West Bengal: State Level Question Paper (SAT) - 2020-21 | NTSE for Class 10 PDF Download

 Page 1


   
 
 
 
NTSE-WEST BENGAL-SAT 
 
Mathematics 
 
 
1. If the algebraic expression 
? ?
2
33 ?? x px be always positive, then 
 (a) –6  < p < 6   (b) p < – 6   (c) p > 6   (d) no such p exists 
 
2. The sum of the roots of ? ?
2
00 ? ? ? ? ax bx c a is equal to the sum of the squares of the roots of the 
equation. Then 
 (a)  2 ?? ab ac be (b)  
2
2 ?? b ab ae (c)  
2
2 ?? ac ab b (d)  
2
2 ?? ab ac b 
 
3. The solution set for the equation 
? ?
22
22 22
3 2.3 3 0
? ??
? ? ?
x x x x
 is 
 (a) {–1, 2}   (b) { 0, 2}   (c) {0, –1}   (d) {2, 4} 
 
4. It is printed on a paper that "The length of a diagonal of a rectangle is 10 cm and its area is 62.5 sq. 
cm". Then which one of the following statements is true? 
 (a) The perimeter of the rectangle is 30 cm.  
(b) The sum of the length and breadth is 20 cm.  
(c) The difference of the length and breadth is 5 cm.  
(d) No such rectangle can exist. 
 
5. The ratio of the lengths of the corresponding sides of two similar triangles are in the ratio of 4 : 9. 
Then the ratio of their areas is 
 (a) 16 : 81   (b) 81 : 16   (c) 4 : 9   (d) 9 : 4 
 
6. Father says to his son: "On the date of birth of yours, I was twice older than you are now." Then 
which one of the following statements is true? 
(a) The present ages of the father and his son are 30 years and 10 years respectively. 
(b) The present ages of the father and his son are 48 years and 12 years respectively. 
(c) Nothing can be said about their ages. 
(d) The ratio of the present ages of the father to the son is 3 : 1. 
 
7. Taking at least one from the numbers 1,2,3, how many different sets can be formed? 
 (a)  8   (b)  7   (c)  3   (d)  
3
3 
 
8. ? ?
23
18 is divided by remainder 17 to give the remainder 
 (a) 11    (b) 9    (c) 5    (d) 1 
 
9. If 
2
4 1 0 ? ? ? mm , then the value of 
3
3
1 ??
?
??
??
m
m
 is 
 (a) 52    (b) 48    (c) 64    (d) 68 
 
10. For 3 81, 81 3
??
??
x y x y
, we get  
 (a)  no solution (b)  
21 21
, 
22
?? xy (c) 
2
2, 
3
?? xy  (d)  
17 15
, 
88
?? xy 
Page 2


   
 
 
 
NTSE-WEST BENGAL-SAT 
 
Mathematics 
 
 
1. If the algebraic expression 
? ?
2
33 ?? x px be always positive, then 
 (a) –6  < p < 6   (b) p < – 6   (c) p > 6   (d) no such p exists 
 
2. The sum of the roots of ? ?
2
00 ? ? ? ? ax bx c a is equal to the sum of the squares of the roots of the 
equation. Then 
 (a)  2 ?? ab ac be (b)  
2
2 ?? b ab ae (c)  
2
2 ?? ac ab b (d)  
2
2 ?? ab ac b 
 
3. The solution set for the equation 
? ?
22
22 22
3 2.3 3 0
? ??
? ? ?
x x x x
 is 
 (a) {–1, 2}   (b) { 0, 2}   (c) {0, –1}   (d) {2, 4} 
 
4. It is printed on a paper that "The length of a diagonal of a rectangle is 10 cm and its area is 62.5 sq. 
cm". Then which one of the following statements is true? 
 (a) The perimeter of the rectangle is 30 cm.  
(b) The sum of the length and breadth is 20 cm.  
(c) The difference of the length and breadth is 5 cm.  
(d) No such rectangle can exist. 
 
5. The ratio of the lengths of the corresponding sides of two similar triangles are in the ratio of 4 : 9. 
Then the ratio of their areas is 
 (a) 16 : 81   (b) 81 : 16   (c) 4 : 9   (d) 9 : 4 
 
6. Father says to his son: "On the date of birth of yours, I was twice older than you are now." Then 
which one of the following statements is true? 
(a) The present ages of the father and his son are 30 years and 10 years respectively. 
(b) The present ages of the father and his son are 48 years and 12 years respectively. 
(c) Nothing can be said about their ages. 
(d) The ratio of the present ages of the father to the son is 3 : 1. 
 
