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NTSE MATHEMATICS SAMPLE PAPER

1.

Tow numbers x, y such that their mean proportional is 12 and their 3rd proportional is 324. x, y are:

2.

3.

4.

(a) 8, 24

(b) 4, 24

(c) 4, 36

(d) 8, 36

(x

k ) is the GCD of x 2

(b) 4

(c) 3

(d) 3

If a b c

0 the value of a 3

b3

c 3 is:

(a) 0

(b) a 2 b 2 c 2

(c) a 3 b 3 c 3

(d) 3abc

If x

(c)

3

2

3

2

and y

1 the value of

x y is: x 3y

5 6

6.

kx 9 then the value of p is:

(a) 4

(a)

5.

x 12 and 2x 2

5

(b) 4

6

6 4 5

(d)

Find the value of

n

x2

n/2

6 4 5

2

is equal to:

(a) 0

(b) 1

(c) x

(d) 1/x 1

If x

then

1

5 5 5

1 1 ..... 5

4

7.

8.

9.

10.

11.

12.

(a) x 2

5x 1 0

(b) x 2

5x 1 0

(c) x 2

5x 1 0

(d) x 2

5x 1 0

1 x

If x

21 THE VALUE OF x 2

1 x

2

x

1 IS: x

(a) 42

(b) 115

(c) 63

(d) 120

The square root of ( x 2

4x

4) ( x 2

6x

9) is :

(a) x 2

5x 6

(b) x 2

5x 6

(c) x 2

6x 5

(d) x 2

5x 6

If x

9 and y

17 the value of ( x 2

y2)

1/ 3

is:

(a)

1 2

(b) 1

(c)

1 3

(d)

If a b c

0 the value of

a2 bc

b2 ca

1 4

c2 is: ab

(a) 1

(b) 1

(c) 0

(d) 3

If 2 x

2x

1

4 then x x is equal to:

(a) 7

(b) 3

(c) 27

(d) 3

The products of 1

1 1 1 1 1 1 .... 1 n n 1 n 2 2n

(a)

n 1 2n

(b)

1 2n

(c)

2n n 1

(d)

1 n

is equal to:

13.

14.

15.

16.

The value of 12

n(n 1) 2

(b)

(c)

n(n 1)( 2n 1) 6

(d)

7 log 2

16 25

19.

5 log 2

25 24

3 log 2

n(n 1)( 2n 1) 6

n(n 1) 2

2

81 is equal to: 80

(a) log2 2

(b) log2 3

(c) log2 5

(d) 0

The ratio of the ages of A and B ten years before was 3 : 5. The ratio of their presents ages is 2 :3 their ages are respectively. (a) 30, 50

(b) 20, 30

(c) 40, 60

(d) 16, 24

A wire of length 25 cm is bent so as to lie along the arc of a circle of diameter 100 cm. The angle subtended at the centre by the arc is:

(c)

18.

33....n 2 is:

(a)

(a)

17.

22

(b)

4

(d)

2

8

The area of sector of a circle which has a central angle of 60 and a radius of 3 cm is: (a) 2.9 cm2

(b) 4.7 cm2

(c) 3.5 cm2

(d) none of these

The ratio of the radii of two circles at the centres of which two arcs of the same length subtended a angles of 60 and 70 is: (a) 5 : 4

(b) 4 : 5

(c) 2 : 6

(d) 4 : 3

An arc of circle of length 11 cm subtends an angle of 30 at the centre of the circle. The radius of the circle is: (a) 21 cm

(b) 22 cm

(c) 72 cm 20.

21.

22.

23.

24.

The angle of a triangle are in AP and the number of degree in the least into the 180 , then greatest angle is: (a) 60

(b) 30

(c) 90

(d) 45

If the miscellaneous charges are Rs 6000 the advertisement charges are: (a) 90000

(b) 1333.33

(c) 27000

(d) 12000

If 550 copies are published miscellaneous expenditures amount to Rs 1848 and publisher’s profit is 25% then marked price of each copy is: (a) 8.40

(b) 12.50

(c) 10.50

(d) 10

25th percentile coincides with the: (a) Q1

(b) D5

(c) P10

(d) Q2

Calculate the mode of the following data: Size Frequency

25.

