# Class 10th Math Practice Paper

The following Questions of Class 10th Math Practice Paper are given below.

## New Sample Paper Class 10 2022 | Maths sample paper | ncert class 10 math sample paper

### Maths Sample Paper 4

1. The decimal expansion of is: 13/3125 is

(a) Terminating

(b) Non-terminating repeating

(c) Both (a) as well as (b)

(d) None of these

Ans. a

2. Look at the equations given below: 4x + 3y = 41 x+3y = 26 The correct method of solving these equations is :

(a) 4x -x+ 3y – 3y= 41- 26

(b) 4 (x+ 3y) + 3y = 41

(c) 4x +x+ 3y- 3y 41 – 26

(d) 4x + 3y+ 3y = 41-26

Ans. a

3. Points (1, 2), (4, y), (x, 6) and (3, 5) form rhombus. The values of x and y are :

(a) (2, 3)

(b) (4, 3)

(c) (6, 3)

(d) (2, 5)

Ans. c

4. The value of the polynomial p(z)=z4-2z3+3 at z =- 1 is :

(a) 2

(b) 3

(c) 5

(d) 6

Ans. x

5. If tan A = 3/4, then the value of (4sin A – cos A) / (4 sin A + cos A) is:

(a)1/2

(b)3/4

(c)1/3

(d)2/3

Ans. a

6. LCM of 17, 23 and 29 is:

(a) 11339

(b) 12339

(c) 15339

(d) 14449

Ans. a

7. The pair of linear equations x+ 3y = 6 and 2x – 3y = 12 is :

(a) consistent

(b) Inconsistent

(c) Both (a) as well as (b)

(d) None of these

Ans.  a

8. If the angle between two radii of a circle is 110°, then the angle between the tangents at the ends of these radii is

(a) 90°

(b) 50°

(c) 70°

(d) 40°

Ans. c

9. The quadratic polynomial, the sum and product of whose zeroes are 4 and 1 respectively is :

(a) x2 + 4x – 1

(c) x2 4x-1

(b) x2 + 4x+1

(d) x2– 4x + 1

Ans. d

10. The distance between the points (2, 3) and (4, 1) is :

(b) 2√2

(a) √2

(d) 4√2

(c) 3 √2

Ans b

12. There is a circular path around a sports field. Rimpi takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point ?

(a) 37

(b) 28

(c) 36

(d) 21

Ans. c

13. The product of zeroes of the cubic polynomial ax3 + bx2 + cx +d is :

(b) c/a

(a) – b/a

(c)-d/a

(d)-c/ a

Ans. c

14. If two tangents inclined at an angle of 6o are drawn to a circle of radius 3 cm from an external point, then the length of each tangent will be:

(b) 4 cm

(a) 6 cm

(c) 3√3 cm

(d) 3 cm

Ans. c

15. Raman draws a circle of diameter 6 units Then he draws another circle with a radius four times that of the first circle. If he divides the circumference of the new circle with its diameter, then the quotient so obtained will be:

(a) Pi

(b) 2pi

(c) 8

(d) 12

Ans. a

16. sin 25° cos 65° + cos 25° sin 65°……

(a) 2

(b) 0

(c) 1

(d) 3

Ans. c

17. The points (-4, 0); (4, 0) and (0, 3) are  the vertices of a ……triangle.

(a) Right angled

(b) Isosceles

(c) Equilateral

(d) None of these

Ans.  b

18. In a lottery, there are 10 prizes and 25″ blanks. A lottery is drawn at random. What is the probability of getting a prize ?

(a) 1/10

(b) 2/5

(c)2/7

(d) 5/7

Ans. c

19. Solve the following pair of equations,  5/(X-1) + 1/(y-2)=2  And 6/(x-1) -3/(y-2)=1

(a) x=-4; y = 5

(c) x= 4:y =- 5

(b) x=4: y= 5

(d) x= -4 y=-5

Ans. b

20. One card is drawn from a well-shuffled  deck of 52 cards. The probability that the card will not be an ace is :

(b) 12/13

(a) 1/13

(d) 4/13

(c) 2/13

Ans. b

21. The length of the minute hand of a clock js 14 cm. The area swept by this hand in 5 minutes is :

(a) 158/3 cm2

(b) 154/3 cm2

(c) 150/3 cm2

(d) 152/3 cm2

Ans. b

22. It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday ?

(a) 0.008

(b) 0.08

(c) 0.004

(d) 0.006

Ans. a

23. If A and B are (-2, -2) and (2, -4), respectively, find the coordinates of P such that AP=3/7 AB and P lies on the line segment AB.

(a) (2/7,20/7)

(b) (-2/7, -20/7)

(c) (3/7, 19/7)

(d) (-3/7, -19/7)

Ans.  b

24.  sin 18°/cos 72° =…..

