Class 10 Pre-Board Sample Paper 2024 Maths Standard

2024

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Page 1 Sample Paper 29 CBSE Mathematics Class 10

Sample Paper
Class- X Exam - 2023-24
Mathematics - Standard

Time Allowed: 3 Hours Maximum Marks : 80
General Instructions :
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment (04 marks each) with sub-parts.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and 2 Questions
of 2 marks has been provided.
8. Draw neat figures wherever required. Take π = 227 wherever required if not stated.

Section - A

Section A consists of 20 questions of 1 mark each.

1. Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14 , then the equation of the second
line will be
(a) 12x + 9x = 42 (b) 12x + 9y = 5
(c) 12x + 8y = 15 (d) 12x + 8y = 42

2. If the height and length of the shadow of a man are equal, then the angle of elevation of the sun is,
(a) 45c (b) 60c
(c) 90c (d) 120c

3. A die is thrown once. What is the probability of getting a prime number?
1
(a) 3 (b) 23
1
(c) 2 (d) 14

4. Thus (a) is correct option. If one root of the equation (k − 1) x2 − 10x + 3 = 0 is the reciprocal of the other then
the value of k is .........
(a) 2 (b) 3
(c) 4 (d) 5

5. If p and q are the zeroes of polynomial f ^x h = 2x2 − 7x + 3 , the value of p2 + q2 will be
39
(a) 5 (b) 395
37
(c) 4 (d) 374

Page 2 Sample Paper 29 CBSE Mathematics Class 10

6. Select the least number that is divisible by all numbers between 1 and 10 (both inclusive).
(a) 2520 (b) 5040
(c) 1010 (d) 2020

7. If m and n are the zeroes of the polynomial 3x2 + 11x − 4 , then value of mn + mn will be
(a) 12
145 (b) - 145
12

(c) - 145
12 (d) 145
12

8. The quadratic equation x2 + x − 5 = 0 has
(a) two distinct real roots (b) two equal real roots
(c) no real roots (d) more than 2 real roots

9. The 4th term from the end of an AP - 11, - 8 , - 5 , ....., 49 is
(a) 37 (b) 40
(c) 43 (d) 58

1 - p 1 - 2p
10. The common difference of the AP 1 , , , ... is
p p p
(a) 1 (b) 1
p

(c) -1 (d) - 1
p

11. If the point C (k, 4) divides the line segment joining two points A (2, 6) and B (5, 1) in ratio 2 : 3, the value of k
is ......... .
5
(a) 16 (b) 165
9
(c) 5 (d) 59

12. If x = 3 sin θ + 4 cos θ and y = 3 cos θ − 4 sin θ then x2 + y2 is
(a) 25 (b) 45
(c) 7 (d) 49

13. TABC and TBDE are two equilateral triangle such that D is the mid-point of BC . Ratio of the areas of triangles
ABC and BDE is ................. .
(a) 1 : 1 (b) 3 : 1
(c) 2:1 (d) 4 : 1

14. In the figure given below, ABCD is a rectangle. The values of x and y will be



Continue on next page....

Page 3 Sample Paper 29 CBSE Mathematics Class 10

(a) 3 and 19 (b) 19 and 3
(c) 4 and 18 (d) 18 and 4

15. If k + 1 = sec2 θ ^1 + sin θh^1 − sin θh, then the value of k. will be
(a) 0 (b) 1
(c) 2 (d) 15

16. If the sum of the areas of two circles with radii R1 and R2 is equal to the area of a circle of radius R , then
(a) R1 + R2 = R (b) R12 + R22 = R2
(c) R1 + R2 < R (d) R12 + R22 < R2

17. The base radii of a cone and a cylinder are equal. If their curved surface areas are also equal, then the ratio of the
slant height of the cone to the height of the cylinder is
(a) 2 : 1 (b) 1 : 2
(c) 1:3 (d) 3 : 1

18. While computing mean of grouped data, we assume that the frequencies are
(a) evenly distributed over all the classes
(b) centred at the class marks of the classes
(c) centred at the upper limits of the classes
(d) centred at the lower limits of the classes


In the question number 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the
correction option.

19. Assertion : The equation x2 + 3x + 1 = ^x − 2h2 is a quadratic equation.
Reason : Any equation of the form ax2 + bx + c = 0 where a ! 0 , is called a quadratic equation.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

20. Assertion : If in a circle, the radius of the circle is 3 cm and distance of a point from the centre of a circle is 5 cm,
then length of the tangent will be 4 cm.
Reason : (hypotenuse) 2 = (base) 2 + (height) 2
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Page 4 Sample Paper 29 CBSE Mathematics Class 10

Section - B

Section B consists of 5 questions of 2 marks each.

