Chapter Wise Test — AI-Powered Exam Practice
Empowering Students with AI-Powered Assessments & Intelligent Learning
☎ +91 99410 52464
✉ admin@chaptertest.in
CBSE(NCERT) · Grade 10 · Maths

CBSE 10th Maths Question Paper 2024 (Set 2)

56 questions from this Grade 10 Maths paper. The first 5 questions are solved free; log in as a Grade 10 student to view all solutions.

Home / Previous Year Papers / Grade 10 / Maths / CBSE 10th Maths Question Paper 2024 (Set 2)
Q1 mcq 1 mark
If ax + by = a2 – b2 and bx + ay = 0, then the value of x + y is :
  • A. a2 – b2
  • B. a + b
  • C. a – b
  • D. a2 + b2
Correct Answer: C — Solution

Given equations: (1) ax + by = a^2 - b^2 and (2) bx + ay = 0. Adding the two equations: (a+b)x + (a+b)y = a^2 - b^2. Factorising gives (a+b)(x+y) = (a-b)(a+b). Dividing both sides by (a+b) (assuming a+b is not 0), we get x + y = a - b. Thus, choice (C) is correct.

Q2 mcq 1 mark
The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x, then the value of x is :
  • A. 5
  • B. 13
  • C. 40
  • D. 8
Correct Answer: A — Solution

We know that for two numbers, HCF × LCM = Product of numbers. So, 13 × (40x) = 65 × 104. Simplifying: 520x = 6760. x = 6760 / 520 = 676 / 52 = 13. Wait, calculating again: 13 * 40 * x = 6760 => 520 * x = 6760 => x = 6760 / 520 = 13. Rechecking the calculation: 65 * 104 = 6760. 6760 / 13 = 520. 520 / 40 = 13. Actually, let's re-verify: HCF*LCM = 65*104 = 6760. 13 * 40x = 6760 => 520x = 6760 => x = 13. Wait, 13/520 * 6760? No. 6760/520 = 13. Choice B is 13.

Q3 mcq 1 mark
If a polynomial p(x) is given by p(x) = x2 – 5x + 6, then the value of p(1) + p(4) is :
  • B. 4
  • C. 2
  • D. – 4
Correct Answer: A — Solution

p(x) = x^2 - 5x + 6. p(1) = 1^2 - 5(1) + 6 = 1 - 5 + 6 = 2. p(4) = 4^2 - 5(4) + 6 = 16 - 20 + 6 = 2. Then p(1) + p(4) = 2 + 2 = 4. Looking at choices, let's recheck. p(1)=2, p(4)=2, sum is 4. Choice (B) is correct.

Q4 mcq 1 mark
If the discriminant of the quadratic equation 3x2 – 2x + c = 0 is 16, then the value of c is :
  • A. 1
  • C. – 1
  • D. 2
Correct Answer: C — Solution

For 3x^2 - 2x + c = 0, D = b^2 - 4ac. Given D = 16, a = 3, b = -2. So, (-2)^2 - 4(3)(c) = 16. 4 - 12c = 16. -12c = 12. c = -1. Thus, choice (C) is correct.

Q5 mcq 1 mark
If an arc subtends an angle of 90° at the centre of a circle, then the ratio of its length to the circumference of the circle is :
  • A. 2 : 3
  • B. 1 : 4
  • C. 4 : 1
  • D. 1 : 3
Correct Answer: B — Solution

Arc length L = (θ/360) * 2πr. Circumference C = 2πr. Ratio L/C = (θ/360). Given θ = 90°, ratio = 90/360 = 1/4. Thus, choice (B) is 1:4.

Q6 mcq 1 mark
The area of the sector of a circle of radius 12 cm is 60p cm2. The central angle of this sector is :
  • A. 120°
  • B. 6°
  • C. 75°
  • D. 150°

Solution hidden

Log in to view solution →
Q7 mcq 1 mark
If the difference of mode and median of a data is 24, then the difference of its median and mean is :
  • A. 12
  • B. 24
  • C. 8
  • D. 36

Solution hidden

Log in to view solution →
Q8 mcq 1 mark
Two dice are tossed simultaneously. The probability of getting odd numbers on both the dice is :
  • A. 6/36
  • B. 3/36
  • C. 12/36
  • D. 9/36

Solution hidden

Log in to view solution →
Q9 mcq 1 mark
The ratio of total surface area of a solid hemisphere to the square of its radius is :
  • A. 2p : 1
  • B. 4p : 1
  • C. 3p : 1
  • D. 1 : 4p

Solution hidden

Log in to view solution →
Q10 mcq 1 mark
If sin q = 1, then the value of 1/2 sin^2(q/2) is :
  • A. 1/2√2
  • B. 1/2
  • C. 1/2

Solution hidden

Log in to view solution →
Q11 mcq 1 mark
Two lines are given to be parallel. The equation of one of these lines is 5x – 3y = 2. The equation of the second line can be :
  • A. – 15x – 9y = 5
  • B. 15x + 9y = 5
  • C. 9x – 15y = 6
  • D. – 15x + 9y = 5