(a) 1

(b) 2

(c) 3

(d) 4

Ans. a

25. The LCM of two numbers is 1200. Which of the following can not be their HCF ?

(a) 600

(b) 500

(c) 400

(d) 200

Ans. b

26. Find the polynomial whose zeroes are 1, – I and I :

(a) x3 – x2 -x +1

(c) x3 +x2 + x -1

(b) x3 + x2 -x+ 1

(d) x3– x2 +x +1

Ans. a

27. If sin A = , then 8/ 17 sec A cos A + cosec A cos A= .. .

(a) 23/8

(b) 15/ 8

(c) 8/15

(d) 6/23

Ans.  a

28. Two concentric circles are of radii 5 cm and 3 cm. The length of the chord of the larger circle which touches the smaller circle is :

(a) 10 cm

(b) 8 cm

(c) 18 cm

(d) 12 cm

Ans. B

29. A child has a die whose six faces show the letters as given below : A D C D E A The die is thrown once. What is the probability of getting A ? 1

(a) 1/6

(b)1/2

(d)1/3

(c) 3/4

Ans. d

30. The product of two irrational numbers:

(a) Is always a rational number

(b) Is always an irrational number

(c) Can be a rational or an irrational number

(d) None of these

Ans. c

32. If the zeroes of the quadratic polynomial x2 + (a+1) x+ b are 2 and 3, then :

(a) a= -7; b=-1

(b) a = 5; b=-1

(c) a=2; b=-6

(d) a= 0; b=-6

Ans.  d

33. 3 sin2 20°-2 tan2 45°+3 sin2 70° =

(a) 0

(b) 1

(d) -1

(c) 2

Ans.  b

34. For what value of k will the following pair of linear equations have infinitely many  solutions : kx + 3y – (k-3)= 0 and 12x + ky –k=0

(a) 4

(b) 3

(c) 6

(d) 2

Ans. c

35. A die is thrown twice. What is the probability that 5 will come up at least once ?

(a) 11/36

(b) 25/36

(c)1/6

(d) 2/6

Ans. a 4

36. The linear pair of equations: 5x-8y+ 1 =0 3x-(24/5)y + 3/5= 0  has:

(a) A unique solution

(b) No solution

(c) Infinitely many solutions

(d) None of these

Ans.  c

37. Find the area of a triangle ABC formed by the points A(5, 2), B(4, 7) and C(7,-4):

(a) 4 square units

(b) 3 square units

(c) 2 square units

(d) 5 square units

Ans. c

38. If cos (40° + A) = sin 30°, then A =…….

(a) 60°

(b) 20°

(c) 40°

(d) 30°

Ans.  b

39. The area of a circle that can be inscribed in a square of side 8 cm is :

(a) 12 pi cm2

(b) 9 pi cm2

(c) 16 pi cm2

(d) 36 pi cm2

Ans. c

40. A piggy bank contains hundred 50p coins. fifty Rs 1 coins, twenty Rs 2 coins and ten3 Rs 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin will be a 50 p coin ?

(a)5/9

(b)6/9

(c) 8/9

(d) 7/9

Ans. a           #### Maths Sample Paper 1

1. Two numbers are in the ratio 15:11.  If their HCF is 13, then the numbers are:

(b) 105, 77

(a) 75, 55

(c) 15, 11

(d) 195, 143

Ans. d

2. Find the values of x and y from the equations : x-y= 3 and x/3+y/2=5

(a) x = 6, y = 9

(b) x= 9, y= 6

(c) x= 10, y = 5

(d) None of these

Ans.  b

3. If the points (a, 0), (0, b) and (1, 1) are collinear, then :

(a) 1/a+1/b=2

(b) 1/a+1/ b= 1

(c) 1/a+1/b = 0

(d) 1/a+1/b=4

Ans. b

4. Which of the following is a factor of the polynomial p(x) = (x)3 + 4x + 5 ?

(a) (x – 1)

(c) (x -2)

(d) (x + 2)

(b) (x+1)

Ans. b

6. The HCF of 6, 72 and 120 is:

(a) 4

(b) 8

(c) 16

(d) 6

Ans. d

7. The following pair of linear equations: 3x+2y = 5 and 2x – 3y = 7 is :

(a) Consistent

(b) Inconsistent

(c) Both (a) as well as (b)

(d) None of these

Ans.  a

8. The word ‘tangent’ was introduced by..

(a) Yulak

(b) Thomas Fineke

(c) Aryabhatta

(d) None of these.

