
the wall. The length of the ladder is
(A) 4.7 m (B) 9.4 m (C) 8.4 m (D) 9.7 m
Direction : In each question 16 to 25 there are two words separated by ‘:’ and other two separated from the
first two by the symbol ‘::’, find the relation between two sets of words and select one word from the right side
of ‘:’ which have the same relation as left set of word of ‘::’ . Fill the circle of the letter denoting yours selected
answer on the OMR answer sheet.
16. Lion : Roar :: Ass : ?
(A) Trumpet (B) Bray (C) Bark (D) Howl
17. Ocean ; Water :: Glacier : ?
(A) Mountain (B) Cave (C) Ice (D) Refrigerator
18. Arc : Circle :: Line segment : ?
(A) Sphere (B) Ellipse (C) Point (D) Square
19. Court : Justice :: School : ?
(A) Student (B) Teacher (C) Education (D) Building
20. Protein : Growth :: Carbohydrates : ?
(A) Immunity (B) Resistance (C) Diseases (D) Energy
21. USA : Congress :: Iran : ?
(A) Cortes (B) Althing (C) Majlis (D) Storting
22. Country : President :: State : ?
(A) Chief Minister (B) Minister of State (C) Speaker (D) Governor
23. AB : ZY :: CD : ?
A) UV (B) WX (C) VU (D) XW
24. 42 : 56 :: 110 : ?
(A) 148 (B) 132 (C) 132 (D) 124
WEST BENGAL NTSE 2021
25. 64 : 144 :: 256 : ?
(A) 484 (B) 412 (C) 625 (D) 402
Direction 26-55: In question 26-55, numbers are placed in figure on the basis of some rules. One place in
figure is indicated by the interrogation sign(?). Find out the correct alternative to replace the question mark
and indicate your answer by filling the circle of the corresponding letter of alternatives in the OMR Sheet .
26.
(A) 22 (B) 32 (C) 30 (D) 23
27.
(A) 120 (B) 0130 (C) 140 (D) 150
28.
(A) 20 (B) 18 (C) 16 (D) 14
29.
(A) 9 (B) 8 (C) 1 (D) 7
30.
(A) 51 (B) 61 (C) 63 (D) 54
Page 4
WEST BENGAL NTSE STAGE 1 2020-21 _MAT
Direction : Read the following questions 1-15 carefully and give answer by filling the circle of the
letter denoting your select answer on the OMR answer Sheet :
1. If there is a common roots of the equation
2
0 x ax b + + = and
2
0 x bx a + + = then the value of ab + is
(A) 1 (B) –1 (C) 0 (D)
1
2
2. A principle becomes twice of its amount in 10 years at a certain rate of simple interest, At the same rate of
simple interest, that principle becomes thrice of its amount in
(A) 15 years (B) 20 years (B) 25 years (D) 30 years
3. The length of each of two parallel chords AB and CD is 12 cm , then the distance between two chords is
(A) 12 cm (B) 14 cm (D) 16 cm (D) 18 cm
4. The ratio of the volumes of two cubes is 1 : 27, the ration of total surface areas of wo cubes is
(A) 1 : 6 (B) 1 : 8 (C) 1 : 9 (D) 1 : 18
5. A box has 210 coins of denomination one – rupee and fifty paise only. The ratio of their respective values is
13 : 11. The number of one-rupee is
(A) 75 (B) 76 (C) 78 (D) 87
6. If the volume of two solid right circular cylinders are same and their height are in the ratio 1:3, then the ratio of
length of radii is
(A) 3 : 1 (B) 1: 3 (C) 1:3 (D) 3:1
7. The product of
( ) ( ) ( ) ( )
2 3 2 5 4 2 3 5 2 - + + - is
(A) 1 (B) 2 (C) 3 (D) 4
8. If
1 1 1
,, x y y z z x
z x y
- ? - ? - ? then sum of three variation constant is
(A) –1 (B) 0 (C) 1 (D) 1 ? .
9. Keeping the radius of a right circular cone. Same. If the height of its increased thrice, the volume of it will be
increased by
(A) 100 % (B) 200 % (C) 300 % (D) 400 %
10. In ABC ? and PQR ? , if 50 AQ ? = ? = ?, AB ; : QP AC QR = and 60 R ? = ? , then B ? is
(A) 50° (B) 60° (C) 70° (D) 80°
11. If the measure of two angles of a triangle are 65°20’3” and 54°37’57”, then the circular value of third angle is
(A)
c
? (B)
2
c
?
(C)
3
c
?
(D)
2
3
c
?
WEST BENGAL NTSE 2021
12. Three squares are based on the sides of a right triangle. The area of the two smaller ones are 225 sq. cm and
400 sq.cm. What is the area of the third one?