26.

27.

(d) 27 cm

1 6

3 9

5 12

7 3

9 15

(a) 9

(b) 7

(c) 5

(d) 3

What is the mean of first five natural numbers? (a) 8

(b) 10

(c) 4

(d) 3

Given the mean (30), the mode (35). What is the median? (a) 40

(b) 30

(c) 55.7

(d) 31.69

A student gets the following percentages in an examination English = 50%, Biology = 40%, Mathematics = 60%, Physics = 70%, Chemistry = 80%

It was suggested that he have been given double weightage on his marks in Physics and Chemistry than in other subjects. What is the arithmetic weightage mean of marks?

28.

(a) 57.4

(b) 59.4

(c) 58.4

(d) 64.28 A

Quadrilateral ABCD is a parallelogram. E is the mid point of the diagonal DB.DE 10 cm DB 16 cm. The length of PQ is: (a) 13 cm (b) 16 cm (c) 8 cm (d) 12 cm

P E

D 29.

Quadrilateral ABCD is a parallelogram. The length of DN is: (a) 10 cm (b) 5 cm (c) 4.8 cm (d) 6 cm

B

Q 8 cm

A

C B 10 cm

6 cm D

C

M N

30.

In the figure ABCD is a rectangle. The area of the shaded region is: 2 2 (a) 16.2 cm (b) 13.8 cm 2 2 (c) 64.8 cm (d) 11.2 cm

A

M

8 cm D

30

C 15 cm

31.

The area of the shaded region in the given figure is: 2 2 (a) 996 cm (b) 946 cm 2 (c) 935.7 cm (d) none of these 18 cm 7 cm

32.

Two identical circles are inscribed in a rectangle such that the ratio of circumference to area of each of the circles 4 : 1. The area of shaded region is

(a)

(c)

2 4 2 2

(b)

(d)

1 4 4 2

B

33.

34.

35.

36.

37.

38.

Find the inradius of a triangle if its area 30 cm2 and hypotenuse is 13 cm: (a) 1.5 cm

(b) 1.755 cm

(c) 2 cm

(d) 2 2

1 litre of water is added to 5 litres of a 20% solution of alcohol in water the strength of alcohol is

1 (a) 12 % 2

2 (b) 16 % 3

(c) 24%

(d) 16%

A man spends 75% of his income. His income is increased by 20% and he increased his expenditure by 10%. His savings are increased by: (a) 10%

(b) 25%

1 (c) 37 % 2

(d) 50%

2 men and 7 boys can do a piece of work in 14 days; 3 men and 8 boys can do the same in 11 days, 8 men and 6 boys can do 3 times the amount of their work is: (a) 21 day

(b) 18 day

(c) 24 day

(d) 36 day

Two partners invested Rs. 1250 and Rs. 850 respectively in a business, they distribute 60% of the profit equally and decide to distribute the remaining 40% as the interest on their capitals. If one partner received Rs. 30 more than the other. The total profit is: (a) Rs. 840

(b) Rs. 393.75

(c) Rs. 590

(d) none of these

In the figure QT = 10 cm. The value of ST is: (a) 2 cm (b) 10 cm (c) 2.5 cm (d) 5 cm

P

S

T

78°

R O Area of ABC = 18 sq. cm D is the mid point of BC and E is the mid point of AB. The area of BDE is: Q

39.

33°

(a) 4.5 cm2

(b) 9 cm2

(c) 5 cm2 40.

41.

(d) 10 cm2

From the given information in the figure. The value of BAC is: (a) 60° (b) 80° (c) 40° (d) 110° In adjoining figure (a) 360° (c) 180°

A

B

C

D

E

A

30° X

40°

B

Y

C D

F is equal to: (b) 72° (d) 300°

C

E

B

F A

42.

In figure (a) 360° (c) 720°

ABC

BCD

CDE

DEA

EAB is equal to:

E

(b) 540° (d) none of these

C A

43.

44.

