PRACTICE EXAMINATIONCLASS X – MATHEMATICS

2021-2022Duration: 90 Minutes MM: 40

General Instructions:● The question paper contains three parts A, B and C● Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted.● Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted● Section C consists of 10 questions based on two Case Studies. Attempt any 8 questions.● There is no negative marking.● Please ensure that the correct option is written along with the correct answer.---------------------------------------------------------------------------------------------------------------

SECTION -ASection A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted

1. A student was observing Railway tracks at secunderabad railway station, thesetracks represent a pair of linear equations as shown below, based on theobservation answer the questions given:

For the pair of linear equations shown in graph

a. c.𝑎

1

𝑎2

≠𝑏

1

𝑏2

𝑎1

𝑎2

=𝑏

1

𝑏2

b. d.𝑎

1

𝑎2

=𝑏

1

𝑏2

≠𝑐

1

𝑐2

𝑎

1

𝑎2

=𝑏

1

𝑏2

=𝑐

1

𝑐2

1

SHIV NADAR SCHOOL Practice Examination - Class X – Mathematics – November 2021 Page 1

2. The least number that is divisible by all the numbers between 1 and 5 (bothinclusive) is:

a. 60 c.12

b. 24 d. 220

1

3. If, in ΔABC, ∠B = 90°, then sin (A + C) =

a. 0 c. 12

b. d. 112

1

4. The path traced by the ball is given by the equation x – 16, then the value of2

𝜶𝜷(𝜶 + 𝜷) if 𝜶 and 𝜷 are the zeroes of the polynomial is:

a. 16 c. 6b. 0 d. 4

1

5. The given points P(5, -2), Q(6, 4) and R(7, -2) are the vertices of:

a. Equilateral Triangle c. Obtuse Triangleb. Isosceles Triangle d. Scalene Triangle

1

6. In the figure, AB is the diameter of the circle, AC = 6 cm and BC = 8 cm. Thearea of the shaded region is:

[Use π = 3.14]

a. 54.5cm c. 281cm2 2

b. 290cm d. 78.5cm2 2

1

SHIV NADAR SCHOOL Practice Examination - Class X – Mathematics – November 2021 Page 2

7. For two number A and B, HCF = 5, the LCM = 150, if A= 10, then B will be

a.25 c.75

b. 50 d. Cannot be determined

1

8. Sharat has ₹2 and ₹5 coins with him.If total number of coins are 16 and theamount of money is ₹ 50, then the number of ₹2 and ₹5 coins are :

a. 8 and 8 c. 10 and 6b. 6 and 10 d. 15 and 4

1

9. A bag contains 15 white and some black balls. If the probability of drawing ablack ball from the bag is twice that of drawing a white ball, the number ofblackballs in the bag is:

a. 30 c. 50b. 45 d. 55

1

10 The graph of the quadratic polynomial , having𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0discriminant equal to zero, will touch x -axis at exactly :

a. One point c. Three pointsb. Two points d. Can't say

1

11. The circumference of a circle is 22 cm. The area of its quadrant is:

[Use : ]π = 227

a. cm c. cm772

2 778

2

b. cm d. cm774

2 7716

2

1

12. If x tan 45° sin 30° = cos 30° tan 30°, then x is equal to :

a. c.3 2

1

SHIV NADAR SCHOOL Practice Examination - Class X – Mathematics – November 2021 Page 3

b. 1 d. 13

13. The decimal expansion of the rational number will terminate after51150

a. one decimal place c. two decimal placesb. three decimal places d. It will not terminate

1

14. If then the value of ( is:4𝑡𝑎𝑛θ = 3, 𝑐𝑜𝑠 2θ − 𝑠𝑖𝑛 2θ)

a. c.425 1

b. d.725

1125

1

15. The number of zeroes of the given polynomial, is:(𝑥 + 1) 2(𝑥 + 2)(𝑥 − 3)

a. 2 c. 3b. 4 d. 1

1

16. If the pair of equations and has no solution, then2𝑥 + 3𝑦 = 7 𝑘𝑥 + 𝑦 = 12the value of k is_____

a. c. 323

b. d. -332

1

17. Two different dice are thrown together. The probability that the number obtainedis a doublet of odd number is:

a. c.1318

112

b. d.49

14

1

SHIV NADAR SCHOOL Practice Examination - Class X – Mathematics – November 2021 Page 4