(A) 484 sq. cm (B) 259 sq.cm (C) 576 sq.cm (D) 625 sq. cm
13. If sin cos 0,0 90 ? - ? = ? ? ? ? ? and sec cosec x ? + ? = then x will be
(A) 1 (B) 2 (C) 22 (D) 2
14. If 32 is removed from the date 32, 25, 23, 21, 17, 15, 13, 12, 10 then median will be
(A) increased by 1. 5 (B) decreased by 1 (C) increase by 1 (D) Same
15. The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.7 m away from
the wall. The length of the ladder is
(A) 4.7 m (B) 9.4 m (C) 8.4 m (D) 9.7 m
Direction : In each question 16 to 25 there are two words separated by ‘:’ and other two separated from the
first two by the symbol ‘::’, find the relation between two sets of words and select one word from the right side
of ‘:’ which have the same relation as left set of word of ‘::’ . Fill the circle of the letter denoting yours selected
answer on the OMR answer sheet.
16. Lion : Roar :: Ass : ?
(A) Trumpet (B) Bray (C) Bark (D) Howl
17. Ocean ; Water :: Glacier : ?
(A) Mountain (B) Cave (C) Ice (D) Refrigerator
18. Arc : Circle :: Line segment : ?
(A) Sphere (B) Ellipse (C) Point (D) Square
19. Court : Justice :: School : ?
(A) Student (B) Teacher (C) Education (D) Building
20. Protein : Growth :: Carbohydrates : ?
(A) Immunity (B) Resistance (C) Diseases (D) Energy
21. USA : Congress :: Iran : ?
(A) Cortes (B) Althing (C) Majlis (D) Storting
22. Country : President :: State : ?
(A) Chief Minister (B) Minister of State (C) Speaker (D) Governor
23. AB : ZY :: CD : ?
A) UV (B) WX (C) VU (D) XW
24. 42 : 56 :: 110 : ?
(A) 148 (B) 132 (C) 132 (D) 124
WEST BENGAL NTSE 2021
25. 64 : 144 :: 256 : ?
(A) 484 (B) 412 (C) 625 (D) 402
Direction 26-55: In question 26-55, numbers are placed in figure on the basis of some rules. One place in
figure is indicated by the interrogation sign(?). Find out the correct alternative to replace the question mark
and indicate your answer by filling the circle of the corresponding letter of alternatives in the OMR Sheet .
26.
(A) 22 (B) 32 (C) 30 (D) 23
27.
(A) 120 (B) 0130 (C) 140 (D) 150
28.
(A) 20 (B) 18 (C) 16 (D) 14
29.
(A) 9 (B) 8 (C) 1 (D) 7
30.
(A) 51 (B) 61 (C) 63 (D) 54
WEST BENGAL NTSE 2021
31.
(A) 77 (B) 78 (D) 86 (D) 88
32.
(A) 185 (B) 165 (C) 175 (D) 195
33.
(A) 46 (B) 42 (C) 43 (D) 44
34.
(A) 78 (B) 80 (C) 84 (D) 82
35.
(A) J (B) K (C) S (D) P
36.
(A) 146 (B) 126 (C) 175 (D) 185
Page 5
WEST BENGAL NTSE STAGE 1 2020-21 _MAT
Direction : Read the following questions 1-15 carefully and give answer by filling the circle of the
letter denoting your select answer on the OMR answer Sheet :
1. If there is a common roots of the equation
2
0 x ax b + + = and
2
0 x bx a + + = then the value of ab + is
(A) 1 (B) –1 (C) 0 (D)
1
2
2. A principle becomes twice of its amount in 10 years at a certain rate of simple interest, At the same rate of
simple interest, that principle becomes thrice of its amount in
(A) 15 years (B) 20 years (B) 25 years (D) 30 years
3. The length of each of two parallel chords AB and CD is 12 cm , then the distance between two chords is
(A) 12 cm (B) 14 cm (D) 16 cm (D) 18 cm
4. The ratio of the volumes of two cubes is 1 : 27, the ration of total surface areas of wo cubes is
(A) 1 : 6 (B) 1 : 8 (C) 1 : 9 (D) 1 : 18
5. A box has 210 coins of denomination one – rupee and fifty paise only. The ratio of their respective values is
13 : 11. The number of one-rupee is
(A) 75 (B) 76 (C) 78 (D) 87
6. If the volume of two solid right circular cylinders are same and their height are in the ratio 1:3, then the ratio of
length of radii is
(A) 3 : 1 (B) 1: 3 (C) 1:3 (D) 3:1
7. The product of
( ) ( ) ( ) ( )
2 3 2 5 4 2 3 5 2 - + + - is
(A) 1 (B) 2 (C) 3 (D) 4
8. If
1 1 1
,, x y y z z x
z x y
- ? - ? - ? then sum of three variation constant is
(A) –1 (B) 0 (C) 1 (D) 1 ? .