Ans. b

9. The maximum number of zeroes of a quadratic polynomial is :

(a) 1 0

(b) 2

(c) 3

(d) 4

Ans. b

10. The area of a quadrilateral whose vertices taken in order, are (- 4, -2), (-3, -5), (3, -2) and (2, 3):

(a) 20 sq. units

(c) 26 sq. units

(b) 24 sq. units

(d) 28 sq. units

Ans. d

11. A line intersecting a circle in two points is called :

(a) Tangent

(c) Both (a) as well as (b)

(b) Chord

(d) None of these

Ans. b

12. Odd number for any positive integer n will be :

(b) n+1

(c) 2n + 1

(d) 2n

(a) n

Ans. c

13. The zeroes of the quadratic polynomial x2 + 99x + 127 are :

(a) Both positive

(b) Both negative

(c) One positive and one negative

(d) Equal

Ans.  b

14. If the distance between two parallel tangents of a circle is 18 cm, then its radius is :

(a) 10 cm

(b) 9 cm

(c) 8 cm

(d) 11 cm

Ans. b

15. The area of a circle is 2464 cm2. Its radius is :

(a) 14 cm

(c) 28 cm

(b) 21 cm

(d) 35 cm

Ans. c

16. If 5 tan θ  4, then : (5 sin θ – 4 cos θ)/(5 sin 0 +4 cos 0 )

(a) 5

(d)

(b) 0

(c)

Ans.  b

17. The distance between the points (0, 5) and (- 5, 0) is :

(b) 5sq2

(c) 10

(d) 2sq5

(a) 5

Ans. b

18. If P(E) = 0.08, then the value of P(E) is

(a) 0.92

(b) 0.95

(c) 0.90

(d) 0.85

Ans. a

19. The pair of linear equations : x- 3y – 3 = 0 and 3x – 9y – 2 = 0 has :

(a) A unique solution

(b) No solution

(c) Infinitely many solutions

(d) None of these

Ans. b

20. A dice is thrown once. The probability of getting an odd number is :

(a)

(b)

(c) 3

(d) 4

Ans. a

21. The area of the sector of a circle of radius R and central angle θ° is :

(a) 180°x 2π R

(b) θ/180° × 2πR?

(d) θ/720°× 2πR2

(c) θ/360° × 2πR

Ans.  d

22. A dice is thrown once. The probability of getting a prime number is :

(a) 2/3

(c) 1/2

(d) 1/4

(b) 1/3

Ans.  c

23. The distance between the points A (a + b, a – b) and B(a-b, a-b) is :

(a) √a2 +b2

(b) a + b

(c) √2/a2 +b2

(d) √a2-b2

Ans.  c

24. sin (45° + θ) cos (45° –θ )

(b) 0

(d) 1

(a) 2 cos θ

(c) 2 sin θ

Ans.  b

25. Given that LCM (306, 657) 22338, The HCF of these numbers is :

(b) 9

(a) 7

(c) 11

(d) 14

Ans. b

26. If a and B are the zeroes of the polynomial x2 + x+ 1, then 1/alpha+ 1/beta

(b) 1

(a) 0

(c) -1

(d) None of these

Ans.  c

27. tan 48° tan 23° tan 42° tan 67° = . ..

(c) 1

(d) 1/3

(b)1/2

(a) 0

Ans. c

29. One card is drawn from a well-shuffled deck of 52 cards. The probability of getting a face card is :

(a) 1/13

(b) 2/3

(c) 3/13

(d) 4/13

Ans. a

30. If A = 2n + 13 and B = n+ 7, where n is natural number, then HCF of A and B is

(a) 2

(b) 1

(c) 3

(d) 4

Ans. c

31. The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour ?

(a) 4275

(b) 4475

(c) 4575

(d) 4375

Ans. b

32. If p(x) = ax2 + bx + c, then – b/a =…….

(a) 0

(c) Product of zeroes

(d) Sum of zeroes

(b) 1

Ans.  d

33. If sin (A + B) = 1, then the value cos (A – B) is :

(b) 1

(a) sin 2B

(c) 0

(d) None of these

Ans. c

34. Which of the following pairs of linear equations is consistent ?

(a) x + y = 5; 2x+ 2y= 10

(b) x – y = 8; 3x – 3y = 16

(C) 2x-2y-2=0; 4x-4y-5 0

(d) 2y-3x-3 = 0; 4x – 5y- 4 = 0

Ans. a

35. The probability of getting a rotten egg from a lot of 400 eggs is 0.035. The number of rotten eggs in the lot is :

(a) 21

(b) 7

(c) 28

(d) 14

Ans. c

36. The solution of the following pair of linear  equations is : and 3x + 2y = 4 8x + 5y = 9

(a) x= 2; y=3

(b) x =-2; y=5

(c) x= 3; y=2

(d) x =-5; y=2

Ans.  b

37. The distance of the point (-6, 8) from the origin is :

(a) 6

(c) 5

(b) 10

(d) 5√ 2

Ans. b

38. 1+ tan2 A/ 1+ cot2 A =

(c) cot2 A

(a) sec2 A

(d) tan2A

(b) -1

Ans. a

39. Five cards- the ten, jack, queen, king and A ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. What is the probability that the card is the queen

(a)3/5

(b) 4/5

(c)2/5

(d) 1/5

Ans. d

40. A lot consists of 144 ball pens of which 20 are defective and the others are good. You will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to you. What la the probability that you will buy it ?

(a) 5/36

(b) 31/36

(c) 6/36

(d)9/36

Ans. c

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