The following Questions of **Sample Paper Class 10 2021-22 Maths** are given below.

## Maths class 10 cbse sample paper 2021-22 | 10th class Maths Model paper

**Maths Sample Paper **5

**1. The largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 is : **

(a) 11

(b) 17

(c) 34

(d) 45

Ans. b

**2. 5 pencils and 7 pens together cost rs. 50, whereas 7 pencils and 5 pens together cost rs. 46. The cost of one pencil and that of one pen is : **

(a) rs.5, rs 3

(b) rs.3, rs.5

(c) rs.4, rs. 4

(d) None of these

Ans. b

**3. The area of a triangle whose vertices are (2, 3), (-1,0) and (2, -4) is : **

(a) 21/2 Square units

(b) 21 Square units

(c) 42 Square units

(d) None of these

Ans. a

**4. Find the quadratic polynomial, the sum and product of whose zeroes are -3 and 2 respectively : **

(a) x^{2} -3x – 2

(c) x^{2} – 3x + 2

(b) x^{2} + 3x + 2

(d) x^{²} + 3x – 2

Ans. b

**5. (1+ tan ^{2} A) / (1+ cot^{2} )=….. **

(a) sec^{2} A

(c) cot^{2} A

(b)-1

(d) tan^{2} A

Ans. d

**6. The HCF of 306 and 657 is 9. Their LCM is : **

(b) 22338

(a) 23338

(d) 26338

(c) 24338

Ans. b

**7. Solve the following equations: x+y= 14 x-y= 4 **

(a) x= 5; y=9

(c) x=-5; y=-9

(d) x=-9, y=-5

(b) x=9; y=5

Ans. b

**8. The number of tangents that can be drawn to a circle through a point outside it is: **

(a) 1

(b) 2

(c) 3

(d) 4

Ans. b

**9. If one zero of the cubic polynomial x ^{3}+ax^{2}+bx+c is 1, then what will be the product of its other two zeroes ? **

(a) b-a-1

(b) b-a+1

(d) a-b-1

(c) a-b+1

Ans. b

**10. If the point Q (0, 1) is equidistant from the points P (5, -3) and R(x, 6), then the value of x is : **

(a) ±2

(b) ±3

(c) ±4

(d) ±5

Ans. c

**11. A circle can have parallel tangents. **

(a) three

(b) Four

(c) Two

(d) Infinite

Ans. c

**12. The LCM of 2 ^{3} x 3^{2} and 2^{2} x 3^{3} is….. **

(a) 2^{3}

(b) 3^{3}

(c) 2^{3} x 3^{3}

(d) 2^{2} x 3^{2}

Ans. c

**13. The quadratic polynomial, the sum and product of whose zeroes are 1/4 and -1 respectively are : **

(a) 4x^{2} – x – 4

(b) x^{2} – 4x + 1

(c) 4x^{2} + x+ 4

(d) x^{2} + 4x – 4

Ans. a

**15. Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60° : **

(b) 136/7 cm^{2}

(a) 132/7cm^{2}

(c) 125/7cm^{2}

(d) 122/7cm^{2}

Ans. a

**16. 9 sec ^{2} A- 9 tan^{2} A =…… **

(b) 9

(a) 1

(d) 0

(c) 8

Ans. b

**17. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2,-1): **

(a) 20 square units

(b) 21 square units

(c) 22 square units

(d) 24 square units

Ans. d

**18. A box contains 3 blue, 2 white, and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will be red ? **

(a) 3/9

(b) 5/9

(c) 4/9

(d) 2/9

Ans. c

**19. The solution of the following pair of linear equations is : 6x + 3y = 6xy and 2x + 4y = 5xy **

(a) x = 2; y= 3

(c) x=-1; y=-2

(b) x= 1; y=2

(d) x= 3; y=4

Ans. b

**20. 12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one : **

(a) 1/11

(b) 1/12

(c) 5/16

(d) 11/12

Ans. d

**21. If the circumference of a circle is equal to the sum of the circumferences of two circles of diameters 36 cm and 20 cm, then its radius is : **

