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SAMPLE QUESTION PAPER
Class X Session 2024- 25
MATHEMATICS BASIC (Code No.241)
TIME: 3 hours MAX.MARKS: 80
General Instructions:
Read the following instructions carefully and follow them:
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 Questions of section B, 2
Questions of section C and 2 Questions of section D has been provided. And 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 =22/7 wherever required if not stated. 11. Use of calculators is not allowed.
Section A
Section A consists of 20 questions of 1 mark each.
HCF OF ( 3
3
× 5
2
× 2 ), ( 3
2
× 5
3
× 2
2
4
× 5 × 2
3
) is
(A) 450 (B) 90 (C) 180 (D) 630
The system of linear equations represented by the lines l and m is
(A) consistent with unique solution (B) inconsistent
(C) consistent with three solutions (D) consistent with many solutions
The value of k for which the quadratic equation 𝑘𝑥
2
− 5 𝑥 + 1 = 0 does not have
a real solution, is
(A) 0 (B)
25
4
(C)
4
25
(D) 7
The distance between the points (𝑎, 𝑏) and (−𝑎, −𝑏) is
(A)√𝑎
2
2
(B) 𝑎
2
2
(C) 2 √𝑎
2
2
(D) 4√𝑎
2
2
In the given figure, PQ and PR are tangents to a circle centred at O. If
∠QPR= 35
∘
then ∠QOR is equal to
(A) 70
∘
(B) 90
∘
(C) 135
∘
(D) 145
∘
If △ 𝐴𝐵𝐶 ∼△ 𝑃𝑄𝑅 such that 3AB = 2PQ and BC=10 cm, then length QR is
equal to
(A) 10 cm (B) 15 cm (C)
20
3
cm (D) 30 cm
If 3 cot 𝐴 =4, where 0° < 𝐴 < 90°, then sec 𝐴 is equal to
(A)
5
4
(B)
4
3
(C)
5
3
(D)
3
4
In the given figure, 𝛥𝐵𝐴𝐶 is similar to
(A) 𝛥𝐴𝐸𝐷 (B) 𝛥𝐸𝐴𝐷 (C) 𝛥𝐴𝐶𝐵 (D) 𝛥𝐵𝐶𝐴
If H.C.F(420,189) = 21 then L.C.M(420,189) is
(A) 420 (B) 1890 (C) 3780 (D) 3680
The 4
𝑡ℎ
term from the end of the A.P − 8 , − 5 , − 2 , … , 49 is
(A) 37 (B) 40 (C) 1 (D) 43
In the given figure, if △ 𝑂𝐶𝐴 ∼△ 𝑂𝐵𝐷 then ∠𝑂𝐴𝐶 is equal to
DIRECTION: In the question number 19 and 20, a statement of Assertion (A)
is followed by a statement of Reason (R).
Choose the correct option
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 and 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.
Assertion(A): The sequence − 1 , − 1 − 1 ,... , − 1 is an AP.
Reason(R): In an AP, 𝑎
𝑛
𝑛− 1
is constant where 𝑛 ≥ 2 and 𝑛 ∈ 𝑁
Assertion(A): ( 2 + √ 3 )√ 3 is an irrational number.
Reason(R): Product of two irrational numbers is always irrational.
Section B
Section B consists of 5 questions of 2 marks each.
21 (A).
𝑃(𝑥, 𝑦) is a point equidistant from the points 𝐴( 4 , 3 ) and 𝐵( 3 , 4 ). Prove that 𝑥 −
OR
21 (B).
In the given figure, 𝛥𝐴𝐵𝐶 is an equilateral triangle. Coordinates of vertices A
and B are ( 0 , 3 ) and ( 0 , − 3 ) respectively. Find the coordinates of points C.
In two concentric circles, a chord of length 8 cm of the larger circle touches the
smaller circle. If the radius of the larger circle is 5 cm, then find the radius of the
smaller circle.
23 (A).