7. Taking at least one from the numbers 1,2,3, how many different sets can be formed? 
 (a)  8   (b)  7   (c)  3   (d)  
3
3 
 
8. ? ?
23
18 is divided by remainder 17 to give the remainder 
 (a) 11    (b) 9    (c) 5    (d) 1 
 
9. If 
2
4 1 0 ? ? ? mm , then the value of 
3
3
1 ??
?
??
??
m
m
 is 
 (a) 52    (b) 48    (c) 64    (d) 68 
 
10. For 3 81, 81 3
??
??
x y x y
, we get  
 (a)  no solution (b)  
21 21
, 
22
?? xy (c) 
2
2, 
3
?? xy  (d)  
17 15
, 
88
?? xy 
   
 
 
 
 
11. 125 identical cubes are cut from a big cube and all the smaller cubes are arranged in a row to form a 
long cuboid. What is the percentage of increase in total surface area of the cuboid over the total 
surface area of the cube?   
 (a)  
2
234 %
3
  (b)  
1
234 %
3
  (c)  
2
134 %
3
  (d)  None of the above 
 
12. A bag contains 4 Red and 3 Black balls and a second bag contains 2 Red and 4 Black balls. After 
choosing a bag at random, a ball is also drawn at random. The probability that the ball is Red is 
(a)  
23
42
   (b)  
17
42
   (c)  
19
42
   (d)  
16
39
 
 
13. If [n] denotes the greatest integer  n and (n) denotes the smallest integer  n ; n being a real number, 
then ? ?
1 1 1 1
1 1 2 1 1.5
5 5 5 5
? ? ? ? ? ? ? ?
? ? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ? ? ? ? ?
 is 
 (a) 1.5    (b) 2    (c) 2.5    (d) 3.5 
 
14. The value of 
2 2 2 2 2 2
3 5 19
.......
1 .2 2 .3 9 .10
? ? ? is 
 (a)  
99
100
  (b)  
1
100
  (c)  
101
100
  (d)  1 
 
15. In a frequency distribution, Mean = 9.1 and 132 5 , 20 ? ? ?
?? i i i
f x k f , then k is 
 (a) 4    (b) 6    (c) 10    (d) 9 
 
16. ABC is a triangle in which ABC > 90° and AD  CB produced. Then 
 
A
B
C D
 
  
 (a)  
2 2 2
? ? ? ? AB AC BC BC BD   (b)  
2 2 2
2 ? ? ? ? AB AC BC BC BD 
 (c)  
2 2 2
2 ? ? ? ? Ac AB BC BC BD  (d)  
2 2 2
? ? ? ? AC AB BC BC BD  
 
17. Given : 0° <  < 90°. then, if sin + cos = x, which one of the following is correct? 
 (a)  1 ? x  (b)  1.5 ? x  (c)  12 ?? x  (d)  12 ?? x 
 
18. If sin cos 2 ?? ?? and 0 , 90 , ?? ??
oo
 then 2 2000 . ?? ?? 
 (a) 180°   (b) 90°   (c) 2180°   (d) Can not be found out 
 
19. sec tan , ? ? ? ? ?? a b a b Q and ? bQ and sec ? is rational, then 
 (a)  
2
1 ?? ba  (b)  
2
1 ?? ab  (c)  
2
1 ?? ba  (d)  
2
1 ?? ab 
 
20. The ratio of in which 9x – 3y – 14 = 0 divides the join of (2, – 4) and (3, 7) is 
 (a) 2 : 1   (b) 1 : 2   (c) 2 : 3   (d) 3 : 2 
 
Page 3


   
 
 
 
NTSE-WEST BENGAL-SAT 
 
Mathematics 
 
 
1. If the algebraic expression 
? ?
2
33 ?? x px be always positive, then 
 (a) –6  < p < 6   (b) p < – 6   (c) p > 6   (d) no such p exists 
 
2. The sum of the roots of ? ?
2
00 ? ? ? ? ax bx c a is equal to the sum of the squares of the roots of the 
equation. Then 
 (a)  2 ?? ab ac be (b)  
2
2 ?? b ab ae (c)  
2
2 ?? ac ab b (d)  
2
2 ?? ab ac b 
 
3. The solution set for the equation 
? ?
22
22 22
3 2.3 3 0
? ??
? ? ?
x x x x
 is 
 (a) {–1, 2}   (b) { 0, 2}   (c) {0, –1}   (d) {2, 4} 
 
4. It is printed on a paper that "The length of a diagonal of a rectangle is 10 cm and its area is 62.5 sq. 
cm". Then which one of the following statements is true? 
 (a) The perimeter of the rectangle is 30 cm.  
(b) The sum of the length and breadth is 20 cm.  
(c) The difference of the length and breadth is 5 cm.  
(d) No such rectangle can exist. 
 
