NBSE Question Papers Mathematics (Basic) for Class 10

Class 10   Code No. 241/10/1 Series NBSE/X/2023 Roll No.  Candidates must write the Code No. on the title page of the Answer sheet. l Please check that this question paper contains 8 pages. l Code number given on the right hand side of the question paper should be written on the title page of the Answer sheet. l Please check that this question paper contains 31 questions. l 15 minutes time has been allotted to read this question paper. MATHEMATICS–BASIC Time: 3 Hours Maximum Marks: 80 General Instructions: 1. This question paper contains two parts, A and B. 2. Both Part A and Part B have internal choices. Part-A: 1. It consists of two sections, I and II. 2. Section I has questions of 1 mark each. 3. Section II has 4 questions on case study. Each case study has 5 case-based sub-parts. An examinee is to attempt any 4 out of 5 sub-parts. Part-B: 1. It consists of three sections III, IV and V. 2. In section III, Question Nos. 16 to 21 are Very Short Answer Type questions of 2 marks each. 3. In section IV, Question Nos. 22 to 28 are Short Answer Type questions of 3 marks each. 4. In section V, Question Nos. 29 to 31 are Long Answer Type questions of 5 marks each. 5. Internal choice is provided in 2 questions of 2 marks, 2 questions of 3 marks and 1 question of 5 marks. NBSE 2023 1 P.T.O.

PART-A SECTION-I Section I has questions of 1 mark each. 1. MCQ (i) When 429 is expressed as a product of its prime factors, we get 1 (a) 2 × 5 × 29 (b) 33 × 13 × 1 (c) 3 × 11 × 9 (d) 3 × 11 × 13 (ii) The value of p, for which (–4) is a zero of the polynomial x2 – 2x – (7p + 3) is 1 (a) 0 (b) 2 (c) 3 (d) None of these (iii) If (1 + cos A)(1 – cos A) = 3 , the value of sec A is 1 4 1 (a) 2 (b) –2 (c) ±2 (d) 0 (iv) The edge of a cube whose volume is equal to that of a cuboid of dimensions 8 cm × 4 cm × 2 cm is (a) 6 cm (b) 4 cm (c) 2 cm (d) 8 cm (v) In the following x = A +  Σfi di  , for finding the mean of grouped frequency distribution, di = 1  Σfi  (a) xi + A (b) A – xi (c) xi – A (d) A − xi fi 2. Assertion-Reason Type Questions In the following questions, a statement of assertion (A) is followed by a statement reason (R). Choose the correct choice as: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). 1 (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. (i) Assertion (A): When we move towards the object, angle of elevation decreases. Reason (R): As we move towards the object, it subtends large angle at our eye than before. (ii) Assertion (A): To find mean of a grouped data, we use x = a + Σfidi where a is the assumed mean and di the deviation. Σfi 1 Reason (R): To find deviation, we use di = a – xi where a is the assumed mean and xi is the class mark. 1 3. Express 5005 as a product of its prime factors. 1 4. Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x. 1 5. H.C.F and L.C.M of two numbers is 9 and 459 respectively. If one of the two numbers is 27. Find the other number. NBSE 2023 2

OR If ab is an irrational number, then show that a + b is also irrational. 6. Find whether the pair of equations 6x – 3y + 10 = 0  and  2x – y + 9 = 0 are consistent or inconsistent. 1 7. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find the area of sector formed by the arc. 1 OR A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope. Find the area of that part of the field in which the horse can graze. 8. Determine if the points (1, 5), (2, 3) and (− 2, − 11) are collinear. 1 9. A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder. 1 10. Prove that the tangents drawn at the ends of a diameter of a circle are parallel. 1 11. Two dice are thrown at the same time and the product of numbers appearing on them is noted. Find the probability that the product is a prime number. 1 SECTION-II Case study-based questions are compulsory. Attempt any 4 sub-parts from each question. Each sub-part carries 1 mark. 12. Case Study Based-1 A In a game, students of class 10th were making some design with the FE x cm combination of triangle and circle. They draw a triangle ABC which x cm circumscribes a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively and perimeter of DABC is 42 cm. Few questions came to their minds while making the design. Give answer O to their questions by looking at the figure. 6 cm 8 cm (i) What is the length of side AB? 1 B C 6 cm D 8 cm (a) 15 cm (b) 13 cm (c) 14 cm (d) 12 cm (ii) What is the length of side AC? 1 (a) 15 cm (b) 13 cm NBSE 2023 3 P.T.O.

(c) 14 cm (d) 12 cm (iii) Area of DABC is 1 (a) 96 sq. cm (b) 216 sq. cm (c) 84 sq. cm (d) 196 sq. cm (iv) The area of the circle is 1 (a) 136 sq. cm (b) 48 sq. cm (c) 60 sq. cm (d) 50.28 sq. cm (v) What is the area of the triangle ABC (excluding the circle)? 1 (a) 33.72 sq. cm (b) 36 sq. cm (c) 25 sq. cm (d) 45 sq. cm 13. Case Study Based-2 10 9 8 B 7 6 5 C A 4 3 2 D 1 (0, 0) 1 2 3 4 5 6 7 8 9 10 In a classroom, 4 friends have decided to seat at the points A, B, C and D as shown in fig. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli some questions which are as follows: (i) What is the coordinates of A and B? (b) A(4, 3), B(7, 6) 1 (a) A(3, 4), B(6, 7) (d) A(–3, –4), B(–6, –7) 1 (c) A(–3, –4), B(–6, –7) 1 (ii) What is the coordinate of C and D? (b) C(9, 4), D(6, 1) (a) C(4, 9), D(1, 6) (d) C(9, –4), D(6, –1) (c) C(–9, –4), D(–6, –1) (iii) What is the distance between AB? (a) 2 (b) 3 (c) 2 3 (d) 3 2 (iv) What is the distance between AC? 1 1 (a) 6 (b) 4 (c) 8 (d) 10 (v) What is the distance between BD? (a) 4 (b) 6 (c) 8 (d) 10 NBSE 2023 4

