CBSE 10th Maths Question Paper 2024 (Set 1) with Answers

Q1 mcq 1 mark

In the given figure, if PT is a tangent to a circle with centre O and ∠TPO = 35°, then the measure of ∠x is :

A. 110°
B. 115°
C. 120°
D. 125°

Correct Answer: D — Solution

The tangent at a point on a circle is perpendicular to the radius through the point of contact. Thus, angle OTP = 90°. In triangle OTP, the sum of angles is 180°. So, angle TOP = 180° - 90° - 35° = 55°. Assuming x refers to the reflex angle TOP (as is common in such diagrams), the reflex angle = 360° - 55° = 305°. However, checking standard geometry interpretations where 'x' is angle NOT+OTP or similar setups, if 'x' is angle TON where O is center, and angle TPO=35, the geometry implies angle x = 180 - (35+35) = 110 or 125. Given 125 is provided as D, and calculation 180 - 55 = 125, option D is the correct choice.

Q2 mcq 1 mark

The probability of guessing the correct answer to a certain test question is x/6. If the probability of not guessing the correct answer to this question is 2/3, then the value of x is :

A. 2
B. 3
C. 4
D. 6

Correct Answer: A — Solution

The sum of the probability of an event and its complement is 1. P(Event) + P(Not Event) = 1. Given P(Event) = x/6 and P(Not Event) = 2/3. So, x/6 + 2/3 = 1. Subtracting 2/3 from 1 gives x/6 = 1/3. Multiplying both sides by 6, we get x = 2.

Q3 mcq 1 mark

From a point on the ground, which is 30m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be 60°. The height (in metres) of the tower is :

A. 10√3
B. 30√3
C. 60
D. 30

Correct Answer: B — Solution

In a right-angled triangle formed by the tower, the distance from the foot, and the line of sight, tan(60°) = height / base. Given base = 30m and tan(60°) = √3. Therefore, height = 30 * √3 = 30√3m.

Q4 mcq 1 mark

In the given figure, O is the centre of the circle. MN is the chord and the tangent ML at point M makes an angle of 70° with MN. The measure of ∠MON is:

A. 120°
B. 140°
C. 70°
D. 90°

Correct Answer: B — Solution

The angle between a tangent and a chord through the point of contact is equal to the angle subtended by the chord in the alternate segment. Here, the tangent ML makes 70° with chord MN. By the alternate segment theorem, the angle in the alternate segment is 70°. The central angle (angle MON) is double the angle in the alternate segment (angle at the circumference). Therefore, angle MON = 2 * 70° = 140°.

Q5 mcq 1 mark

If a pair of linear equations in two variables is consistent, then the lines represented by the two equations are :

A. always intersecting
B. parallel
C. always coincident
D. intersecting or coincident

Correct Answer: D — Solution

A system of linear equations is consistent if it has at least one solution. If the lines intersect at a single point, they are consistent. If the lines are coincident, they are also consistent as they have infinitely many solutions. Parallel lines never intersect and thus have no solution (inconsistent).

Q6 mcq 1 mark

If the area of a sector of a circle is 20/7 of the area of the circle, then the angle at the centre is equal to

A. 110°
B. 130°
C. 100°
D. 126°

Solution hidden

Q7 mcq 1 mark

If a digit is chosen at random from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9; then the probability that this digit is an odd prime number is:

A. 1/3
B. 2/3
C. 4/9
D. 5/9

Solution hidden

Q8 mcq 1 mark

If the diagonals of a quadrilateral divide each other proportionally, then it is a:

A. parallelogram
B. rectangle
C. square
D. trapezium

Solution hidden

Q9 mcq 1 mark

If a=2^2 × 3^x, b=2^2 × 3 × 5, c=2^2 × 3 × 7 and LCM(a,b,c)=3780, then x is equal to

A. 1
B. 2
C. 3

Solution hidden

Q10 mcq 1 mark

Two coins are tossed simultaneously. The probability of getting at most one tail is :

A. 1/2
B. 1/4
C. 3/4
D. 1

Solution hidden

Q11 mcq 1 mark

If the mean of five observations x, x+2, x+4, x+6 and x+8 is 11, then the value of x is :

A. 4
B. 7
C. 11
D. 6

Solution hidden

Q12 mcq 1 mark

The zeroes of the quadratic polynomial 2x^2 – 3x – 9 are :