5. The ratio of the lengths of the corresponding sides of two similar triangles are in the ratio of 4 : 9. 
Then the ratio of their areas is 
 (a) 16 : 81   (b) 81 : 16   (c) 4 : 9   (d) 9 : 4 
 
6. Father says to his son: "On the date of birth of yours, I was twice older than you are now." Then 
which one of the following statements is true? 
(a) The present ages of the father and his son are 30 years and 10 years respectively. 
(b) The present ages of the father and his son are 48 years and 12 years respectively. 
(c) Nothing can be said about their ages. 
(d) The ratio of the present ages of the father to the son is 3 : 1. 
 
7. Taking at least one from the numbers 1,2,3, how many different sets can be formed? 
 (a)  8   (b)  7   (c)  3   (d)  
3
3 
 
8. ? ?
23
18 is divided by remainder 17 to give the remainder 
 (a) 11    (b) 9    (c) 5    (d) 1 
 
9. If 
2
4 1 0 ? ? ? mm , then the value of 
3
3
1 ??
?
??
??
m
m
 is 
 (a) 52    (b) 48    (c) 64    (d) 68 
 
10. For 3 81, 81 3
??
??
x y x y
, we get  
 (a)  no solution (b)  
21 21
, 
22
?? xy (c) 
2
2, 
3
?? xy  (d)  
17 15
, 
88
?? xy 
   
 
 
 
 
11. 125 identical cubes are cut from a big cube and all the smaller cubes are arranged in a row to form a 
long cuboid. What is the percentage of increase in total surface area of the cuboid over the total 
surface area of the cube?   
 (a)  
2
234 %
3
  (b)  
1
234 %
3
  (c)  
2
134 %
3
  (d)  None of the above 
 
12. A bag contains 4 Red and 3 Black balls and a second bag contains 2 Red and 4 Black balls. After 
choosing a bag at random, a ball is also drawn at random. The probability that the ball is Red is 
(a)  
23
42
   (b)  
17
42
   (c)  
19
42
   (d)  
16
39
 
 
13. If [n] denotes the greatest integer  n and (n) denotes the smallest integer  n ; n being a real number, 
then ? ?
1 1 1 1
1 1 2 1 1.5
5 5 5 5
? ? ? ? ? ? ? ?
? ? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ? ? ? ? ?
 is 
 (a) 1.5    (b) 2    (c) 2.5    (d) 3.5 
 
14. The value of 
2 2 2 2 2 2
3 5 19
.......
1 .2 2 .3 9 .10
? ? ? is 
 (a)  
99
100
  (b)  
1
100
  (c)  
101
100
  (d)  1 
 
15. In a frequency distribution, Mean = 9.1 and 132 5 , 20 ? ? ?
?? i i i
f x k f , then k is 
 (a) 4    (b) 6    (c) 10    (d) 9 
 
16. ABC is a triangle in which ABC > 90° and AD  CB produced. Then 
 
A
B
C D
 
  
 (a)  
2 2 2
? ? ? ? AB AC BC BC BD   (b)  
2 2 2
2 ? ? ? ? AB AC BC BC BD 
 (c)  
2 2 2
2 ? ? ? ? Ac AB BC BC BD  (d)  
2 2 2
? ? ? ? AC AB BC BC BD  
 
17. Given : 0° <  < 90°. then, if sin + cos = x, which one of the following is correct? 
 (a)  1 ? x  (b)  1.5 ? x  (c)  12 ?? x  (d)  12 ?? x 
 
18. If sin cos 2 ?? ?? and 0 , 90 , ?? ??
oo
 then 2 2000 . ?? ?? 
 (a) 180°   (b) 90°   (c) 2180°   (d) Can not be found out 
 
19. sec tan , ? ? ? ? ?? a b a b Q and ? bQ and sec ? is rational, then 
 (a)  
2
1 ?? ba  (b)  
2
1 ?? ab  (c)  
2
1 ?? ba  (d)  
2
1 ?? ab 
 
20. The ratio of in which 9x – 3y – 14 = 0 divides the join of (2, – 4) and (3, 7) is 
 (a) 2 : 1   (b) 1 : 2   (c) 2 : 3   (d) 3 : 2 
 
   
 
 
 
Physics 
21. The mass, linear momentum and kinetic energy of a body are m, p and E respectively, then  
 (a) p 2mE ?  (b) E 2mp ?  (c) p 2E ?  (d) E 2p ?
 
 
22. A stone is allowed to fall freely downwards initially at rest from the top of a tower. The time taken by the 
stone to reach the bottom of the tower is 4 seconds. What is the height of the tower? Take, acceleration due 
to gravity = 32 ft/s
2
 
(a) 64 ft.   (b) 32 ft.   (c) 48 ft.   (d) 256 ft. 
 
