CBSE 10th Maths Answer Key 2024 (Available): Detailed solutions PDF

Updated On: March 21, 2024 03:40 pm IST

Students can check CBSE 10th Maths Answer Key 2024 here and estimate their marks in the March 9 exam. The answer key is provided for all QP Codes for the objective-type questions.

CBSE 10th Mathematics Answer Key 2024

CBSE 10th Maths Answer Key 2024: The Central Board of Secondary Education has conducted today, March 9, 2024, the examinations for Maths Standard (Subject Code: 041) and Maths Basic (Subject Code: 241). Both papers were held from 10:30 AM to 1:30 PM. The Mathematics Standard paper had five major question paper sets, each with three sub-sets. The questions across the subsets are the same but only the order is shuffled. On this page, CBSE Class 10 Mathematics Answer Key 2024 for all QP Codes of Maths Standard exam are now provided here for:

QP Codes: 30/1/2 (Set 2), 30/2/3 (Set 3), 30/3/3 (Set 3), 30/4/1 (Set 1), 30/5/2 (Set 2), and 30/5/3 (Set 3).

Also Read| CBSE Class 10 Result Expected Release Date 2024

CBSE Class 10 Maths Answer Key 2024 for QP Code: 30/1/2

The answer key for all 20MCQs from section A for QP Code: 30/1/2 (Set 2) is provided here:

Question Number	CBSE Class 10 Maths Answer Key 2024 for QP Code: 30/1/2
1. AD is a median of △ABC with vertices A(5, 6), B(6, 4) and C(0, 0) Length AD is equal to	(A) √68 units
2. If secθ - tanθ = m, then the value of sec θ + tan θ is	(C) 1/m
3. If the distance between the points (3, 5) and (x, -5) is 15 units, then the values of x are	(B) -12, 18
4. If sinA = 2/3, then value of cotA is	(C) √3/2
5. In the given figure, graphs of two linear equations are shown. The pair of these linear equations is:	(D) inconsistent but can be made consistent by extending these lines
6. The centre of a circle is at (2, 0) If one end of a diameter is at (6, 0). then the other end is at	(C) (-2, 0)
7. Which of the following is not probability of an event?	(D) 1/0.89
8. The zeroes of a polynomial x² + px + q are twice the zeroes of the polynomiat 4x² - 5x - 6 The value of p is:	(B) 5/2
9. The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm is	(D) 2π/3 cu.cm.
10. The middle most observation of every data arranged in order is called:	(B) Median
11. If the roots of equation ax² + bx + c = 0, a ≠0 are real and equal, then which of the following relation is true?	(C) ac = b²/4
12. If the probability of a player winning a game is 0.79, then the probability of his losing the same game is	(D) 0.21
13. If the sum and the product of zeroes of a quadratic polynomial are 2√3 and 3 respectively, then a quadratic polynormal is.	(B) (x - √3)²
14. For some data x₁, x₂, ..., x_n with respective frequencies f₁, f₂, ..., f_n, the value of Σ f_i (x_i - x̄) is equal to:	(D) 0
15. A solid sphere is cut into two hemispheres. The ratio of the surface areas of the sphere to that of two hemispheres taken together is	(C) 2:3
16. If two positive integers p and q can be expressed as p = 18 a²b⁴ and a = 20 a³b². where a and b are prime numbers, then LCM (p, q)	(D) 180 a³ b⁴
17. nth term of an A P. is 7n + 4 The common difference is	(C) 7
18. From the data 1, 4, 7, 9, 16, 21, 25, if all the even numbers are removed, then the probability of getting at random a prime number from the remaining is	(B) 1/5
19. Assertion (A): If the graph of a polynomial touches x-axis at only one point, then the polynomial cannot be a quadratic polynomial. Reason (R): A polynomial of degree in 1) can have at most n zeroes.	(D) Assertion (A) is false, but Reason (R) is true.
20. Assertion (A): The tangents drawin at the end points of a diameter of a circle, are parallel. Reason (R):- Diameter of a circle is the longest chord.	(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

CBSE Class 10 Maths Answer Key 2024 for QP Code: 30/2/3

The answer key for all 20MCQs from section A for QP Code: 30/2/3 (Set 3) is provided here:

