Jemapu 02

CBSE Maths Class 10 Sample Paper 02 Page 1
Sample Paper 02
Class - 10th Exam - 2024 - 25
Mathematics - Standard
Time : 3 Hours Max. Marks : 80
General Instructions :
1. This question paper contains 38 questions.
2. This Question Paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are
Assertion - Reason based questions of 1 mark each.
4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each.
5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each.
6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each.
7. In Section E, Questions no. 36-38 are case study based questions carrying 4 marks each with sub parts
of the values of 1, 1 and 2 marks each respectively.
8. All Questions are compulsory. However, an internal choice in 2 Question of Section B, 2 Questions of
Section C and 2 Questions of Section D has been provided. An internal choice has been provided in all
the 2 marks questions of Section E.
9. Draw neat and clean figures wherever required.
10. Take π = 227 wherever required if not stated.
11. Use of calculators is not allowed.
Section - A
Section A consists of 20 questions of 1 mark each.
1. If α and β are the roots of ax2 − bx + c = 0 (a ! 0), then value of α + β is
(a) b (b) a
a b
(c) 2a (d) a
b 2b
2. What are the values of x and y for the following pair of linear equations ?
99x + 101y = 499 and 101x + 99y = 501
(a) 3 and 6 (b) 3 and 2

(c) 2 and 3 (d) 6 and 3
3. The zeroes of polynomial p ^x h = ax2 + bx + c are reciprocal of each other if

(a) b = 2a (b) c = b
(c) b = a (d) c = a
4. If - 1 is a zero of the polynomial p ^x h = kx2 − 4x + k, the value of k is

(a) –4 (b) –2
(c) 2 (d) 4
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Page 2 Sample Paper 02 CBSE Maths Class 10
5. If a number x is chosen at random from the numbers - 3 , - 2 , - 1. 0, 1, 2, 3, then What is the probability
of x2 < 4 ?
(a) 4 (b) 3
7 7
(c) 1 (d) 2
7 7
6. Which of the following value of k should be selected so that the pair of equations x + 2y = 5 and
3x + ky + 15 = 0 has a unique solution ?
(a) k ! 5 (b) k ! 6
(c) k = 5 (d) k = 6
7. The quadratic equation x2 + 3x + 2 2 = 0 has

(a) two distinct real roots (b) two equal real roots
(c) no real roots (d) more than 2 real roots
8. A ladder 10 m long reaches a window 8 m above the ground. The distance of the foot of the ladder from
the base of the wall is ................ m.
(a) 8 m (b) 2 m
(c) 6 m (d) 4 m
9. The value of x for which 2x, (x + 10) and (3x + 2) are the three consecutive terms of an AP, is
(a) 6 (b) - 6
(c) 18 (d) - 18
10. If points A (- 3, 12), B (7, 6) and C (x, 9) are collinear, then the value of x is ......... .
(a) 2 (b) 3
(c) 4 (d) 5
11. If the sum of the circumferences of two circles with radii R1 and R2 is equal to the circumference of a
circle of radius R , then
(a) R1 + R2 = R (b) R1 + R2 > R
(c) R1 + R2 > R (d) R1 + R2 < R
12. The value of sin2 41º + sin2 49º will be

(a) 1 (b) 2
(c) 2 (d) 3
13. The number 7 will have -

75
(a) non-terminating repeating decimal expansion.
(b) terminating decimal expansion.
(c) non-terminating non repeating decimal expansion.
(d) terminating non repeating decimal expansion
14. A tree casts a shadow 15 m long on the level of ground, when the angle of elevation of the sun is 45c. The
height of a tree is
(a) 10 m (b) 14 m
(c) 8 m (d) 15 m
15. The famous mathematician associated with finding the sum of the first 100 natural numbers is
(a) Pythagoras (b) Newton
(c) Gauss (d) Euclid
16. If the perimeter of one face of a cube is 20 cm, then its surface area is
(a) 120 cm2 (b) 150 cm2
(c) 125 cm2 (d) 400 cm2
17. sin2 60c − 2 tan 45c − cos2 30c = ?

(a) 2 (b) –2
(c) 1 (d) –1
18. If xi ’s are the mid-points of the class intervals of grouped data, f i ’s are the corresponding frequencies and
x is the mean, then / (f i xi - x ) is equal to
(a) 0 (b) - 1
(c) 1 (d) 2
19. Assertion : The two tangents are drawn to a circle from an external point, then they subtend equal angles
at the centre.
Reason : A parallelogram circumscribing a circle is a rhombus.
(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 : The values of x are - a , a for a quadratic equation 2x2 + ax − a2 = 0 .