18. Given that and are the zeroes of a quadratic polynomial such thatα βand . Select the quadratic polynomial having asα + β = 24 α − β = 8 α 𝑎𝑛𝑑 β

its zeroes.

a. c.𝑥 2 − 24𝑥 + 128 𝑥 2 + 24𝑥 − 128b. d.𝑥 2 − 128 + 24 𝑥 2 + 128𝑥 − 24

1

19. A circular park has a path of uniform width around it. The difference between

outer and inner circumference of the circular path is 132m. Its width is:

[Use ]π = 227

a. 22m c. 21m

b. 20m d. 24m

1

20. is equal to :8𝑐𝑜𝑠 230° + 4𝑠𝑖𝑛 230° − 4𝑡𝑎𝑛 20°

a. 3 c. 18b. 10 d. None of these

1

SECTION -B

Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted

21.The value of + sin A=

𝑐𝑜𝑠𝐴𝑐𝑜𝑡𝐴

a. cotA c. 2cosAb. 2sinA d. secA

1

SHIV NADAR SCHOOL Practice Examination - Class X – Mathematics – November 2021 Page 5

22. If the lines given by and are parallel, then3𝑥 + 2𝑘𝑦 = 2 2𝑥 + 5𝑦 + 1 = 0the value of k is______

a. c.54

154

b. d.25

32

1

23. A letter chosen at random from the letters of the words “CAPTAIN AMERICA”are placed at random in a row, if the probability that the letter chosen is a vowel

is in the form of , then the value of x is:142𝑥+2

a. 13 c. 12b. 14 d. 24

1

24. 416.3567893456432........ is

a. an Integer c. An Irrational Numberb. a rational number d. A natural Number

1

25. Which of these options complete the sentence below: 1

SHIV NADAR SCHOOL Practice Examination - Class X – Mathematics – November 2021 Page 6

The sum of the area of the four minor sectors is equal to the_________.

a. area of the semicircle of diameter rb. area of the circle of diameter 2rc. circumference of the circle of radius rd. circumference of the circle of diameter r

26. Two isosceles triangles have equal angles and their areas are in the ratio 16: 25.The ratio of corresponding heights is:

a. 4:5 c. 3:2b. 5:4 d. 5:7

1

27. If 2 and α are zeroes of , then the value of α is :𝑥 2 − 3𝑥 + 2

a. 2 c. 1b. 3 d. 5

1

28. A girl calculates that the probability of her winning the first prize in a lottery is0.08. If 6000 tickets are sold, then number of tickets she has bought is:

a. 40 c. 480b. 240 d. 750

1

29. Given that tan A = √3 and cos B = 0, then the value of B - A is:

a. 0 c. 60b. 90 d. 30

1

30. Two positive numbers have their HCF as 12 and their product as 6336.Thenumber of pairs possible for the numbers, is....

a. 2 c. 4b. 3 d. 5

1

SHIV NADAR SCHOOL Practice Examination - Class X – Mathematics – November 2021 Page 7

31. A fair dice is rolled. Probability of getting a number x such that 1 is:≤ 𝑥 ≤ 6,

a. 0 c. between 0 and 1b. d. 1> 1

1

32. On which of the following equations, the point of the form (m, –m) lies?a. c.𝑥 =− 𝑚 𝑦 = 𝑥b. d.𝑥 + 𝑦 = 0 𝑦 = 2𝑥

1

33 Three coins are tossed simultaneously. The probability of getting all heads is:

a. 1 c. 14

b. d. 12

18

1

34. The length of an arc of a circle with radius 12 cm is 10 π cm. The central angleof this arc is:

a. 120° 𝑐. 75°b. d. None of these6°

1

35. The graph of y = p(x) is given as:

The number of zeroes of p(x) are:

a. 7 c. 6b. 5 d. 4

1

SHIV NADAR SCHOOL Practice Examination - Class X – Mathematics – November 2021 Page 8