Question Number	CBSE Class 10 Maths Answer Key 2024 for QP Code: 30/2/3
1. The distance between the points (a cos θ, - a sin θ) and (a sin θ, a cos θ) is :	(B) a√2
2. In the given figure, tangents PA and PB to the circle centred at O from point P are perpendicular to each other. If PA = 5 cm, then length of AB is equal to	(B) 5√2 cm
3. Which term of the A.P. -29, -26, -23........ 61 is 16?	(B) 16^th
4. A box contains cards numbered 6 to 55. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square, is	(C) 1/10
5. AB and CD are two chords of a circle intersecting at P. Choose the correct statement from the following	(D) △ADP ~ △CBP
6. Two dice are rolled together. The probability of getting the sum of the two numbers to be more than 10, is	(D) 1/12
7. After an examination, a teacher wants to know the marks obtained by maximum number of the students in her class. She requires to calculate _____ of marks.	(B) mode
8. The roots of the quadratic equation 4x² - 5x + 4 = 0 are	(C) not real
9. The common difference of an A.P. in which a₂₀ - a₁₅ = 20 is	(A) 4
10. If value of each observation in a data is increased by 2, then median of the new data	(A) increases by 2
11. The perimeters of two similar triangles ABC and PQR are 56 cm and 48 cm respectively. PQ/AB is equal to	(B) 6/7
12. If α and β (α > β) are the zeroes of the polynomial - x2 + 8x + 9 then (α - β) is equal to	(C) ±10
13. The value of k for which the system of equations 3x - y + 8 = 0 and 6x - ky + 16=0 has infinitely many solutions, is	(B) 2
14. If sin θ = cos θ (0° < θ < 90°) then the value of (sec θ * sin θ ) is:	(C) 1
15. Point P divides the line segment joining the points A (4, -5) and B(1, 2) in the ratio 5:2. Co-ordinates of point Pare	(C) (13/7, 0)
16. In the given figure, in △ ABC, DE is parallel to BC. If AD = 5 cm, DB = 2.5 cm and BC = 12 cm, then DE is equal to:	(C) 8 cm
17. Given HCF (2520, 6600) = 40, LCM (2520, 6600) = 252 x k, then the value of k is:	(D) 1625
18. In the given figure, AT is tangent to a circle centred at O. If ∠CAT = 40°, then ∠CBA is equal to	(D) 40°
19. Assertion (A): If sin A = 1/3 (0° < A < 90°), then the value of cos A is (2√2)/3. Reason (R): For every angle θ, sin²θ+cos²θ = 1.	(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
20. Assertion (A): Two cubes each of edge length 10 cm are joined together. The total surface area of the newly formed cuboid is 1200 cm². Reason (R): Area of each surface of a cube of side 10 cm is 100 cm².	(D) Assertion (A) is false, but Reason (R) is true.

CBSE Class 10 Maths Answer Key 2024 for QP Code: 30/3/3

The answer key for all 20MCQs from section A for QP Code: 30/3/3 (Set 3) is provided here:

Question Number	CBSE Class 10 Maths Answer Key 2024 for QP Code: 30/3/3
1. A bag contains 3 red balls, 6 white balls and 7 black balls. The probability that a ball drawn from the bag at random will be neither red nor black is:	(A) 1/3
2. The probability of getting a bad egg in a lot of 400 eggs is 0.045. The number of good eggs in the lot is :	(C) 382
3. Perimeter of a sector of a circle whose central angle is 90° and radius 7 cm is:	(D) 25 cm
4. A pair of irrational numbers whose product is a rational number is :	(C) (√3, √27)
5. Maximum number of common tangents that can be drawn to two circles intersecting at two distinct points is :	(C) 2
6. From a point on the ground, which is 30 m 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:	(B) 30√3
7. Given HCF (2520, 6600) = 40, LCM (2520, 6600) = 252 x k, then the value of k is:	(D) 1625
8. The mean of five numbers is 15. If we include one more number, the mean of six numbers becomes 17. The included number is:	(A) 27
9. The pair of linear equations x + 2y + 5 = 0 and -3x = 6y - 1 has	(D) no solution
10. 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:	(B) 140°
11. In A ABC, DE \|\| BC (as shown in the figure). If AD = 2 cm, BD = 3 cm BC = 7.5 cm, then the length of DE (in cm) is:	(B) 3
12. Two dice are thrown together. The probability that they show different numbers is:	(B) 5/6
13. If sin α = √3/2, cos β = √3/2, then tan α * tan β is:	(C) 1
14. What should be added from the polynomial x² -5x + 4, so that 3 is the zero of the resulting polynomial?	(B) 2
15. The smallest irrational number by which √20 should be multiplied so as to get a rational number, is:	(D) √5
16. If the diagonals of a quadrilateral divide each other proportionally, then it is a:	(D) trapezium
17. The common difference of the A.P. 1/2x, (1-4x)/2x, (1-8x)/2x, ....... is:	(B) -2
18. In the given figure, if PT is a tangent to a circle with centre O and ∠TPO = 35°, then the measure of ∠x is	(D) 125°
19. 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) ).	(D) Assertion (A) is false, but Reason (R) is true.
20. 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 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).