23. The coefficient of linear expansion of a solid is x and the coefficient of volume expansion of the solid is y, then 
(a) 
y
x
3
? 
(b) 
x
y
3
? 
(c) 
y
x
2
? 
(d) 
x
y
2
? 
 
24. In case of refraction of light from a medium to air the critical angle is found to be 45°. What is the refractive 
index of the medium with respect to air? . 
 (a) 2   (b) 3   (c) 2   (d) 3 
 
25. Which of the following pair have same unit? 
 (a) Heat and Specific heat 
(b) Thermal capacity and Water equivalent  
(c) Specific heat and Thermal capacity 
(d) Heat and Work 
 
26. Which of the following   is an electromagnetic wave? 
 (a) a-ray   (b) ß-ray   (c) ?-ray   (d) cathode ray 
 
27. In case of a convex lens, what is the minimum distance between an object and its real image? 
 (a) 2.5 times of focal length    (b) 2 times of focal length  
(c) 4 times of focal length    (d) equal to focal length 
 
28. What will be the power consumed by a 50 ? wire if it is kept across a potential difference of 200V? 
 (a) 0.8 kW   (b) 80 kW   (c) 400 W   (d) 8 Kw 
 
29. I cm ot main scale of a vernier callipers is divided into 10 divisions. The least count  of  the callipers is 0.005 
cm, then what is the number of divisions in the vernier scale? 
 (a) 10    (b) 20    (c) 25    (d) 50 
 
30. If an x-ray tube is operated at 20kV, what is the cut-off wave length? (Take, planks constant  
 
34
h 6.62 10
?
?? J.S) 
 (a) 0.89 Å   (b) 0.75 Å   (c) 0.62 Å   (d) 0.31 Å 
 
 
Page 4


   
 
 
 
NTSE-WEST BENGAL-SAT 
 
Mathematics 
 
 
1. If the algebraic expression 
? ?
2
33 ?? x px be always positive, then 
 (a) –6  < p < 6   (b) p < – 6   (c) p > 6   (d) no such p exists 
 
2. The sum of the roots of ? ?
2
00 ? ? ? ? ax bx c a is equal to the sum of the squares of the roots of the 
equation. Then 
 (a)  2 ?? ab ac be (b)  
2
2 ?? b ab ae (c)  
2
2 ?? ac ab b (d)  
2
2 ?? ab ac b 
 
3. The solution set for the equation 
? ?
22
22 22
3 2.3 3 0
? ??
? ? ?
x x x x
 is 
 (a) {–1, 2}   (b) { 0, 2}   (c) {0, –1}   (d) {2, 4} 
 
4. It is printed on a paper that "The length of a diagonal of a rectangle is 10 cm and its area is 62.5 sq. 
cm". Then which one of the following statements is true? 
 (a) The perimeter of the rectangle is 30 cm.  
(b) The sum of the length and breadth is 20 cm.  
(c) The difference of the length and breadth is 5 cm.  
(d) No such rectangle can exist. 
 
5. The ratio of the lengths of the corresponding sides of two similar triangles are in the ratio of 4 : 9. 
Then the ratio of their areas is 
 (a) 16 : 81   (b) 81 : 16   (c) 4 : 9   (d) 9 : 4 
 
6. Father says to his son: "On the date of birth of yours, I was twice older than you are now." Then 
which one of the following statements is true? 
(a) The present ages of the father and his son are 30 years and 10 years respectively. 
(b) The present ages of the father and his son are 48 years and 12 years respectively. 
(c) Nothing can be said about their ages. 
(d) The ratio of the present ages of the father to the son is 3 : 1. 
 
7. Taking at least one from the numbers 1,2,3, how many different sets can be formed? 
 (a)  8   (b)  7   (c)  3   (d)  
3
3 
 
8. ? ?
23
18 is divided by remainder 17 to give the remainder 
 (a) 11    (b) 9    (c) 5    (d) 1 
 
9. If 
2
4 1 0 ? ? ? mm , then the value of 
3
3
1 ??
?
??
??
m
m
 is 
 (a) 52    (b) 48    (c) 64    (d) 68 
 
10. For 3 81, 81 3
??
??
x y x y
, we get  
 (a)  no solution (b)  
21 21
, 
22
?? xy (c) 
2
2, 
3
?? xy  (d)  
17 15
, 
88
?? xy 
   
 
 
 
 
11. 125 identical cubes are cut from a big cube and all the smaller cubes are arranged in a row to form a 
long cuboid. What is the percentage of increase in total surface area of the cuboid over the total 
surface area of the cube?   
 (a)  
2
234 %
3
  (b)  
1
234 %
3
  (c)  
2
134 %
3
  (d)  None of the above 
 
