Hbse 10th Exam 2026 Maths TEST ASSIGNMENT

Hbse 10th Exam 2026 maths : HARYANA BOARD OF SCHOOL EDUCATION, BHIWANI

MATHEMATICS-X

Time Allowed: 3 hours

General Instructiona

(1) There are Sections A. B. C. D and E in this question paper

(2) Section: ‘A’ consists of one mark questions from 1 to 20, 1 to 18 are Multiple Cho (MCQ), One Word Answer, Fill in the blank, True/False and question number Amerikon-Reasoning based questione

(3) Section ‘IF consists of Very Short Answer (VSA) type questions of two marka sach n

(4) Section: ‘C’ consists of Short-Answer (SA) type questions of three marka each from 26

(5) Section: ‘D’ consists of Long-Answer (LA) type questions of five marks each from 32 ts

(n) Question number 30 to 38 in Section E are case study based questions of four marks ex choice is given in each case study question of two marks each.

All questions are compulsory However, provision of internal choice has been make in2

Section B, 2 questions of Section C, 4 questions of Section D.

If(-1)+(-1)=0, then in is a/an:

(a) positive integer

(b) negative integer

If HCF (72, 120)=24, then LCM (72, 120) is

(a) 72

(b) 120

(0) 360

(79640)

It the lines represented by equational 3x + 2my = 2 nd 2x + 5y + 1 = 0 are parallel , then the palue of m is:

2 5 3 15

5 ( b) 4 © 2 (d) 4

In ^ ABC, the vertices A ( – 1, 4) ; 9 5, 2) and the centroid is (0, -3) , then the co-ordinates of are

(4, 3) (b) (4, 15) © (-4, -15) (d) (-15, – 4)

The Value (s) of k for which the roots of quadratic equation X + 4x + k = 0 are real, is :

k>4 (b) 5>4 © k>-4 (d) k > -4

6. A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.

A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel

7. The co-ordinates of the centre of a circle are (2a, a – 7). If this circle passes through the point (11, -9) and its diameter is 10√2 units, then find the value of a.

(Or)

A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding (i) minor segment, (ii) major segment. [Use π = 3.14]

8. Find the zeros of the polynomial p(x) = 2x²-7x-15 and verify the relationship between its coefficients and zeroes.

9. Prove that √6 is an irrational number.

10. A man wanted to exchange 1000 in 2 types of notes of 5 and 10 denomination. If he got 180 notes in all, find the notes of each kind.

11. LCM of (23 x 3 x 5) and (2ª x 5 x 7) is:

( a) 40

(b) 560

(d) 1120

12. If it is a natural number, then 8″ cannot end with digit:

(a) 0

(b) 2

(d) 6

13. The system of equation 2x + 1 = 0 and 3y – 5 = 0 has:

(a) a unique solution

(b) two solutions

(d) infinite number of solutions

14. The distance of the point A(-3,-4) from the x-axis is:

(a) 3

(b) 4

21.

(d) 7

15. The value of: 34 + 32 + 30+ …. + 10 is:

(a) 294

(b) 289

(d) 386

16. Find the area of the sector of a circle with radius 4 cm and angle at the centre is 45°.

(Or)

A chord of a circle of radius 12 cin subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle.

[Use π = 3.14 and √3 = 1.73]

17. If a, ẞ are zeros of the quadratic polynomial x² + 3x + 2, find a quadratic polynomial whose zeros are a + 1, β + 1.

18.Prove that (7 – 2√3) is an irrational number, given that √3 is an irrational number.

19.Five years ago, Amit was thrice as old as Baljeet. Ten years hence, Amit shall be twice as old as Baljeet. What are their present ages?

(Or)

The diagonal of a rectangular field is 60 m more than the shorter side. If the longer side is 30 m more than the shorter side, find the length of the sides of the field.

20. In the given figure, TP and TQ are two tangents to the circle with centre O. If ∠OPQ = 15° and ZPTQ = 0, then find the value of sin 20.

21. Lokesh, a production manager in Mumbai, hires a taxi everyday to go to his office. The taxi charges in Mumbai consists of a fixed charges together with the charges for the distance covered. His office is at a distance of 10 km from his home. For a distance of 10 km to his office, Lokesh paid ₹ 105. While coming back home, he took another route. He covered a distance of 15 km and the charges paid by him were 155.

Based on the above information, answer the following questions.

(1) What are the fixed charges?

(ii) What are the charges per km?

(iii) (a) If fixed charges are 20 and charges per km are 10, then how much Lokesh have to pay for travelling a distance of 10 km?

( b) find the total amount paid by Lokesh for travelling 10 km from home to office and 25 km from office to home. [ Fix charge and charger per kilometer are as in ( i) and ( ii) ]

22. Find the area of the sector of a circle with radius 4 cm and of angle 30°. Also, find the area of the corresponding major sector. (Use π = 3.14)

(Or)

A rectangle ABCD is formed circumscribing a circle with a radius of 10 cm. Prove that rectangle ABCD is a square. Hence, find the perimeter of ABCD.

23. Find the zeros of the polynomial 4u² + 8u and verify the relationship between the zeros and the coefficients.

24. Prove that 3+7√2 is an irrational number, given that √2 is an irrational number.

25. The difference between two numbers is 26 and one number is three times the other. Find them.

(Or)

The ratio of incomes of two persons is 9: 7 and the ratio of their expenditures is 4: 3, if each of them manages to save 2000 per month, find the monthly incomes.

27. Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.

28. Satellite image of a colony is shown below. In this view, a particular house is pointed out by a flag, which is situated at the point of intersection of x and y-axis. If we go 2 cm east and 3 cm north from the house, then we reach to a Grocery store. If we go 4 cm west and 6 cm south from the house, then we reach to an Electrician’s shop. If we go 6 cm east and 8 cm south from the house, then we reach to a food card. If we go 6 cm west and 8 cm north from the house, then we reach to a bus stand.

Based on the above information, answer the following questions.

(1) Find the distance between grocery store and food cart.

(a) 12 cm

(b) 15 cm

(d) None of these

(ii) Find the distance of the bus stand from the house.

(iii) (a) If the grocery store and electrician’s shop lie on the line, find the ratio of distance of house from grocery store to that from electrician’s shop.

29. A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and diameter of the base is 4 cm. Determine the volume of the toy, If a right circular cylinder circumscibes the toy, find the difference of the volume of the cylinder and the toy. (Take π = 3.14)

(Or)

Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same)