(a) 600

(b) 612

(c) 624

(d) none of these

The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 27. The common difference is :

1 7

(b) 7

(c) 3

(d)

1 3

The distance between the points:

( 2 2, 3 2) and ( 5 1, 3 1) is:

46.

47.

B

In an A.P. 3rd term is 18 and 7th term is 30. The sum of i is 17th term is:

(a)

45.

D

(a) 3 5

(b) 4 3

(c) 3 2

(d) none of these

In what ratio does the line 2x 3y

7

0 divide the join of (3, 4) and (7, 8):

(a) 4 : 7 internally

(b) 4 : 7 externally

(c) 4 : 7 internally

(d) 5 : 9 externally

A dice is thrown what is the probability of getting a prime number?

48.

49.

50.

(a)

1 6

(b)

1 3

(c)

1 3

(d) 1

If a fair coin is tossed twice, what is the probability of getting heads in both the trial: (a) 1/4

(b) 1/2

(c) 3/4

(d) 1

A coin is tossed successively three times. The probability of getting one head or two heads is: (a) 2/3

(b) 3/4

(c) 4/9

(d) 1/9

In a simultaneous throw of two dice the probability of getting a total of 7 is: (a) 7/36

(b) 1/7

(c) 1/4

(d) 1/6

NTSE MATHEMATICS SAMPLE PAPER

1.

(c)

2. (c)

3.

(a)

4. (d)

5.

(b)

6. (a)

7.

(b)

8. (d)

9.

(d)

10. (d)

11.

(c)

12. (a)

13.

(b)

14. (a)

15.

(c)

16. (c)

17.

(b)

18. (a)

19.

(a)

20. (c)

21.

(c)

22. (c)

23.

(a)

24. (a)

25.

(d)

26. (d)

27.

(d)

28. (d)

29.

(c)

30. (c)

31.

(b)

32. (a)

33.

(a)

34. (b)

35.

(d)

36. (a)

37.

(b)

38. (d)

39.

(a)

40. (c)

41.

(a)

42. (b)

43.

(b)

44. (a)

45.

(c)

46. (d)

47.

(c)

48. (a)

49.

(b)

50. (d)

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1.

Tow numbers x, y such that their mean proportional is 12 and their 3rd proportional is 324. x, y are:

2.

3.

4.

(a) 8, 24

(b) 4, 24

(c) 4, 36

(d) 8, 36

(x

k ) is the GCD of x 2

(b) 4

(c) 3

(d) 3

If a b c

0 the value of a 3

b3

c 3 is:

(a) 0

(b) a 2 b 2 c 2

(c) a 3 b 3 c 3

(d) 3abc

If x

(c)

3

2

3

2

and y

1 the value of

x y is: x 3y

5 6

6.

kx 9 then the value of p is:

(a) 4

(a)

5.

x 12 and 2x 2

5

(b) 4

6

6 4 5

(d)

Find the value of

n

x2

n/2

6 4 5

2

is equal to:

(a) 0

(b) 1

(c) x

(d) 1/x 1

If x

then

1

5 5 5

1 1 ..... 5

4

7.

8.

9.

10.

11.

12.

(a) x 2

5x 1 0

(b) x 2

5x 1 0

(c) x 2

5x 1 0

(d) x 2

5x 1 0

1 x

If x

21 THE VALUE OF x 2

1 x

2

x

1 IS: x

(a) 42

(b) 115

(c) 63

(d) 120

The square root of ( x 2

4x

4) ( x 2

6x

9) is :

(a) x 2

5x 6

(b) x 2

5x 6

(c) x 2

6x 5

(d) x 2

5x 6

If x

9 and y

17 the value of ( x 2

y2)

1/ 3

is:

(a)

1 2

(b) 1

(c)

1 3

(d)

If a b c

0 the value of

a2 bc

b2 ca

1 4

c2 is: ab

(a) 1

(b) 1

(c) 0

(d) 3

If 2 x

2x

1

4 then x x is equal to:

(a) 7

(b) 3

(c) 27

(d) 3

The products of 1

1 1 1 1 1 1 .... 1 n n 1 n 2 2n

(a)

n 1 2n

(b)

1 2n

(c)

2n n 1

(d)

1 n

is equal to:

13.