12. A bag contains 4 Red and 3 Black balls and a second bag contains 2 Red and 4 Black balls. After 
choosing a bag at random, a ball is also drawn at random. The probability that the ball is Red is 
(a)  
23
42
   (b)  
17
42
   (c)  
19
42
   (d)  
16
39
 
 
13. If [n] denotes the greatest integer  n and (n) denotes the smallest integer  n ; n being a real number, 
then ? ?
1 1 1 1
1 1 2 1 1.5
5 5 5 5
? ? ? ? ? ? ? ?
? ? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ? ? ? ? ?
 is 
 (a) 1.5    (b) 2    (c) 2.5    (d) 3.5 
 
14. The value of 
2 2 2 2 2 2
3 5 19
.......
1 .2 2 .3 9 .10
? ? ? is 
 (a)  
99
100
  (b)  
1
100
  (c)  
101
100
  (d)  1 
 
15. In a frequency distribution, Mean = 9.1 and 132 5 , 20 ? ? ?
?? i i i
f x k f , then k is 
 (a) 4    (b) 6    (c) 10    (d) 9 
 
16. ABC is a triangle in which ABC > 90° and AD  CB produced. Then 
 
A
B
C D
 
  
 (a)  
2 2 2
? ? ? ? AB AC BC BC BD   (b)  
2 2 2
2 ? ? ? ? AB AC BC BC BD 
 (c)  
2 2 2
2 ? ? ? ? Ac AB BC BC BD  (d)  
2 2 2
? ? ? ? AC AB BC BC BD  
 
17. Given : 0° <  < 90°. then, if sin + cos = x, which one of the following is correct? 
 (a)  1 ? x  (b)  1.5 ? x  (c)  12 ?? x  (d)  12 ?? x 
 
18. If sin cos 2 ?? ?? and 0 , 90 , ?? ??
oo
 then 2 2000 . ?? ?? 
 (a) 180°   (b) 90°   (c) 2180°   (d) Can not be found out 
 
19. sec tan , ? ? ? ? ?? a b a b Q and ? bQ and sec ? is rational, then 
 (a)  
2
1 ?? ba  (b)  
2
1 ?? ab  (c)  
2
1 ?? ba  (d)  
2
1 ?? ab 
 
20. The ratio of in which 9x – 3y – 14 = 0 divides the join of (2, – 4) and (3, 7) is 
 (a) 2 : 1   (b) 1 : 2   (c) 2 : 3   (d) 3 : 2 
 
   
 
 
 
Physics 
21. The mass, linear momentum and kinetic energy of a body are m, p and E respectively, then  
 (a) p 2mE ?  (b) E 2mp ?  (c) p 2E ?  (d) E 2p ?
 
 
22. A stone is allowed to fall freely downwards initially at rest from the top of a tower. The time taken by the 
stone to reach the bottom of the tower is 4 seconds. What is the height of the tower? Take, acceleration due 
to gravity = 32 ft/s
2
 
(a) 64 ft.   (b) 32 ft.   (c) 48 ft.   (d) 256 ft. 
 
23. The coefficient of linear expansion of a solid is x and the coefficient of volume expansion of the solid is y, then 
(a) 
y
x
3
? 
(b) 
x
y
3
? 
(c) 
y
x
2
? 
(d) 
x
y
2
? 
 
24. In case of refraction of light from a medium to air the critical angle is found to be 45°. What is the refractive 
index of the medium with respect to air? . 
 (a) 2   (b) 3   (c) 2   (d) 3 
 
25. Which of the following pair have same unit? 
 (a) Heat and Specific heat 
(b) Thermal capacity and Water equivalent  
(c) Specific heat and Thermal capacity 
(d) Heat and Work 
 
26. Which of the following   is an electromagnetic wave? 
 (a) a-ray   (b) ß-ray   (c) ?-ray   (d) cathode ray 
 
27. In case of a convex lens, what is the minimum distance between an object and its real image? 
 (a) 2.5 times of focal length    (b) 2 times of focal length  
(c) 4 times of focal length    (d) equal to focal length 
 
28. What will be the power consumed by a 50 ? wire if it is kept across a potential difference of 200V? 
 (a) 0.8 kW   (b) 80 kW   (c) 400 W   (d) 8 Kw 
 
29. I cm ot main scale of a vernier callipers is divided into 10 divisions. The least count  of  the callipers is 0.005 
cm, then what is the number of divisions in the vernier scale? 
 (a) 10    (b) 20    (c) 25    (d) 50 
 
30. If an x-ray tube is operated at 20kV, what is the cut-off wave length? (Take, planks constant  
 
34
h 6.62 10
?
?? J.S) 
 (a) 0.89 Å   (b) 0.75 Å   (c) 0.62 Å   (d) 0.31 Å 
 
 
   
 
 