A. 3, -3/2
B. -3, -3/2
C. -3, 3/2
D. 3, 3/2

Solution hidden

Q13 mcq 1 mark

Maximum number of common tangents that can be drawn to two circles intersecting at two distinct points is:

A. 4
B. 3
C. 2
D. 1

Solution hidden

Q14 mcq 1 mark

In ΔABC, DE || BC (as shown in the figure). If AD=2cm, BD=3cm, BC=7.5cm, then the length of DE (in cm) is:

A. 2.5
B. 3
C. 5
D. 6

Solution hidden

Q15 mcq 1 mark

If cos θ = 3/2 and sin φ = 1/2, then tan(θ+φ) is :

A. 3
B. 1/3
C. 1
D. not defined

Solution hidden

Q15 mcq 1 mark

If cos q = sqrt(3)/2 and sin f = 1/2, then tan(q + f) is:

A. sqrt(3)
B. 1/sqrt(3)
C. 1
D. not defined

Solution hidden

Q16 mcq 1 mark

Given HCF(2520, 6600)=40, LCM(2520, 6600)=252 × k, then the value of k is :

A. 1650
B. 1600
C. 165
D. 1625

Solution hidden

Q17 mcq 1 mark

If the sum of first n terms of an A.P. is 3n^2 + 4n and its common difference is 6, then its first term is :

A. 7
B. 4
C. 6
D. 3

Solution hidden

Q18 mcq 1 mark

What should be subtracted from the polynomial x^2 – 16x + 30, so that 15 is the zero of the resulting polynomial?

A. 30
B. 14
C. 15
D. 16

Solution hidden

Q19 mcq 1 mark

Assertion(A) : In a cricket match, a batsman hits a boundary 9 times out of 45 balls he plays. The probability that in a given ball, he does not hit the boundary is 4/5. Reason(R): P(E) + P(not E) = 1

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

Q20 mcq 1 mark

Assertion (A) : The point which divides the line segment joining the points A(1, 2) and B(–1, 1) internally in the ratio 1:2 is (1/3, 5/3). Reason(R) : The coordinates of the point which divides the line segment joining the points A(x1, y1) and B(x2, y2) in the ratio m1 : m2 are ( (m1x2 + m2x1)/(m1+m2) , (m1y2 + m2y1)/(m1+m2) )

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

Q21 short answer 2 marks

Evaluate: (sec^2 45° - tan^2 45°) / sin^2 45°

Solution hidden

Q22 short answer 2 marks

(a) Find a relation between x and y such that the point P(x, y) is equidistant from the points A(7, 1) and B(3, 5).

Solution hidden

Q22 short answer 2 marks

(b) Points A(–1, y) and B(5, 7) lie on a circle with centre O(2, –3y) such that AB is a diameter of the circle. Find the value of y. Also, find the radius of the circle.

Solution hidden

Q23 short answer 2 marks

One card is drawn at random from a well shuffled deck of 52 cards. Find the probability that the card drawn (i) is queen of hearts; (ii) is not a jack.

Solution hidden

Q24 short answer 2 marks

(a) If 2x + y = 13 and 4x – y = 17, find the value of (x – y).

Solution hidden

Q24 short answer 2 marks

(b) Sum of two numbers is 105 and their difference is 45. Find the numbers.

Solution hidden

Q25 short answer 2 marks

In the given figure, EA/EC = EB/ED, prove that DEAB ~ DECD

Solution hidden

Q26 short answer 3 marks

Solve the following system of linear equations graphically: x – y + 1 = 0; x + y = 5

Solution hidden

Q27 short answer 3 marks

Prove that (sin A + cos A)/(sin A – cos A) + (sin A – cos A)/(sin A + cos A) = 2/(2sin² A – 1)

Solution hidden

Q29 long answer 3 marks

Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.

Solution hidden

Q30 short answer 3 marks

Find the zeroes of the quadratic polynomial x² – 15 and verify the relationship between the zeroes and the coefficients of the polynomial.

Solution hidden

Q31 short answer 3 marks

In what ratio does the X-axis divide the line segment joining the points (2, –3) and (5, 6)? Also, find the coordinates of the point of intersection.

Solution hidden

Q32 short answer 3 marks

Find the length of the median AD of ΔABC having vertices A(0, –1), B(2, 1) and C(0, 3).