2
Reason : For quadratic equation ax2 + bx + c = 0
2
x = − b ! b − 4ac
2a
(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.
Section - B
Section B consists of 5 questions of 2 marks each.
21. The mid-point of the line-segment AB is P (0, 4), if the coordinates of B are (- 2, 3) then find the co-
ordinates of A.
22. Two different dice are tossed together. Find the probability :
(i) that the number on each die is even.
(ii) that the sum of numbers appearing on the two dice is 5.
23. Given that HCF (306, 1314) = 18. Find LCM (306, 1314).
24. If α and β are the zeroes of a polynomial x2 − 4 3 x + 3, then find the value of α + β − αβ .
O
If one of the zeroes of the quadratic polynomial f ^x h = 14x2 − 42k2 x − 9 is negative of the other, find the
value of ‘k ’.
25. In the given figure, G is the mid-point of the side PQ of TPQR and GH || QR. Prove that H is the mid-
point of the side PR or the triangle PQR.
O
In the figure of TABC, the points D and E are on the sides CA, CB respectively such that DE || AB,
AD = 2x, DC = x + 3, BE = 2x − 1 and CE = x. Then, find x.
Section - C
Section C consists of 6 questions of 3 marks each.
26. Evaluate :
3 tan2 30º + tan2 60º + cosec 30º − tan 45º
cot2 45º
27. Prove that the rectangle circumscribing a circle is a square.
28. A solid is in the shape of a cone surmounted on a hemisphere. The radius of each of them being 3.5 cm
and the total height of the solid is 9.5 cm. Find the volume of the solid.
O
A heap of rice is in the form of a cone of base diameter 24 m and height 3.5 m. Find the volume of the
rice. How much canvas cloth is required to just cover the heap?
29. Write the smallest number which is divisible by both 306 and 657.
30. The mean of the following distribution is 48 and sum of all the frequency is 50. Find the missing
frequencies x and y .
Class 20-30 30-40 40-50 50-60 60-70

Frequency 8 6 x 11 y
O
The table below shows the daily expenditure on food of 25 households in a locality. Find the mean daily
expenditure on food.
Daily expenditure (in <) 100-150 150-200 200-250 250-300 300-350

Number of households 4 5 12 2 2
31. 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 ................. .
Section - D
Section D consists of 4 questions of 5 marks each.
32. Prove that the point ^3, 0h , ^6, 4h and ^- 1, 3h are the vertices of a right angled isosceles triangle.
33. Find the values of k for which the equation ^3k + 1h x2 + 2 ^k + 1h x + 1 has equal roots. Also find the roots.
O
A person on tour has < 4200 for his expenses. If he extends his tour for 3 days, he has to cut down his
daily expenses by < 70. Find the original duration of the tour.
34. In figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC
, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, +B = 90c and
DS = 5 cm, then find the radius of the circle (in cm).
O
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the
centre of the circle.
35. In Figure, a square OABC is inscribed in a quadrant OPBQ . If OA = 15 cm , find the area of the shaded
region. (Use π = 3.14 ).
Section - E
Section E consists of 3 case study based questions of 4 marks each.
36. Eiffel Tower : The Eiffel Tower is a landmark and an early example of wrought-iron construction on a
gigantic scale. The lower section consists of four immense arched legs set on masonry piers. The legs curve
inward until they unite in a single tapered tower. Platforms, each with an observation deck, are at three
levels; on the first is also a restaurant.
The tower, constructed of about 7000 tons of iron, has stairs and elevators. A meteorological station, a
radio communications station, and a television transmission antenna, as well as a suite of rooms that were
used by Eiffel are located near the top of the tower.
(i) For a person standing 324 m from the center of the base of the Eiffel Tower, the angle of elevation
to the top of the tower is 45c . How tall is the Eiffel Tower?
(ii) A car is moving at uniform speed towards the Eiffel tower. It takes 15 minutes for the angle of
depression from the top of tower to the car to change from 30c to 60c . After how much time after
this, the car will reach the base of the tower?
37. Bequests to Charity : At the time our mother left this Earth, she gave ` 90000 to her children of birth.
This we kept and each year added ` 30000 more, as a lasting memorial from the children she bore. When
` 4,20,000 is thusly attained, all goes to charity that her memory be maintained.
(i) What was the balance in the sixth year?
(ii) In what year was the goal of ` 420,000 met?
38. Double-six Dominos : It is a game played with the 28 numbered tiles shown in the diagram.
The 28 dominos are placed in a bag, shuffled, and then one domino is randomly drawn. Give the following
answer.
(i) What is the probability the total number of dots on the domino is three or less ?
(ii) What is the probability the total number of dots on the domino is greater than three ?
(iii) What is the probability the total number of dots on the domino does not have a blank half ?
(iv) What is the probability the total number of dots on the domino is not a “double” (both sides the
same) ?
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CBSE Maths Class 10 Sample Paper 02 Page 1

1. If α and β are the roots of ax2 − bx + c = 0 (a ! 0), then value of α + β is

(a) 3 and 6 (b) 3 and 2

3. The zeroes of polynomial p ^x h = ax2 + bx + c are reciprocal of each other if

4. If - 1 is a zero of the polynomial p ^x h = kx2 − 4x + k, the value of k is

7. The quadratic equation x2 + 3x + 2 2 = 0 has

12. The value of sin2 41º + sin2 49º will be

13. The number 7 will have -

17. sin2 60c − 2 tan 45c − cos2 30c = ?

20. Assertion : The values of x are - a , a for a quadratic equation 2x2 + ax − a2 = 0 .

27. Prove that the rectangle circumscribing a circle is a square.

Class 20-30 30-40 40-50 50-60 60-70

Daily expenditure (in <) 100-150 150-200 200-250 250-300 300-350

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