Solution hidden

Log in to view solution →
Q12 mcq 1 mark
Three numbers in A.P. have the sum 30. What is its middle term ?
  • A. 4
  • B. 10
  • C. 16
  • D. 8

Solution hidden

Log in to view solution →
Q13 mcq 1 mark
In ∆ ABC, DE || BC (as shown in the figure). If AD = 4 cm, AB = 9 cm and AC = 13.5 cm, then the length of EC is :
  • A. 6 cm
  • B. 7.5 cm
  • C. 9 cm
  • D. 5.7 cm

Solution hidden

Log in to view solution →
Q14 mcq 1 mark
At some time of the day, the length of the shadow of a tower is equal to its height. Then, the Sun’s altitude at that time is :
  • A. 30°
  • B. 45°
  • C. 60°
  • D. 90°

Solution hidden

Log in to view solution →
Q15 mcq 1 mark
In the given figure, AB and AC are tangents to the circle. If Ð ABC = 42°, then the measure of Ð BAC is :
  • A. 96°
  • B. 42°
  • C. 106°
  • D. 86°

Solution hidden

Log in to view solution →
Q16 mcq
The fourth vertex D of a parallelogram ABCD whose three vertices are A(– 2, 3), B(6, 7) and C(8, 3) is :
  • A. (0, 1)
  • B. (0, – 1)
  • C. (– 1, 0)
  • D. (1, 0)

Solution hidden

Log in to view solution →
Q17 mcq
For an event E, if P(E) + P(E) = q, then the value of q2 – 4 is :
  • A. – 3
  • B. 3
  • C. 5
  • D. – 5

Solution hidden

Log in to view solution →
Q18 mcq
In the given figure, QR is a common tangent to the two given circles touching externally at A. The tangent at A meets QR at P. If AP = 4.2 cm, then the length of QR is :
  • A. 4.2 cm
  • B. 2.1 cm
  • C. 8.4 cm
  • D. 6.3 cm

Solution hidden

Log in to view solution →
Q19 mcq
Assertion (A) : Mid-point of a line segment divides the line segment in the ratio 1 : 1. Reason (R) : The ratio in which the point (– 3, k) divides the line segment joining the points (– 5, 4) and (– 2, 3) is 1 : 2.
  • A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
  • B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
  • C. Assertion (A) is true, but Reason (R) is false.
  • D. Assertion (A) is false, but Reason (R) is true.

Solution hidden

Log in to view solution →
Q20 mcq
Assertion (A) : If the circumference of a circle is 176 cm, then its radius is 28 cm. Reason (R): Circumference = 2p ´ radius of a circle.
  • A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
  • B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
  • C. Assertion (A) is true, but Reason (R) is false.
  • D. Assertion (A) is false, but Reason (R) is true.

Solution hidden

Log in to view solution →
Q21 short answer 2 marks
Three bells toll at intervals of 9, 12 and 15 minutes respectively. If they start tolling together, after what time will they next toll together ?

Solution hidden

Log in to view solution →
Q22 short answer 2 marks
The minute hand of a clock is 14 cm long. Find the area on the face of the clock described by the minute hand in 5 minutes.

Solution hidden

Log in to view solution →
Q23 short answer 2 marks
Find the length of the arc of a circle which subtends an angle of 60° at the centre of the circle of radius 42 cm.

Solution hidden

Log in to view solution →
Q24 short answer 2 marks
Evaluate : (5 cos^2 60° + 4 sec^2 30° – tan^2 45°) / (sin^2 30° + sin^2 60°)

Solution hidden

Log in to view solution →
Q24 short answer
In the given figure, O is the centre of the circle. If Angle AOB = 145°, then find the value of x.

Solution hidden

Log in to view solution →
Q25 short answer 2 marks
If sin (A – B) = 1/2, cos (A + B) = 1/2 ; 0 < A + B ≤ 90°, A > B; find ∠ A and ∠ B.

Solution hidden

Log in to view solution →
Q25 short answer
In the given figure, ∆ AHK ~ ∆ ABC. If AK = 8 cm, BC = 3.2 cm and HK = 6.4 cm, then find the length of AC.

Solution hidden

Log in to view solution →
Q26 short answer 2 marks
Evaluate: (sin^2 30 + sin^2 60) / (cos^2 60 + 4 sec^2 30 - tan^2 45)

Solution hidden

Log in to view solution →
Q26 short answer 3 marks
Prove that: (sec theta - tan theta) / (sin theta + cos theta - 1) = 1 / (sin theta - cos theta + 1)

Solution hidden

Log in to view solution →
Q28 short answer 3 marks
Rehana went to a bank to withdraw 2,000. She asked the cashier to give her 50 and 100 notes only. Rehana got 25 notes in all. Find how many notes of 50 and 100 did she receive.

Solution hidden

Log in to view solution →
Q30 short answer 3 marks
Three coins are tossed simultaneously. What is the probability of getting at least one head?

Solution hidden

Log in to view solution →
Q30 short answer 3 marks
Prove that 5 / 2 - 3 is an irrational number, given that 3 is an irrational number.

