CBSE 10th Mathematics Question Paper 2023 with Solutions: Download CBSE 10th Maths solutions 2023

CBSE 10th Mathematics Question Paper 2023 with Solutions are given on this page. Students can check the solutions of the CBSE Class 10 Mathematics Question Paper 2023 set 2 and download CBSE 10th Maths solutions 2023 PDF.

CBSE Class 10 Maths Solutions 2023: We have provided the CBSE 10th Maths solutions 2023 on this page. Students can check the answers of CBSE Class 10 Maths question paper 2023. They can use our CBSE class 10 Maths solutions 2023 to check whether their answers are correct. CBSE 10th Mathematics Question Paper 2023 with Solutions - Set 2 is provided on this page. They should note that this is not the official CBSE answer key. We will update the page with more solutions. CBSE Class 10 Mathematics exam 2023 was held on March 21, 2023. Check the CBSE Maths Question paper answer key 2023.

The CBSE Class 10 Maths Solutions are given in a detailed manner so that students can understand it easily. We have also provided a PDF of the CBSE 10th Mathematics Question Paper 2023 with Solutions . Students can download and save the CBSE Class 10 Maths solutions for future reference. 

CBSE 10th Mathematics Question Paper 2023 with Solutions - Set 2

Section A

Question 1: In what ratio, does the x-axis divide the line segment joining the points A(3, 6) and B(-12, -3)? 

(A) 1:2 

(B) 1:4 

(C) 4:1 

(D) 2:1 

Solution: 

Question 2: In the given figure, PQ is a tangent to the circle centred at O. If ∠AOB = 95⁰, then the measure of ∠ABQ will be

Solution:

We know the tangent at any point of a circle is perpendicular to the radius through the point of contact.

∠OBQ = 90⁰

OA = OB (Radius of circle)

So ∠OAB = ∠OBA

Question 3: If 2 tan A = 3, then the value of (4 sin A plus 3 cos A)/(4 sin A - 3 cos A) is

(A) 7/√13

(B) 1/√13

(C) 3

(D) does not exist

Solution:

Question 4. In a group of 20 people, 5 can't swim. If one person is selected at random, then the probability that he/she can swim, is

(A) 3/4

(B) 1/3

(C) 1

(D) 1/4

Solution:

Total number of people = 20

No. of people who can swim = 15

Required probability = 15/20 = 3/4

Hence option A is the answer.

Question 5. The distribution below gives the marks obtained by 80 students on a test.

The modal class of this distribution is

(A) 10-20

(B) 20-30

(C) 30-40

(D) 50-60

Solution:

In a frequency distribution,  the class that consists of the highest frequency is known as the modal class.

Modal class is 30-40.

Hence option C is the answer.

Question 6. The curved surface area of a cone having height 24 cm and radius 7 cm, is

(A) 528 cm²

(B) 1056 cm²

(C) 550 cm²

(D) 500 cm²

Solution:

Given that height of cone = 24 cm

Radius = 7 cm

Slant height, l = √625 (find slant height using h and r, root of sum of square of h and r)

= 25

CSA = πrl

= (22/7)×7×25

= 550 cm²

Hence option C is the answer.

Question 7. The end-points of a diameter of a circle are (2, 4) and (-3, -1). The radius of the circle is 

(A) 2√5

(B) (5/2)√5

(C) (5/2)√2

(D) 5√2

Solution:

The length of the diameter can be found by using the distance formula.

Distance between (2, 4) and (-3, -1) = √50

= 5√2

Radius = diameter/2

= (5/2)√2

Hence option C is the answer.

Question 8. Which of the following is a quadratic polynomial with zeros (5/3) and 0?

(A) 3x(3x-5)

(B) 3x(x-5)

(C) x²-5/3

(D) 5x²/3

Question 9. The graph of y = p(x) is given, for a polynomial p(x). The number of zeroes of p(x) from the graph is

(A) 3

(B) 1

(C) 2

(D) 0

Solution:

Look at the graph and find how many points the graph cuts or touches the x-axis.