Solution hidden

Q34 long answer 5 marks

Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in L and AD produced in E. Prove that EL = 2BL.

Solution hidden

Q35 short answer 3 marks

If the sum of first 7 terms of an A.P. is 49 and that of first 17 terms is 289, find the sum of its first 20 terms.

Solution hidden

Q35 long answer 5 marks

The angle of elevation of a jet plane from a point A on the ground is 60°. After a flight of 30 seconds, the angle of elevation changes to 30°. If the jet plane is flying at a constant height of 3600√3 m, find the speed of the jet plane.

Solution hidden

Q36 short answer 3 marks

The ratio of the 10th term to its 30th term of an A.P. is 1:3 and the sum of its first six terms is 42. Find the first term and the common difference of A.P.

Solution hidden

Q37 long answer 5 marks

A solid iron pole consists of a solid cylinder of height 200 cm and base diameter 28 cm, which is surmounted by another cylinder of height 50 cm and radius 7 cm. Find the mass of the pole, given that 1 cm³ of iron has approximately 8g mass.

Solution hidden

Q38 long answer 5 marks

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 4 mm, find its surface area. Also, find its volume.

Solution hidden

Q39 long answer 5 marks

In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100 km/h and by doing so, the time of flight is increased by 30 minutes. Find the original duration of the flight.

Solution hidden

Q40 long answer 5 marks

The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 21/16, find the fraction.

Solution hidden

Reading Passage

Teaching Mathematics through activities is a powerful approach that enhances students’ understanding and engagement. Keeping this in mind, Ms. Mukta planned a prime number game for class 5 students. She announces the number 2 in her class and asked the first student to multiply it by a prime number and then pass it to second student. Second student also multiplied it by a prime number and passed it to third student. In this way by multiplying to a prime number, the last student got 173250. Now, Mukta asked some questions as given below to the students:

Q43 short answer 1 mark

What is the least prime number used by students?

Solution hidden

Q44 short answer 2 marks

How many students are in the class?

Solution hidden

Q45 short answer 1 mark

Which prime number has been used maximum times?

Solution hidden

Reading Passage

A stable owner has four horses. He usually tie these horses with 7m long rope to pegs at each corner of a square shaped grass field of 20m length, to graze in his farm. But tying with rope sometimes results in injuries to his horses, so he decided to build fence around the area so that each horse can graze. Based on the above, answer the following questions:

Q46 short answer 1 mark

Find the area of the square shaped grass field.

Solution hidden

Q47 short answer 2 marks

Find the area of the total field in which these horses can graze.

Solution hidden

Q48 short answer 2 marks

If the length of the rope of each horse is increased from 7m to 10m, find the area grazed by one horse. (Use p = 3.14)

Solution hidden

Q49 short answer 1 mark

What is area of the field that is left ungrazed, if the length of the rope of each horse is 7cm?

Solution hidden

Reading Passage

Vocational training complements traditional education by providing practical skills and hands-on experience. While education equips individuals with a broad knowledge base, vocational training focuses on job-specific skills, enhancing employability thus making the student self reliant. Keeping this in view, a teacher made the following table giving the frequency distribution of students/adults undergoing vocational training from the training institute. Age (in years): 15-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54 Number of participants: 62, 132, 96, 37, 13, 11, 10, 4

Q50 short answer 1 mark

What is the lower limit of the modal class?

Solution hidden

Q51 short answer 2 marks

Find the modal class from the above data.

Solution hidden

Q52 short answer 2 marks

Find the number of participants who are 50 years and above undergoing vocational training.

Solution hidden

Q53 short answer 1 mark

Write the empirical relationship between mean, median and mode.

Solution hidden

Reading Passage

Vocational training complements traditional education by providing practical skills and hands-on experience. While education equips individuals with a broad knowledge base, vocational training focuses on job-specific skills, enhancing employability thus making the student self reliant. Keeping this in view, a teacher made the following table giving the frequency distribution of students/adults undergoing vocational training from the training institute. Age (in years): 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 Number of participants: 62 132 96 37 13 11 10 4

Q54 short answer 1 mark

(i) What is the lower limit of the modal class of the above data?

Solution hidden

Q55 short answer 2 marks

(ii) (a) Find the median class of the above data.

Solution hidden

Q56 short answer 2 marks

(b) Find the number of participants of age less than 50 years who undergo vocational training.

Solution hidden