 
31. An ideal gas is found to obey the equation p
2
V = constant along with the ideal gas equation (here, p = 
pressure and V= volume). If initial temperature and volume are T
0
 and V
0
 respectively and it expands to a 
volume 3V
0
 then what is the final temperature? 
 (a) 
0
3T  (b) 
0
2T  (c) 
0
T
3
  (d) 
0
T
2
 
 
32. Specific heat (S) of a metal at low temperature varies according to S = aT
3
, where ‘a’ is a constant and T is a 
absolute temperature. The amount of heat energy needed to raise the temperature of unit mass of the metal 
from T = 1K  to T = 2K is 
(a) 3a   (b) 
15a
4
  (c) 
2a
3
   (d) 
13a
4
 
 
33. An object of weight W and density  is submerged wholly in a liquid of density , its apparent weight will be 
 (a) () ???  (b) ( ) / W ??? (c)  W1
?? ?
?
??
?
??
   (d) W1
? ??
?
??
?
??
 
 
Chemistry 
34. The ratio of  and  bonds in propyne is 
 (a) 1 : 3   (b) 3 : 1   (c) 2 : 3    (d) 3 : 2 
 
35. The element having the lowest first ionization energy is 
 (a) He    (b) Cl    (c) F    (d) I 
 
36. If the four tubes of a car are filled to the same pressure with N
2,
O
2
,H
2
  and Ne gas separately then which will 
fill the tube first? 
 (a) N
2   
(b) O
2   
(c) H
2   
(d) Ne 
 
37. At a given temperature what will be the percentage increase in pressure for a 5% decrease in the volume of 
the gas 
 (a) 5%    (b) 5.26   (c) 6.26%   (d) 10.26% 
 
38. 
2 O
?
  is isoelectronic with 
 (a) H
2   
(b) N
2   
(c) F
2   
(d) 
2
HF
?
 
 
39. Which of the following forms a homologous series? 
(a) Ethane, Ethylene, Acetylene   (b) Ethane, Propane, Butanone 
(c) Methanol, Ethanol, Propanoic acid  (d) Butane, 2-Methyl Butane, 2, 3, dimethyl Butane. 
 
40. The gas that gives a black precipitate with aqueous Pb(NO)
3
  solutuion and a white precipitate with aqueous 
ZnCl
2
 solution is 
 (a) CO
2   
(b) NO
2   
(c) NH
3   
(d) H
2
S 
 
Page 5


   
 
 
 
NTSE-WEST BENGAL-SAT 
 
Mathematics 
 
 
1. If the algebraic expression 
? ?
2
33 ?? x px be always positive, then 
 (a) –6  < p < 6   (b) p < – 6   (c) p > 6   (d) no such p exists 
 
2. The sum of the roots of ? ?
2
00 ? ? ? ? ax bx c a is equal to the sum of the squares of the roots of the 
equation. Then 
 (a)  2 ?? ab ac be (b)  
2
2 ?? b ab ae (c)  
2
2 ?? ac ab b (d)  
2
2 ?? ab ac b 
 
3. The solution set for the equation 
? ?
22
22 22
3 2.3 3 0
? ??
? ? ?
x x x x
 is 
 (a) {–1, 2}   (b) { 0, 2}   (c) {0, –1}   (d) {2, 4} 
 
4. It is printed on a paper that "The length of a diagonal of a rectangle is 10 cm and its area is 62.5 sq. 
cm". Then which one of the following statements is true? 
 (a) The perimeter of the rectangle is 30 cm.  
(b) The sum of the length and breadth is 20 cm.  
(c) The difference of the length and breadth is 5 cm.  
(d) No such rectangle can exist. 
 
5. The ratio of the lengths of the corresponding sides of two similar triangles are in the ratio of 4 : 9. 
Then the ratio of their areas is 
 (a) 16 : 81   (b) 81 : 16   (c) 4 : 9   (d) 9 : 4 
 
6. Father says to his son: "On the date of birth of yours, I was twice older than you are now." Then 
which one of the following statements is true? 
(a) The present ages of the father and his son are 30 years and 10 years respectively. 
(b) The present ages of the father and his son are 48 years and 12 years respectively. 
(c) Nothing can be said about their ages. 
(d) The ratio of the present ages of the father to the son is 3 : 1. 
 