21. Explain whether 3 # 12 # 101 + 4 is a prime number or a composite number.

22. Form a quadratic polynomial p ^x h with 3 and - 2 as sum and product of its zeroes, respectively.
5


O

If α and β are the zeroes of the polynomial f (x) = 5x2 − 7x + 1 then find the value of ` αβ + αβ j

23. If A ^ m3 , 5h is the mid-point of the line segment joining the points Q (- 6, 7) and R (- 2, 3), then what is the value
of m ?

24. In Figure, in TABC , DE z BC such that AD = 2.4 cm, AB = 3.2 cm and AC = 8 cm, then what is the length
of AE ?



O
In Figure +D = +E and AD = AE , prove that TBAC is an isosceles triangle.
DB EC

25. A bag contains cards bearing numbers from 11 to 30. A card is taken out from the bag at random. Find the
probability that the selected card has multiple of 5 on it.

Section - C


Section C consists of 6 questions of 3 marks each.

26. Given that 2 is irrational, prove that (5 + 3 2 ) is an irrational number.

Page 5 Sample Paper 29 CBSE Mathematics Class 10

27. What is the value of x in given figure?

28. Evaluate : cos 45º + 1
sec 30º sec 60º

29. An isosceles triangle ABC , with AB = AC , circumscribes a circle, touching BC at P , AC at Q and AB at R .
Prove that the contact point P bisects BC .

30. A glass is in the shape of a cylinder of radius 7 cm and height 10 cm. Find the volume of juice in litre required to
fill 6 such glasses. Use π = 227


O
The volume of a right circular cylinder with its height equal to the radius is 25 71 cm3 . Find the height of the
cylinder. ^Use π = 227 h

31. Find the mode of the following frequency distribution :

Class 15-20 20-25 25-30 30-35 35-40 40-45
Frequency 3 8 9 10 3 2



O
The marks obtained by 110 students in an examination are given below

Marks 30-35 35-40 40-45 45-50 50-55 55-60 60-65
Number of Students 14 16 28 23 18 8 3

Find the mean marks of the students.

Section - D

Section D consists of 4 questions of 5 marks each.

32. Write all the values of p for which the quadratic equation x2 + px + 16 = 0 has equal roots. Find the roots of the
equation so obtained.



O
In a flight of 600 km, an aircraft was slowed down due to bad weather. The average speed of the trip was reduced
by 200 km/hr and the time of flight increased by 30 minutes. Find the duration of flight.

Page 6 Sample Paper 29 CBSE Mathematics Class 10

33. If the point P ^x, y h is equidistant from the points Q ^a + b, b − a h and R ^a − b, a + b h , then prove that bx = ay .

34. a, b and c are the sides of a right triangle, where c is the hypotenuse. A circle, of radius r , touches the sides of
the triangle. Prove that r = a + b − c .
2


O
In figure O is the centre of a circle of radius 5 cm. T is a point such that OT = 13 cm and OT intersects circle at
E . If AB is a tangent to the circle at E , find the length of AB , where TP and TQ are two tangents to the circle.

35. Four equal circles are described at the four corners of a square so that each touches two of the others. The shaded
area enclosed between the circle is 247 cm2. Find the radius of each circle.

Section - E

Case study based questions are compulsory.

36. Arc of a Baby Swing : When Mackenzie’s baby swing is started, the first swing (one way) is a 30 inch arc. As the
swing slows down, each successive arc is 1.5 inch less than the previous one.
(i) Find the length of the tenth swing.
(ii) How far Mackenzie has travelled during the 10 swings ?

Page 7 Sample Paper 29 CBSE Mathematics Class 10

37. Statue of Unity : It is a colossal statue of Indian statesman and independence activist Sardar Vallabh bhai Patel,
who was the first Deputy Prime Minister and Home minister of independent India.

Patel was highly respected for his leadership in uniting the 562 princely states of India to form the single Union
of India. It is located in the state of Gujarat and it is the world’s tallest statue.
(i) For a person standing 240 m from the center of the base of the statue, the angle of elevation to the top of
the statue is 45c . How tall is the statue?
(ii) A cop in helicopter near the top of the statue, notices a car wreck some distance from the statue. If the angle
of depression from the cop’s eyes to the wreck is 60c , how far away is the accident from the centre of base
of the statue?

38. Eight Ball : This is a game played on a pool table with 15 balls numbered 1 through 15 and a cue ball that is solid
white. Of the 15 numbered balls, 8 are a solid (nonwhite) color and numbered 1 through 8, and seven are striped
balls numbered 9 through 15.

The fifteen numbered pool balls (no cueball) are placed in a large bowl and mixed, then one is drawn out.
(i) What is the probability of drawing the eight ball ?
(ii) What is the probability of drawing a number greater than fifteen ?
(iii) What is the probability of drawing an even number ?
(iv) What is the probability of drawing a multiple of three ?



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