CBSE Class 10 Maths Answer Key 2024 for QP Code: 30/4/1

The answer key for all 20MCQs from section A for QP Code: 30/4/1 (Set 1) is provided here:

Question Number	CBSE Class 10 Maths Answer Key 2024 for QP Code: 30/4/1
1. If ax + by = a²- b² and bx + ay = 0, then the value of x + y is:	(C) a - b
2. The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x, then the value of x is:	(B) 13
3. If a polynomial p(x) is given by p(x) = x² - 5x + 6, then the value of p(1) + p(4) is:	(B) 4
4. If the discriminant of the quadratic equation 3x²- 2x + c = 0 is 16, then the value of c is:	(C) -1
5. 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 :	(B) 1:4
6. The area of the sector of a circle of radius 12 cm is 60π cm². The central angle of this sector is :	(D) 150°
7. If the difference of mode and median of a data is 24, then the difference of its median and mean is:	(A) 12
8. Two dice are tossed simultaneously. The probability of getting odd numbers on both the dice is :	(D) 9/36
9. The ratio of total surface area of a solid hemisphere to the square of its radius is:	(C) 3π : 1
10. If sinθ = 1, then the value of [(1/2)*(sin(θ/2))] is:	(A) 1/2√2
11. 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 :	(D) - 15x + 9y = 5
12. Three numbers in A.P. have the sum 30. What is its middle term?	(B) 10
13. 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 :	(B) 7.5 cm
14. 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 :	(B) 45°
15. In the given figure, AB and AC are tangents to the circle. If ∠ABC = 42°, then the measure of ∠BAC is :	(A) 96°
16. The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2, 3), B(6, 7) and C(8, 3) is :	(B) (0, -1)
17. For an event E, if P(E) + P(Ē) = q, then the value of q² - 4 is:	(A) -3
18. 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 :	(C) 8.4 cm
19. Assertion : 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.	(C) Assertion (A) is true, but Reason (R) is false.
20. Assertion (A): If the circumference of a circle is 176 cm, then its radius is 28 cm. Reason (R): Circumference = 2π × radius of a circle.	(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

CBSE Class 10 Maths Answer Key 2024 for QP Code: 30/5/2

The answer key for all 20MCQs from section A for QP Code: 30/5/2 (Set 2) is provided here:

Question Number	CBSE Class 10 Maths Answer Key 2024 for QP Code: 30/5/2
1. If α and β are the zeroes of the polynomial p(x) = kx² - 30x + 45k and α + β = αβ, then the value of k is:	(D) 2/3
2. A chord of a circle of radius 10 em subtends a right angle at its centre. The length of the chord (in cm) is:	(B) 10√2
3. The next (4th) term of the A.P. √7, √28, √63, ... is	(D) √112
4. If the product of two co-prime numbers is 553, then their HCF is :	(A) 1
5. If x = a cos θ and y = b sin θ, then the value of b²x² + a²y² is:	(A) a²b2
6. If the quadratic equation ax² + bx + c = 0 has real and equal roots, then the value of c is:	(C) b²/4a
7. In the given figure, in △ ABC, DE \|\| BC. If AD = 2.4 cm, DB = 4 cm and AE = 2 cm, then the length of AC is:	(C) 16/3 cm
8. The length of an arc of a circle with radius 12 cm is 10π cm. The angle subtended by the arc at the centre of the circle, is:	(D) 150°
9. If 4 sec θ - 5 = 0 then the value of cot θ is:	(D) 4/3
10. The perimeter of the sector of a circle of radius 21 cm which subtends an angle of 60° at the centre of circle is:	(C) 64 cm
11. In the given figure, RJ and RL. are two tangents to the circle. If ∠RJL = 42°, then the measure of ∠JOL is	(B) 84°
12. If the prime factorisation of 2520 is 2³ x 3^a x b x 7, then the value of a + 2b is:	(A) 12
13. Which out of the following type of straight lines will be represented by the system of equations 3x + 4y = 5 and 6x + 8y = 7?	(A) Parallel
14. One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number which is a multiple of 7 is:	(B) 1/8
15. The LCM of three numbers 28, 44, 132 is:	(D) 924
16. The number of terms in the A.P. 3, 6, 9, 12, ..., 111 in	(C) 37
17. The ratio of the length of a pole and its shadow on the ground is 1 : √3. The angle of elevation of the Sun is:	(D) 30°
18. If the mean and mode of a data are 24 and 12 respectively, then its median is:	(C) 20
19. Assertion (A): ABCD is a trapezium with DC \|\| AB. E and F are points on AD and BC respectively, such that EF \|\| AB. Then AE/ED = BF/FC. Reason (R): Any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally.	(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
20. Assertion (A): Degree of a zero polynomial is not defined. Reason (R): Degree of a non-zero constant polynomial is 0.	(B) Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of the Assertion (A).