Solution hidden

Log in to view solution →
Q31 short answer 3 marks
A box contains 90 discs which are numbered 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a 2-digit number less than 40.

Solution hidden

Log in to view solution →
Q31 short answer 3 marks
Prove that the parallelogram circumscribing a circle is a rhombus.

Solution hidden

Log in to view solution →
Q32 long answer 5 marks
Two poles of equal heights are standing opposite each other on either side of the road, which is 100 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of each pole and the distances of the point from the poles. (Use 3 = 1.732)

Solution hidden

Log in to view solution →
Q32 long answer 5 marks
Two pillars of equal lengths stand on either side of a road which is 100 m wide, exactly opposite to each other. At a point on the road between the pillars, the angles of elevation of the tops of the pillars are 60° and 30°. Find the length of each pillar and distance of the point on the road from the pillars. (Use √3 = 1·732)

Solution hidden

Log in to view solution →
Q33 short answer 3 marks
Find the zeroes of the polynomial 4x^2 + 4x – 3 and verify the relationship between zeroes and coefficients of the polynomial.

Solution hidden

Log in to view solution →
Q34 short answer 3 marks
If a and b are the zeroes of the polynomial x^2 + x – 2, then find the value of (a/b) + (b/a).

Solution hidden

Log in to view solution →
Q35 long answer 5 marks
The following table shows the ages of the patients admitted in a hospital during a year : Age (in years) 5 – 15 15 – 25 25 – 35 35 – 45 45 – 55 55 – 65 Number of patients 6 11 21 23 14 5 Find the mode and mean of the data given above.

Solution hidden

Log in to view solution →
Q38 long answer 5 marks
E is a point on side AD produced of a parallelogram ABCD such that BE intersects CD at F. Show that triangle ABE ~ triangle CFB.

Solution hidden

Log in to view solution →
Q39 long answer 5 marks
Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of triangle PQR. Prove that triangle ABC ~ triangle PQR.

Solution hidden

Log in to view solution →
Q40 long answer 5 marks
A train travels a distance of 90 km at a uniform speed. If the speed had been 15 km/h more, it would have taken 30 minutes less for the journey. Find the original speed of the train.

Solution hidden

Log in to view solution →
Q41 long answer 5 marks
Find the value of 'c' for which the quadratic equation (c + 1)x^2 – 6(c + 1)x + 3(c + 9) = 0; c != –1 has real and equal roots.

Solution hidden

Log in to view solution →
Q43 long answer 5 marks
Sides AB, BC and the median AD of ∆ ABC are respectively proportional to sides PQ, QR and the median PM of another ∆ PQR. Prove that ∆ ABC ~ ∆ PQR.

Solution hidden

Log in to view solution →
Reading Passage

Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So he started to sketch his own rocket designs on the graph sheet. One such design is given below : Based on the above, answer the following questions :

Q45 short answer 1 mark
Find the mid-point of the segment joining F and G.

Solution hidden

Log in to view solution →
Q46 short answer 2 marks
What is the distance between the points A and C ?

Solution hidden

Log in to view solution →
Q47 short answer 2 marks
Find the coordinates of the point which divides the line segment joining the points A and B in the ratio 1 : 3 internally.

Solution hidden

Log in to view solution →
Q48 short answer 1 mark
What are the coordinates of the point D ?

Solution hidden

Log in to view solution →
Reading Passage

Treasure Hunt is an exciting and adventurous game where participants follow a series of clues/numbers/maps to discover hidden treasures. Players engage in a thrilling quest, solving puzzles and riddles to unveil the location of the coveted prize. While playing a treasure hunt game, some clues (numbers) are hidden in various spots collectively forming an A.P. If the number on the nth spot is 20 + 4n, then answer the following questions to help the players in spotting the clues :

Q49 short answer 1 mark
Which number is on first spot ?

Solution hidden

Log in to view solution →
Q50 short answer 2 marks
Which spot is numbered as 112 ?

Solution hidden

Log in to view solution →
Q51 short answer 2 marks
What is the sum of all the numbers on the first 10 spots ?

Solution hidden

Log in to view solution →
Q52 short answer 1 mark
Which number is on the (n – 2)th spot ?

Solution hidden

Log in to view solution →
Reading Passage

Tamper-proof tetra-packed milk guarantees both freshness and security. This milk ensures uncompromised quality, preserving the nutritional values within and making it a reliable choice for health-conscious individuals. 500 mL milk is packed in a cuboidal container of dimensions 15 cm ´ 8 cm ´ 5 cm. These milk packets are then packed in cuboidal cartons of dimensions 30 cm ´ 32 cm ´ 15 cm. Based on the above given information, answer the following questions :

Q53 short answer 1 mark
Find the volume of the cuboidal carton.

Solution hidden

Log in to view solution →
Q54 short answer 2 marks
Find the total surface area of a milk packet.

Solution hidden

Log in to view solution →
Q55 short answer 2 marks
How many milk packets can be filled in a carton ?

Solution hidden

Log in to view solution →
Q56 short answer 1 mark
How much milk can the cup (as shown in the figure) hold ?

Solution hidden

Log in to view solution →