14. Case Study Based-3 Due to sudden floods, some welfare associations jointly requested the government to get lh 2.8 m 100 tents fixed immediately and ordered to contribute 50% of the cost. If the lower part of each tent is of the form of a cylinder of diameter 4.2 m and height 4 m, and a conical upper 2.1 m part of same diameter and height 2.8 m. The canvas to be used costs ` 100 per sq. m. Find the amount that the associations will have to pay. 4m (i) Find the formula to find the volume of the cylinder. 1 (a) pr2h (b) pr3h 4.2 m (c) pr2h2 (d) 1 ≠r2h 1 3 (ii) What is the formula for the lateral surface of the conical portion of the tent? (a) 1 pr2h (b) pr2h 3 (c) prl (d) 2prh (iii) What is the volume of the tent? 1 1 (a) 85.66 cu.m (b) 100 cu.m (c) 225.66 cu.m (d) 125.66 cu.m 1 (d) 95.9 sq.m (iv) What is the curved surface area of the tent? (d) ` 279,500 (a) 75.9 sq.m (b) 85.6 sq.m (c) 65.9 sq.m (v) What is the cost of canvas to be used to cover 100 such tents from all around? (a) ` 580,000 (b) ` 379,500 (c) ` 448,000 15. Case Study Based-4 Due to heavy storm and rainfall, electric wire broke down on a chauraha and it disturbed the traffic. One piece of the wire is shown in the figure which followed some mathematical shape. Answer the following questions below: 5 P.T.O. NBSE 2023

(i) Find the coordinates where does the graph cut the x-axis. 1 1 (a) (–5, 0), (–2, 0), (2, 0) (b) (–5, 0), (–2, 0), (0, 2) (c) (–2, 0), (0, 2), (2, 0) (d) (–5, 0), (0, 2), (2, 0) 1 (ii) Find number of zeroes of the graph y = f(x) (d) 3 1 (d) –5, –2, 0 1 (a) 0 (b) 2 (c) 1 (d) x3 – 5x2 + 4x + 20 (d) 1 (iii) Find the zeroes of the graph y = f(x) (a) –5, 0, 2 (b) –5, –2, 2 (c) –2, 0, 2 (iv) What will be the expression of the polynomial? (a) x3 + 5x2 – 4x – 20 (b) x3 + 5x2 + 4x – 20 (c) x3 + 5x2 + 4x + 20 (v) What is the value of the polynomial if x = –5? (a) –125 (b) 125 (c) 0 PART-B SECTION-III All questions are compulsory. In case of internal choices, attempt anyone. 16. Find the fourth vertex D of a parallelogram ABCD whose three vertices are A(– 2, 3), B(6, 7), and C(8, 3). 2 OR C E B If the distances of P(x, y) from the points A(3, 6) and B(–3, 4) are equal, prove that 3x + y = 5. F 17. In the given figure, AB  DE and BD  EF. D Prove that DC2 = CF × AC. 2 A 18. Prove that the parallelogram circumscribing a circle is a rhombus. 2 19. In the figure, O is the centre of a circle of radius 5 cm. T is a point such that OT = 13 cm and OT intersects circle at E. If AB is a tangent to the circle at E, find the length of AB, where TP and TQ are two tangents to the circle. 2 2mn 2 20. Find the value of other t-ratios if tan q = m2 – n2 . OR NBSE 2023 6

If cot q = 7 , then what is the value of (1 + cos θ) (1 − cos θ) ? 8 (1 − sin θ) (1 + sin θ) 21. Find the sum of the first 51 terms of an AP whose second term is 2 and fourth term is 8. 2 SECTION-IV 3 22. Prove that 2 3 − 7 is an irrational.  3 23. If two tangents inclined at an angle 60° are drawn to a circle of radius 5 cm, then find the length of each tangent. Q 5 cm O 60° P 5 cm R 24. A number consists of two digits, where the number is divided by the sum of its digits, the quotient is 7. If 27 is subtracted from the number, the digits interchange their places, find the number. 3 25. A school has five houses, A, B, C, D and E. A class has 23 students, 4 from house A, 8 from house B, 5 from house C, 2 from house D and rest from house E. A single student is selected at random to be the class monitor. Find the probability that the selected student is not from A, B and C. 3 OR A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is: (i) a jack or a king (ii) a non-ace (iii) a red card 26. A circus tent is cylindrical to a height of 3 m and conical above it. If its base radius is 52.5 m and slant height of the conical portion is 53 m, find the area of the canvas needed to make the tent. [Use π = 22 ]. 3 27. Prove that: tan2 A – tan2 B = sin2A − sin2B  7 3 cos2A ⋅ cos2B 28. Find two numbers whose sum is 27 and product is 182. 3 OR The two numbers differ by 2 and their product is 360. Find the numbers. SECTION-V 29. A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree. 5 NBSE 2023 7 P.T.O.

OR A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min. 30. 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 n terms. 5 31. The mean of the following frequency distribution is 57.6. and the number of observation is 50. Find the missing frequencies f1 and f2. 5 Class 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 100 – 120 Frequency 7 f1 12 f2 8 5 NBSE 2023 8