The sum of the first 12 terms of an A.P. is 900. If its first term is 20 then find the
common difference and 12
th
term.
OR
23 (B).
The sum of first 𝑛 terms of an A.P. is represented by 𝑆
𝑛
2
. Find the
common difference.
If 𝑠𝑖𝑛
1
2
1
2
∘
∘
𝑎𝑛𝑑 𝐴 > 𝐵, then find the
values of 𝐴 and 𝐵.
Calculate mode of the following distribution:
Class 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35
Frequency 5 6 15 10 5 4
Section C
Section C consists of 6 questions of 3 marks each.
Prove that √ 5 is an irrational number.
27 (A).
Find the ratio in which the y-axis divides the line segment joining the points
( 4 , − 5 ) and (− 1 , 2 ). Also find the point of intersection.
OR
27 (B).
Line 4 𝑥 + 𝑦 = 4 divides the line segment joining the points (− 2 , − 1 ) and ( 3 , 5 )
in a certain ratio. Find the ratio.
Prove that: (𝑐𝑜𝑠𝑒𝑐𝐴 − 𝑠𝑖𝑛𝐴)(𝑠𝑒𝑐𝐴 − 𝑐𝑜𝑠𝐴) =
1
tan 𝐴+cot 𝐴
Find the mean using the step deviation method.
Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50
Frequency 6 10 15 9 10
30. (A)
In the given figure, PA and PB are tangents to a circle centred at O. Prove that
(i) OP bisects ∠𝐴𝑃𝐵 (ii) OP is the right bisector of AB.
OR
30 (B). Prove that the lengths of tangents drawn from an external point to a circle are
equal.
The sum of a two-digit number and the number obtained by reversing the order
of its digits is 99. If ten’s digit is 3 more than the unit’s digit, then find the number.
Section - D
Remaining students preferred to be dropped off by car.
Based on the above information, answer the following questions:
(i) What is the probability that a randomly selected student does not prefer to walk
to school?
(ii) Find the probability of a randomly selected student who prefers to walk or use a
bicycle.
(iii)(A)
(B)
One day 50% of walking students decided to come by bicycle. What is the
probability that a randomly selected student comes to school using a bicycle on
that day?
OR
What is the probability that a randomly selected student prefers to be dropped
off by car?
Radha, an aspiring landscape designer, is tasked with creating a visually
captivating pool design that incorporates a unique arrangement of fountains.
The challenge entails arranging the fountains in such a way that when water is
thrown upwards, it forms the shape of a parabola. The graph of one such
parabola is given below.
The height of each fountain rod above water level is 10 cm. The equation of the
downward-facing parabola representing the water fountain is given by
2
Based on the above information, answer the following questions:
(i)
Find the zeroes of the polynomial p(x) from the graph.
(ii)
Find the value of x at which water attains maximum height.
(iii)(A)
(B)
If h is the maximum height attained by the water stream from the water level of
the pool, then find the value of h.
OR
At what point(s) on x- axis, the height of water above x- axis is 2 m?
38. Rinku was very happy to receive a fancy jumbo pencil from his best friend Rohan
on his birthday. Pencil is a basic writing tool, when sharpened its shape is a
combination of cylinder & cone as given in the picture.
Cylindrical pencil with conical head is a common shape worldwide since ages.
Commonly pencils are made up of wood & plastic but we should promote pencils
made up of eco-friendly material (many options available in the market these
days) to save environment.
The dimensions of Rinku’s pencil are given as follows:
Length of cylindrical portion is 21cm. Diameter of the base is 1 cm and height of
the conical portion is 1.2 cm
Based on the above information, answer the following questions:
(i)
Find the slant height of the sharpened part.
(ii)
Find curved surface area of sharpened part (in terms of 𝜋).
(iii)(A)
(B)
Find the total surface area of the pencil (in terms of 𝜋).
OR
The pencil’s total height decreases by 8.2 cm after sharpening it many times,
what is the volume of the cylindrical part of the shortened pencil (in terms of 𝜋)?