36. The line segment joining the points (3, -1) and (-6, 5) is trisected. Thecoordinates of point of trisection are :

a. (3,3) c. (3,-3)b. (-3,3) d. (3,-3)

1

37.If x = a cos θ and y = b sin θ, then b + =2𝑥 2 𝑎 2𝑦 2

a. c.𝑎 2𝑏 2 𝑎 4𝑏 4

b. d.𝑎𝑏 𝑎 2 + 𝑏 2

1

38. What is the greatest possible speed at which a man can walk 52 km and 91 km inan exact number of minutes?

a. 17 m/min c. 13m/minb. 7m/min d. 26 m/min

1

39. The area of an equilateral triangle is 9√3 cm sq. Taking each angular point ascentre, the circle is drawn with a radius equal to half the length of the side of thetriangle. The area of the triangle not included in the circles is:

[Take √3=1.73]

1

SHIV NADAR SCHOOL Practice Examination - Class X – Mathematics – November 2021 Page 9

a. 1.43 cm c. 1.23 cm2 2

b. 1.33 cm d. 1.13 cm2 2

40. Solve 2𝑥 + 3𝑦 = 11and 2𝑥 − 4𝑦 = −24 and hence the value of ‘m’ for such that

2y = mx + 4 is:

a. 3 c. -6b. 6 d. -3

1

SECTION -C

Case study based questions:

Section C consists of 10 questions of 1 mark each. Any 4 questions from each case studyare to be attempted.

CASE STUDY 1:

Minister of a state went to city Q from city P. There is a route via city Rsuch that PR ⊥ RQ. PR = 2 km and RQ = 2( + 7) km. He noticed that𝑥 𝑥there is a proposal to construct a 26 km highway which directly connects thetwo cities P and Q.

SHIV NADAR SCHOOL Practice Examination - Class X – Mathematics – November 2021 Page 10

Based on the above information, answer the following questions.

41. Which concept can be used to get the value of x?a. Thales theorem c. Pythagoras Theoremb. Converse of Thales Theorem d. Converse of Pythagoras Theorem

1

42. The value of x is :

a. 4 c. 5b. 6 d. 8

1

43. The value of PR is :

a. 10 km c. 15kmb. 20km d. 25km

1

44. The value of RQ is :

a. 12km c. 16kmb. 24km d. 20km

1

45. How much distance will be saved in reaching city Q after the constructionof the highway?

a. 10km c. 4kmb. 9km d. 8km

1

Case Study 2:

Mr. Jaskirat Singh is living in Jalandhar, Punjab. As per the government hetakes his dose of vaccine in the months of June 2021 in the Civil HospitalJalandhar. Now he wants to take his second dose. The following map showsthree vaccination centres near his home. O represents his home. Observethis condition and answer the following questions. Vaccination centre A, B& C as shown in the figure.

SHIV NADAR SCHOOL Practice Examination - Class X – Mathematics – November 2021 Page 11

46. The coordinates of the nearest vaccination centre is:

a. (3,1) c. (0,4)b. (4,2) d. (7,4)

1

47. According to the figure, vaccination centre B is dividing the line joiningvaccination centre A to C in the ratio of :

a. 2:3 c. 3:2b. 3:1 d. 1:1

1

48. Distance between centre A to C is:

a. 4 c. 412 2b. 5 d. 502

1

49. Assuming he went to centre B and doses are finished. Then what is theclosest distance he has to cover to reach another Vaccination centre?

a. c.4 2 2 2b. d. 62 2

1

50. A relation between x and y such that the point (x , y) is equidistant from thepoints A(3, 1) and B(6, 4) is :

1

SHIV NADAR SCHOOL Practice Examination - Class X – Mathematics – November 2021 Page 12

a. c.2𝑥 + 𝑦 = 21 𝑥 + 2𝑦 = 21b. d.𝑥 + 𝑦 = 42 𝑥 + 𝑦 = 7

SHIV NADAR SCHOOL Practice Examination - Class X – Mathematics – November 2021 Page 13