7. Taking at least one from the numbers 1,2,3, how many different sets can be formed? 
 (a)  8   (b)  7   (c)  3   (d)  
3
3 
 
8. ? ?
23
18 is divided by remainder 17 to give the remainder 
 (a) 11    (b) 9    (c) 5    (d) 1 
 
9. If 
2
4 1 0 ? ? ? mm , then the value of 
3
3
1 ??
?
??
??
m
m
 is 
 (a) 52    (b) 48    (c) 64    (d) 68 
 
10. For 3 81, 81 3
??
??
x y x y
, we get  
 (a)  no solution (b)  
21 21
, 
22
?? xy (c) 
2
2, 
3
?? xy  (d)  
17 15
, 
88
?? xy 
   
 
 
 
 
11. 125 identical cubes are cut from a big cube and all the smaller cubes are arranged in a row to form a 
long cuboid. What is the percentage of increase in total surface area of the cuboid over the total 
surface area of the cube?   
 (a)  
2
234 %
3
  (b)  
1
234 %
3
  (c)  
2
134 %
3
  (d)  None of the above 
 
12. A bag contains 4 Red and 3 Black balls and a second bag contains 2 Red and 4 Black balls. After 
choosing a bag at random, a ball is also drawn at random. The probability that the ball is Red is 
(a)  
23
42
   (b)  
17
42
   (c)  
19
42
   (d)  
16
39
 
 
13. If [n] denotes the greatest integer  n and (n) denotes the smallest integer  n ; n being a real number, 
then ? ?
1 1 1 1
1 1 2 1 1.5
5 5 5 5
? ? ? ? ? ? ? ?
? ? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ? ? ? ? ?
 is 
 (a) 1.5    (b) 2    (c) 2.5    (d) 3.5 
 
14. The value of 
2 2 2 2 2 2
3 5 19
.......
1 .2 2 .3 9 .10
? ? ? is 
 (a)  
99
100
  (b)  
1
100
  (c)  
101
100
  (d)  1 
 
15. In a frequency distribution, Mean = 9.1 and 132 5 , 20 ? ? ?
?? i i i
f x k f , then k is 
 (a) 4    (b) 6    (c) 10    (d) 9 
 
16. ABC is a triangle in which ABC > 90° and AD  CB produced. Then 
 
A
B
C D
 
  
 (a)  
2 2 2
? ? ? ? AB AC BC BC BD   (b)  
2 2 2
2 ? ? ? ? AB AC BC BC BD 
 (c)  
2 2 2
2 ? ? ? ? Ac AB BC BC BD  (d)  
2 2 2
? ? ? ? AC AB BC BC BD  
 
17. Given : 0° <  < 90°. then, if sin + cos = x, which one of the following is correct? 
 (a)  1 ? x  (b)  1.5 ? x  (c)  12 ?? x  (d)  12 ?? x 
 
18. If sin cos 2 ?? ?? and 0 , 90 , ?? ??
oo
 then 2 2000 . ?? ?? 
 (a) 180°   (b) 90°   (c) 2180°   (d) Can not be found out 
 
19. sec tan , ? ? ? ? ?? a b a b Q and ? bQ and sec ? is rational, then 
 (a)  
2
1 ?? ba  (b)  
2
1 ?? ab  (c)  
2
1 ?? ba  (d)  
2
1 ?? ab 
 
20. The ratio of in which 9x – 3y – 14 = 0 divides the join of (2, – 4) and (3, 7) is 
 (a) 2 : 1   (b) 1 : 2   (c) 2 : 3   (d) 3 : 2 
 
   
 
 
 
Physics 
21. The mass, linear momentum and kinetic energy of a body are m, p and E respectively, then  
 (a) p 2mE ?  (b) E 2mp ?  (c) p 2E ?  (d) E 2p ?
 
 
22. A stone is allowed to fall freely downwards initially at rest from the top of a tower. The time taken by the 
stone to reach the bottom of the tower is 4 seconds. What is the height of the tower? Take, acceleration due 
to gravity = 32 ft/s
2
 
(a) 64 ft.   (b) 32 ft.   (c) 48 ft.   (d) 256 ft. 
 
23. The coefficient of linear expansion of a solid is x and the coefficient of volume expansion of the solid is y, then 
(a) 
y
x
3
? 
(b) 
x
y
3
? 
(c) 
y
x
2
? 
(d) 
x
y
2
? 
 
24. In case of refraction of light from a medium to air the critical angle is found to be 45°. What is the refractive 
index of the medium with respect to air? . 
 (a) 2   (b) 3   (c) 2   (d) 3 
 
25. Which of the following pair have same unit? 
 (a) Heat and Specific heat 
(b) Thermal capacity and Water equivalent  
(c) Specific heat and Thermal capacity 
(d) Heat and Work 
 
26. Which of the following   is an electromagnetic wave? 
 (a) a-ray   (b) ß-ray   (c) ?-ray   (d) cathode ray 
 
27. In case of a convex lens, what is the minimum distance between an object and its real image? 
 (a) 2.5 times of focal length    (b) 2 times of focal length  
(c) 4 times of focal length    (d) equal to focal length 
 
28. What will be the power consumed by a 50 ? wire if it is kept across a potential difference of 200V? 
 (a) 0.8 kW   (b) 80 kW   (c) 400 W   (d) 8 Kw 
 