14.

15.

16.

The value of 12

n(n 1) 2

(b)

(c)

n(n 1)( 2n 1) 6

(d)

7 log 2

16 25

19.

5 log 2

25 24

3 log 2

n(n 1)( 2n 1) 6

n(n 1) 2

2

81 is equal to: 80

(a) log2 2

(b) log2 3

(c) log2 5

(d) 0

The ratio of the ages of A and B ten years before was 3 : 5. The ratio of their presents ages is 2 :3 their ages are respectively. (a) 30, 50

(b) 20, 30

(c) 40, 60

(d) 16, 24

A wire of length 25 cm is bent so as to lie along the arc of a circle of diameter 100 cm. The angle subtended at the centre by the arc is:

(c)

18.

33....n 2 is:

(a)

(a)

17.

22

(b)

4

(d)

2

8

The area of sector of a circle which has a central angle of 60 and a radius of 3 cm is: (a) 2.9 cm2

(b) 4.7 cm2

(c) 3.5 cm2

(d) none of these

The ratio of the radii of two circles at the centres of which two arcs of the same length subtended a angles of 60 and 70 is: (a) 5 : 4

(b) 4 : 5

(c) 2 : 6

(d) 4 : 3

An arc of circle of length 11 cm subtends an angle of 30 at the centre of the circle. The radius of the circle is: (a) 21 cm

(b) 22 cm

(c) 72 cm 20.

21.

22.

23.

24.

The angle of a triangle are in AP and the number of degree in the least into the 180 , then greatest angle is: (a) 60

(b) 30

(c) 90

(d) 45

If the miscellaneous charges are Rs 6000 the advertisement charges are: (a) 90000

(b) 1333.33

(c) 27000

(d) 12000

If 550 copies are published miscellaneous expenditures amount to Rs 1848 and publisher’s profit is 25% then marked price of each copy is: (a) 8.40

(b) 12.50

(c) 10.50

(d) 10

25th percentile coincides with the: (a) Q1

(b) D5

(c) P10

(d) Q2

Calculate the mode of the following data: Size Frequency

25.

26.

27.

(d) 27 cm

1 6

3 9

5 12

7 3

9 15

(a) 9

(b) 7

(c) 5

(d) 3

What is the mean of first five natural numbers? (a) 8

(b) 10

(c) 4

(d) 3

Given the mean (30), the mode (35). What is the median? (a) 40

(b) 30

(c) 55.7

(d) 31.69

A student gets the following percentages in an examination English = 50%, Biology = 40%, Mathematics = 60%, Physics = 70%, Chemistry = 80%

It was suggested that he have been given double weightage on his marks in Physics and Chemistry than in other subjects. What is the arithmetic weightage mean of marks?

28.

(a) 57.4

(b) 59.4

(c) 58.4

(d) 64.28 A

Quadrilateral ABCD is a parallelogram. E is the mid point of the diagonal DB.DE 10 cm DB 16 cm. The length of PQ is: (a) 13 cm (b) 16 cm (c) 8 cm (d) 12 cm

P E

D 29.

Quadrilateral ABCD is a parallelogram. The length of DN is: (a) 10 cm (b) 5 cm (c) 4.8 cm (d) 6 cm

B

Q 8 cm

A

C B 10 cm

6 cm D

C

M N

30.

In the figure ABCD is a rectangle. The area of the shaded region is: 2 2 (a) 16.2 cm (b) 13.8 cm 2 2 (c) 64.8 cm (d) 11.2 cm

A

M

8 cm D

30

C 15 cm

31.

The area of the shaded region in the given figure is: 2 2 (a) 996 cm (b) 946 cm 2 (c) 935.7 cm (d) none of these 18 cm 7 cm

32.

Two identical circles are inscribed in a rectangle such that the ratio of circumference to area of each of the circles 4 : 1. The area of shaded region is

(a)

(c)

2 4 2 2

(b)

(d)

1 4 4 2

B

33.

34.

35.

36.

37.

38.