(a) 28 cm

(b) 16 cm

(c) 56 cm

(d) 42 cm

Ans. a

**22. Two dice are thrown together. The probability of getting 3 as the sum is : **

(b) 1/18

(a) 1/36

(d) 3/18

(c) 2/18

Ans. b

**23. A(4, 5). B (x, y), C(6, -3) and D (2,-3) are the vertices of rhombus. The value of x is: **

(b) 5

(a) 2

(c) 6

(d) 8

Ans. d

**24. If tan A = cot B, then, A + B= ? **

(b) 90°

(a) 45°

(c) 60°

(d) 30°

Ans. b

**25. The largest number that will divide 70 and 125 leaving remainders 5 and 8 is : **

(a) 13

(b) 65

(c) 875

(d) 1750

Ans. a

**26. If √(5/3) and -√(5/3) are the two zeroes of the polynomial 3x ^{4}+ 6x^{3}-2x^{2}-10x-5, then its other two zeroes are : **

(a) 1, 1

(b) 1,-1

(c) -1, -1

(d) None of these

Ans. c

**27. If sin A + sin ^{2} A = 1, then cos^{2} A + cos^{4} A …….. **

(a) 1

(b) 1/2

(c) 2

(d) 3

Ans. a

**28. In two concentric circles, the chord of the larger circle which touches the smaller circle is at the point of contact: …… **

(a) Divided in the ratio 1: 2

(b) Bisected

(c) Divided in the ratio I: 3

(d) None of these

Ans. b

**29. Five cards-the ten, jack, queen, king and 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 ? **

(b)4/5

(a) 3/5

(d)1/5

(c) 2/5

Ans. d

**30. The sum of two numbers is 216 and their HCF is 27. The numbers are : **

(b) 154, 162

(a) 27, 189

(d) 81, 189

Ans. a

**31. A chord of a circle of radius 10 cm subtends a right angle at the centre. The area of the corresponding major sector is : **

(b) 235.5 cm²

(a) 230.5 cm^{2}

(d) 245.5 cm²

(c) 228.5 cm^{2}

Ans. b

**32. If alpha and Beta are the zeroes of the quadratie polynomial x ^{2}– 6x +k and 3alpha + 2Beta= 20, then k = ……. **

(a) 8

(b) -16

(c)-8

(d) 2

Ans. b

**33. [cos A/ (1+sin A)] + [(1+sin A)/cos A]=…… **

(a) 2 sec A

(b) 2 sin A

(c) 2 cos A

(d) 2 tan A

Ans. a

**34. The pair of linear equations, 5x-8y+1= 0 and 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

**35. There are 40 students in Class X of a school of whom 25 are girls and 15 are boys. The class teacher has to select one student as a class representative. She writes the name of each student on a separate card, the cards being identical. Then she puts cards in a bag and stirs them thoroughly. She then draws one card from the bag. What is the probability that the name written on the card is the name of a girl ? **

(b) 1/2

(a) 3/8

(c) 5/8

(d) 2/3

Ans. c

**36. The following pair of linear equations: 5x- 3y =11 and -10x + 6y=-22 is : **

(a) Consistent

(b) Inconsistent

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

(d) None of these

Ans. a

**37. If the distance between the points A (2, -2) and B (-1, x) is 5, then x= **

(a) 1

(b) -1

(c) 2

(d) -2

Ans. c

**38. Cos 45° /sec 30° +cosec 30°= 3 **

(a) 3 √2-√6/8

(b) 3√2-6/8

(c) 4√2+7 /8

(d) 4√2-7/8

Ans. b

**39. A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. The area of the corresponding minor sector is: **

(a) 22.4 cm2

(b) 20.4 cm2

(c) 28.4 cm2

(d) 32.4 cm2

Ans. b

**40. A die is thrown twice. What is the probability that 5 will not come up either time ? **

(a) 11/36

(b)25/ 36

(d) 29/36

(c) 5/36

Ans. b

Maths Sample Paper 1 Class 10 |

Maths Sample Paper 2 Class 10 |

Maths Sample Paper 3 Class 10 |

Maths Sample Paper 4 Class 10 |

Maths Sample Paper 5 Class 10 |

**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

Maths Sample Paper 1 Class 10 |

Maths Sample Paper 2 Class 10 |

Maths Sample Paper 3 Class 10 |

Maths Sample Paper 4 Class 10 |

Maths Sample Paper 5 Class 10 |

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