CBSE Class 10 Maths Answer Key 2024 for QP Code: 30/5/3

The answer key for all 20MCQs from section A for QP Code: 30/5/3 (Set 3) is provided here:

Question Number	CBSE Class 10 Maths Answer Key 2024 for QP Code: 30/5/3
1. The LCM of the smallest prime number and the smallest odd composite number is:	(D) 18
2. If the mean of the first n natural numbers is 5n/9 , then the value of n is:	(C) 9
3. If 5 tan θ - 12 = 0. then the value of sin θ is:	(B) 12/13
4. The next (4th) term of the A.P. √18, √50, √98, ... is	(D) √162
5. In the given figure, in △ ABC, DE \|\| BC. If AD = 2.4 cm, DB = 4 cm and AE = 2 cm, then the length of AC is:	(C) 16/3 cm
6. In the given figure, RJ and RL. are two tangents to the circle. If ∠RJL = 42°, then the measure of ∠JOL is	(B) 84°
7. The perimeter of the sector of a circle of radius 21 cm which subtends an angle of 60° at the centre of circle is:	(A) 64 cm
8. The ratio of the sum and product of the roots of the quadratic equation 5x²- 6x + 21= 0 is :	(B) 2:7
9. The 14th term from the end of the A.P. - 11, - 8, - 5, ..., 49 is:	(B) 10
10. The length of the shadow of a tower on the plane ground is √3 times the height of the tower. The angle of elevation of the Sun is :	(A) 30°
11. What is the probability that a number selected randomly from the numbers 1, 2, 3, ..., 15 is a multiple of 4?	(C) 3/15
12. If x/3 = 2 sin A, y/3 = 2 cos A, then the value of x² + y² is:	(A) 36
13. If α and β are the zeroes of the polynomial p(x) = kx² - 30x + 45k and α + β = αβ, then the value of k is:	(D) 2/3
14. The length of an arc of a circle with radius 12 cm is 10π cm. The angle subtended by the arc at the centre of the circle, is:	(D) 150°
15. The LCM of three numbers 28, 44, 132 is:	(D) 924
16. A chord of a circle of radius 10 em subtends a right angle at its centre. The length of the chord (in cm) is:	(B) 10√2
17. Which out of the following type of straight lines will be represented by the system of equations 3x + 4y = 5 and 6x + 8y = 7?	(A) Parallel
18. The greatest number which divides 281 and 1249, leaving remainder 5 and 7 respectively, is:	(C) 138
19. Assertion (A): Degree of a zero polynomial is not defined. Reason (R): Degree of a non-zero constant polynomial is 0.	(B) Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of the Assertion (A).
20. Assertion (A): ABCD is a trapezium with DC \|\| AB. E and F are points on AD and BC respectively, such that EF \|\| AB. Then AE/ED = BF/FC. Reason (R): Any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally.	(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

CBSE Class 10 Maths 2024: Analysis and Question Paper

The analysis and question paper for CBSE 10th Mathematics held on March 9, 2024, can be checked at the following links:

CBSE Class 10 Mathematics Question Paper 2024
CBSE 10th Mathematics Exam Analysis 2024

CBSE Class 10 Answer Key 2024 Links |

The answer keys for the respective day-wise exams are available at the links below:

Subject	CBSE 10th Answer Key 2024 Link
Computer Applications	CBSE 10th Computer Applications Answer Key 2024
Information Technology	CBSE 10th Information Technology Answer Key 2024
Social Science	CBSE Class 10 Social Science Answer Key 2024
Science	CBSE Class 10 Science Answer Key 2024
English	CBSE Class 10 English Answer Key 2024
Hindi Course A	CBSE Class 10 Hindi (Course A) Answer Key 2024
Hindi Course B	CBSE 10th Hindi Course B Answer Key 2024

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