Find the inradius of a triangle if its area 30 cm2 and hypotenuse is 13 cm: (a) 1.5 cm

(b) 1.755 cm

(c) 2 cm

(d) 2 2

1 litre of water is added to 5 litres of a 20% solution of alcohol in water the strength of alcohol is

1 (a) 12 % 2

2 (b) 16 % 3

(c) 24%

(d) 16%

A man spends 75% of his income. His income is increased by 20% and he increased his expenditure by 10%. His savings are increased by: (a) 10%

(b) 25%

1 (c) 37 % 2

(d) 50%

2 men and 7 boys can do a piece of work in 14 days; 3 men and 8 boys can do the same in 11 days, 8 men and 6 boys can do 3 times the amount of their work is: (a) 21 day

(b) 18 day

(c) 24 day

(d) 36 day

Two partners invested Rs. 1250 and Rs. 850 respectively in a business, they distribute 60% of the profit equally and decide to distribute the remaining 40% as the interest on their capitals. If one partner received Rs. 30 more than the other. The total profit is: (a) Rs. 840

(b) Rs. 393.75

(c) Rs. 590

(d) none of these

In the figure QT = 10 cm. The value of ST is: (a) 2 cm (b) 10 cm (c) 2.5 cm (d) 5 cm

P

S

T

78°

R O Area of ABC = 18 sq. cm D is the mid point of BC and E is the mid point of AB. The area of BDE is: Q

39.

33°

(a) 4.5 cm2

(b) 9 cm2

(c) 5 cm2 40.

41.

(d) 10 cm2

From the given information in the figure. The value of BAC is: (a) 60° (b) 80° (c) 40° (d) 110° In adjoining figure (a) 360° (c) 180°

A

B

C

D

E

A

30° X

40°

B

Y

C D

F is equal to: (b) 72° (d) 300°

C

E

B

F A

42.

In figure (a) 360° (c) 720°

ABC

BCD

CDE

DEA

EAB is equal to:

E

(b) 540° (d) none of these

C A

43.

44.

(a) 600

(b) 612

(c) 624

(d) none of these

The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 27. The common difference is :

1 7

(b) 7

(c) 3

(d)

1 3

The distance between the points:

( 2 2, 3 2) and ( 5 1, 3 1) is:

46.

47.

B

In an A.P. 3rd term is 18 and 7th term is 30. The sum of i is 17th term is:

(a)

45.

D

(a) 3 5

(b) 4 3

(c) 3 2

(d) none of these

In what ratio does the line 2x 3y

7

0 divide the join of (3, 4) and (7, 8):

(a) 4 : 7 internally

(b) 4 : 7 externally

(c) 4 : 7 internally

(d) 5 : 9 externally

A dice is thrown what is the probability of getting a prime number?

48.

49.

50.

(a)

1 6

(b)

1 3

(c)

1 3

(d) 1

If a fair coin is tossed twice, what is the probability of getting heads in both the trial: (a) 1/4

(b) 1/2

(c) 3/4

(d) 1

A coin is tossed successively three times. The probability of getting one head or two heads is: (a) 2/3

(b) 3/4

(c) 4/9

(d) 1/9

In a simultaneous throw of two dice the probability of getting a total of 7 is: (a) 7/36

(b) 1/7

(c) 1/4

(d) 1/6

NTSE MATHEMATICS SAMPLE PAPER

1.

(c)

2. (c)

3.

(a)

4. (d)

5.

(b)

6. (a)

7.

(b)

8. (d)

9.

(d)

10. (d)

11.

(c)

12. (a)

13.

(b)

14. (a)

15.

(c)

16. (c)

17.

(b)

18. (a)

19.

(a)

20. (c)

21.

(c)

22. (c)

23.

(a)

24. (a)

25.

(d)

26. (d)

27.

(d)

28. (d)

29.

(c)

30. (c)

31.

(b)

32. (a)

33.

(a)

34. (b)

35.

(d)

36. (a)

37.

(b)

38. (d)

39.

(a)

40. (c)

41.

(a)

42. (b)

43.

(b)

44. (a)

45.

(c)

46. (d)

47.

(c)

48. (a)

49.

(b)

50. (d)

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