9. Keeping the radius of a right circular cone. Same. If the height of its increased thrice, the volume of it will be
increased by
(A) 100 % (B) 200 % (C) 300 % (D) 400 %
10. In ABC ? and PQR ? , if 50 AQ ? = ? = ?, AB ; : QP AC QR = and 60 R ? = ? , then B ? is
(A) 50° (B) 60° (C) 70° (D) 80°
11. If the measure of two angles of a triangle are 65°20’3” and 54°37’57”, then the circular value of third angle is
(A)
c
? (B)
2
c
?
(C)
3
c
?
(D)
2
3
c
?
WEST BENGAL NTSE 2021
12. Three squares are based on the sides of a right triangle. The area of the two smaller ones are 225 sq. cm and
400 sq.cm. What is the area of the third one?
(A) 484 sq. cm (B) 259 sq.cm (C) 576 sq.cm (D) 625 sq. cm
13. If sin cos 0,0 90 ? - ? = ? ? ? ? ? and sec cosec x ? + ? = then x will be
(A) 1 (B) 2 (C) 22 (D) 2
14. If 32 is removed from the date 32, 25, 23, 21, 17, 15, 13, 12, 10 then median will be
(A) increased by 1. 5 (B) decreased by 1 (C) increase by 1 (D) Same
15. The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.7 m away from
the wall. The length of the ladder is
(A) 4.7 m (B) 9.4 m (C) 8.4 m (D) 9.7 m
Direction : In each question 16 to 25 there are two words separated by ‘:’ and other two separated from the
first two by the symbol ‘::’, find the relation between two sets of words and select one word from the right side
of ‘:’ which have the same relation as left set of word of ‘::’ . Fill the circle of the letter denoting yours selected
answer on the OMR answer sheet.
16. Lion : Roar :: Ass : ?
(A) Trumpet (B) Bray (C) Bark (D) Howl
17. Ocean ; Water :: Glacier : ?
(A) Mountain (B) Cave (C) Ice (D) Refrigerator
18. Arc : Circle :: Line segment : ?
(A) Sphere (B) Ellipse (C) Point (D) Square
19. Court : Justice :: School : ?
(A) Student (B) Teacher (C) Education (D) Building
20. Protein : Growth :: Carbohydrates : ?
(A) Immunity (B) Resistance (C) Diseases (D) Energy
21. USA : Congress :: Iran : ?
(A) Cortes (B) Althing (C) Majlis (D) Storting
22. Country : President :: State : ?
(A) Chief Minister (B) Minister of State (C) Speaker (D) Governor
23. AB : ZY :: CD : ?
A) UV (B) WX (C) VU (D) XW
24. 42 : 56 :: 110 : ?
(A) 148 (B) 132 (C) 132 (D) 124
WEST BENGAL NTSE 2021
25. 64 : 144 :: 256 : ?
(A) 484 (B) 412 (C) 625 (D) 402
Direction 26-55: In question 26-55, numbers are placed in figure on the basis of some rules. One place in
figure is indicated by the interrogation sign(?). Find out the correct alternative to replace the question mark
and indicate your answer by filling the circle of the corresponding letter of alternatives in the OMR Sheet .
26.
(A) 22 (B) 32 (C) 30 (D) 23
27.
(A) 120 (B) 0130 (C) 140 (D) 150
28.
(A) 20 (B) 18 (C) 16 (D) 14
29.
(A) 9 (B) 8 (C) 1 (D) 7
30.
(A) 51 (B) 61 (C) 63 (D) 54
WEST BENGAL NTSE 2021
31.
(A) 77 (B) 78 (D) 86 (D) 88
32.
(A) 185 (B) 165 (C) 175 (D) 195
33.
(A) 46 (B) 42 (C) 43 (D) 44
34.
(A) 78 (B) 80 (C) 84 (D) 82
35.
(A) J (B) K (C) S (D) P
36.
(A) 146 (B) 126 (C) 175 (D) 185
WEST BENGAL NTSE 2021
37.
(A) 18 (B) 33 (C) 135 (D) 145
38.
(A) 117 (B) 115 (C) 127 (D) 112
39.
(A) 13 (B) 16 (C) 15 (D) 17
40.
(A) 2 (B) 3 (C) 4 (D) 5
41.
(A) 1 (B) 731 (C) 1625 (D) 2031
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