Here it is only at 1 point.

Hence option B is the answer.

Question 10.

Question 11: If a, b, c form an A.P. with common difference d, then the value of a -2b-c is equal to

(A) 2a 4d

(B) 0

(C) -2a-4d

(D) -2a-3d

Question 12. If the value of each observation of a statistical data is increased by 3, then the mean of the data

(A) remains unchanged

(B) increases by 3

(C) increases by 6

(D) increases by 3n

Solution:

If each observation of the data is increased by 3, then their mean is increased by 3.

Hence option B is the answer.

Question 13. Probability of happening of an event is denoted by p and probability or non-happening of the event is denoted by q. Relation between p and q is

Question 14. A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought ?

(A) 40

(B) 240

(C) 480

(D) 750

Solution:

Given, total number of tickets sold = 6000

Probability of her winning = 0.08

Total number of tickets she bought = 6000 × 0.08 

= 480

Hence option C is the answer.

Question 15. If α, β are the zeroes of a polynomial p(x) = x² plus x- 1, (1/α) plus (1/ β) equals is

Question 16. The least positive value of k, for which the quadratic equation x² plus kx-4 = 0 has rational roots, is

(A) ±2√2

(B) 2

(C) ±2

(D) √2

Solution:

The least positive value of k is 2.

Hence option B is the answer.

Question 17. [(5/8)sec²60 - tan²60 plus cos²45] is equal to

(A) -5/3

(B) -1/2

(C) 0

(D) -1/4

Question 18. Curved surface area of a cylinder of height 5 cm is 94.2 cm². Radius of the cylinder is

(A) 2 cm

(B) 3 cm

(C) 2.9 cm

(D) 6 cm

Solution:

Given height of cylinder = 5 cm

Curved surface area = 94.2 cm²

CSA = 2πrh

94.2 = 2×3.14×r×5

Solving we get, r = 3

Hence option B is the answer.

Assertion-Reason Type Questions

In Question 19 and 20, an Assertion (A) statement is followed by a statement of Reason (R). Select the correct option out of the following:

(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.

Question 19. Assertion (A) :The perimeter of triangle ABC is a rational number.

Reason (R) : The sum of the squares of two rational numbers is always rational.

Question 20. Assertion (A) : Point P(0, 2) is the point of intersection of y-axis with the line 3x plus 2y = 4. 

Reason (R) : The distance of point P(0, 2) from x-axis is 2 units. 

Section B

Question 21. Find the least number which when divided by 12, 16 and 24 leaves the remainder 7 in each case.

Solution:

The least number which is divisible by 12, 16, and 24 is the LCM of 12, 16, and 24.

LCM of 12, 16 and 24 = 48

So the least number which when divided by 12, 16 and 24 leaves the remainder 7 in each case = sum of 48 and 7 

= 55

Question 22. A bag contains 4 red, 3 blue and 2 yellow balls. One ball is drawn at random from the bag. Find the probability that drawn ball is 

(i) red 

(ii) yellow

Solution:

No. of red balls = 4

No. of blue balls = 3

No. of yellow balls = 2

Total number balls = 9

Probability of getting red ball = 4/9

Probability of getting yellow ball = 2/9

Question 23 (a). Solve the pair of equations x = 5 and y = 7 graphically.

Solution:

Below is the graph of x = 5 and y = 7

The lines intersect at (5, 7)

Question 23. (b)  Using graphical method, find whether pair of equations x = 0 and y= -3, is consistent or not.

Solution:

x = 0 and y= -3 intersect at (0, -3). 

Unique solution exists.

Hence the equations are consistent.

Question 24 (a). If sin x plus cos x =  √3, then find the value of sin x cos x. 

Question 24 (b): If sin A = 1/√2 and cot B = √3, then find the value of cosec A plus cosec B.