29. I cm ot main scale of a vernier callipers is divided into 10 divisions. The least count  of  the callipers is 0.005 
cm, then what is the number of divisions in the vernier scale? 
 (a) 10    (b) 20    (c) 25    (d) 50 
 
30. If an x-ray tube is operated at 20kV, what is the cut-off wave length? (Take, planks constant  
 
34
h 6.62 10
?
?? J.S) 
 (a) 0.89 Å   (b) 0.75 Å   (c) 0.62 Å   (d) 0.31 Å 
 
 
   
 
 
 
31. An ideal gas is found to obey the equation p
2
V = constant along with the ideal gas equation (here, p = 
pressure and V= volume). If initial temperature and volume are T
0
 and V
0
 respectively and it expands to a 
volume 3V
0
 then what is the final temperature? 
 (a) 
0
3T  (b) 
0
2T  (c) 
0
T
3
  (d) 
0
T
2
 
 
32. Specific heat (S) of a metal at low temperature varies according to S = aT
3
, where ‘a’ is a constant and T is a 
absolute temperature. The amount of heat energy needed to raise the temperature of unit mass of the metal 
from T = 1K  to T = 2K is 
(a) 3a   (b) 
15a
4
  (c) 
2a
3
   (d) 
13a
4
 
 
33. An object of weight W and density  is submerged wholly in a liquid of density , its apparent weight will be 
 (a) () ???  (b) ( ) / W ??? (c)  W1
?? ?
?
??
?
??
   (d) W1
? ??
?
??
?
??
 
 
Chemistry 
34. The ratio of  and  bonds in propyne is 
 (a) 1 : 3   (b) 3 : 1   (c) 2 : 3    (d) 3 : 2 
 
35. The element having the lowest first ionization energy is 
 (a) He    (b) Cl    (c) F    (d) I 
 
36. If the four tubes of a car are filled to the same pressure with N
2,
O
2
,H
2
  and Ne gas separately then which will 
fill the tube first? 
 (a) N
2   
(b) O
2   
(c) H
2   
(d) Ne 
 
37. At a given temperature what will be the percentage increase in pressure for a 5% decrease in the volume of 
the gas 
 (a) 5%    (b) 5.26   (c) 6.26%   (d) 10.26% 
 
38. 
2 O
?
  is isoelectronic with 
 (a) H
2   
(b) N
2   
(c) F
2   
(d) 
2
HF
?
 
 
39. Which of the following forms a homologous series? 
(a) Ethane, Ethylene, Acetylene   (b) Ethane, Propane, Butanone 
(c) Methanol, Ethanol, Propanoic acid  (d) Butane, 2-Methyl Butane, 2, 3, dimethyl Butane. 
 
40. The gas that gives a black precipitate with aqueous Pb(NO)
3
  solutuion and a white precipitate with aqueous 
ZnCl
2
 solution is 
 (a) CO
2   
(b) NO
2   
(c) NH
3   
(d) H
2
S 
 
   
 
 
 
41. The organic product that is obtained by  absorbing  Ethylene into concentrated HSO
4
 and subsequently 
boiling the mixture with water is 
(a) an aldehyde   (b) an amide   (c) a ketone   (d) an alcohol 
 
42. Equal volumes of two solutions of pH = 4 and pH = 10 are mixed. pH of the resultant solution will be 
 (a) 6    (b) 7    (c) 8    (d) 9 
 
43. Find out the position isomers from the following pairs of compounds 
(a) 
C
CH
3
CH
2
OH, C H
2
C
CH
3
OCH
3
C H
2
 
(b) CH C H
2
CH
2
COOH, CH C H
2
COOCH
3
 
(c) CH
CH
3
C H
3
O CH
3
, CH
2
C H
3
CH
2
O CH
3
 
(d) 
CH
2
C H
3
C
O
CH
3
, C H
CH
3
C H
3
C
O
O H
 
 
44. Egg albumin in water is a 
 (a) True solution  (b) Colloid   (c) Suspension   (d) Supersaturated Solution 
 
45. Lithium is generally used as an electode in high energy density batteries. This is because 
(a) Lithium is the lightest of all metals    (b) Lithium has quite high negative reduction potential  
(c) Lithium is quite reactive      (d) Lithium does not corrode easily 
 
46 
NH
3
+ O
2
                   A + H
2
O
Pt- Rh
 ?
A + O
2
          B
B + O
2
 + H
2
O          C
 
A, B and C respectively are 
 
(a) N
2
O, NO
2
 and HNO
3
    (b) NO, NO
2
 and HNO
3
   
(c) NO
2,
NO and HNO
3
   (d) N
2
O, NO and HNO
3