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# NBSE_Math_Basic

## Description: NBSE_Math_Basic

General Instructions: 1. This Question Paper has 5 Sections A, B, C, D, and E. 2. Section A has 20 Multiple Choice Questions (MCQs) carrying 1 mark each. 3. Section B has 5 Short Answer-I (SA-I) type questions carrying 2 marks each. 4. Section C has 6 Short Answer-II (SA-II) type questions carrying 3 marks each. 5. Section D has 4 Long Answer (LA) type questions carrying 5 marks each. 6. Section E has 3 Case Based integrated units of assessment (4 marks each) with sub-parts of the values of 1, 1 and 2 marks each respectively. 7. All Questions are compulsory. However, an internal choice in 2 Qs of 2 marks, 2 Qs of 3 marks and 2 Questions of 5 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E. 8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated. SECTION-A Section A consists of 20 questions of 1 mark each. 1. The LCM of 23 × 32­ and 22 × 33 is 1 1 (a) 23 (b) 33 1 1 (c) 23 × 33 (d) 22 × 32 1 2. The HCF of two numbers is 18 and their product is 12,960. Their LCM will be (a) 420 (b) 600 (c) 720 (d) 800 3. If –1 is a zero of the polynomial p(x) = x2 – 7x – 8, then the other zero is (a) –8 (b) –7 (c) 1 (d) 8 4. The pair of linear equations y = 0 and y = –5 has (a) One solution (b) Two solutions (c) Infinitely many solutions (d) No solution 5. The value of k, for which the equation 2x2 – 10x + k = 0 has real roots is (a) k ≤ 25 (b) k ≥ 25 2 2 (c) k = 25 (d) k > 25 2 2 NBSE 2023 2

6. AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0), and B(5, 0). The length of its diagonal is 1 (a) 5 (b) 3 (c) 34 (d) 4 1 A 7. In the given figure, DE || BC. Which of the following is true? (a) x = a+b (b) y= ax a ay a+b (c) x = ay (d) x=a D xE a+b yb B b 8. The value of a, so that the point (4, a) lies on the line 3x – 2y = 5 is 1 yC (a) 2 (b) 3 (c) 7 (d) 5 22 9. In the given figure, if TP and TQ are tangents to a circle with centre O, so that ∠POQ = 110°, then ∠PTQ is 1 (a) 110° (b) 90° (c) 80° (d) 70° 10. If sin q = x and sec q = y, then tan q is 1 (a) xy (b) x y (c) y (d) 1 x xy 11. If x = 2 sin2 q and y = 2 cos2 q + 1, then x + y is 1 (a) 3 (b) 2 (c) 1 1 (d) 2 12. Given that sin q = a , then tan q is equal to 1 b (a) b (b) b a2 + b2 b2 − a2 (c) a (d) a a2 − b2 b2 − a2 13. Area of a sector of a circle is 1 to the area of circle. The degree measure of its minor arc is 6 given by 1 (a) 90° (b) 60° (c) 45° (d) 30° NBSE 2023 3 P.T.O.

14. If the perimeter and area of a circle are numerically equal; its radius will be 1 (a) 1 unit (b) 2 units (c) 4 units (d) None of these 15. If the volume of a 7 cm high right circular cylinder is 448p cm3, then its radius is equal to  1 (a) 2 cm (b) 4 cm (c) 6 cm (d) 8 cm 16. Consider the following frequency distribution of the heights of 60 students of a class 1 Height (in cm) 150–155 155–160 160–165 165–170 170–175 175–180 No. of students 15 13 10 8 9 5 The upper limit of the median class in the given data is (a) 165 (b) 155 (c) 160 (d) 170 17. If xi are the mid-points of the class intervals of grouped data, fis are the corresponding frequencies and x is the mean, then S( fixi – x) is equal to 1 (a) 0 (b) –1 (c) 1 (d) 2 18. A box contains cards numbered 6 to 50. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square like 4, 9, .... is 1 12 (a) 45 (b) 15 (c) 4 (d) 1 9 45 Direction for questions 19 & 20: In question numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option. 19. Assertion (A): The number 6n, n being a natural number, ends with the digit 5. 1 Reason (R): The number 9n cannot end with digit 0 for any natural number n. (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). NBSE 2023 4

(c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. 20. Assertion (A): The point (–1, 6) divides the line segment joining the points (–3, 10) and (6, –8) in the ratio 2 : 7 internally. 1 Reason (R): Given three points, i.e. A, B, C form an equilateral triangle, then AB = BC = AC. (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. SECTION-B Section B consists of 5 questions of 2 marks each 21. For what value of k, will the following system of equations have infinite solutions:2 2x – 3y = 7, (k + 2)x – (2k + 1)y = 3 (2k – 1)? 22. In the given figure, prove that AD = BE if ∠A = ∠B and DE || AB. 2 C DE AB OR In the given figure, if LM || CB and LN || CD, prove that AM = AN . AB AD B M C AL N D 23. A circle is inscribed in a ∆ABC having sides 8 cm, 10 cm and 12 cm as shown in the following figure. Find AD, BE and CF. 2 NBSE 2023 5 P.T.O.

24. If 5 tan q = 3, then what is the value of  5 sin θ − 3 cos θ  2  4 sin θ + 3 cos θ 25. Find the area of a quadrant of a circle whose circumference is 25 cm. 2 OR What is the area of the circle that can be inscribed in a square of side 6 cm. SECTION-C Section C consists of 6 questions of 3 marks each. 26. Prove that 2 is an irrational number. 3 27. Find k, if the sum of the zeroes of the polynomial x2 – (k + 6) x + 2 (2k – 1) is half their product. 3 28. A part of monthly Hostel charge is fixed and the remaining depends on the number of days one has taken food in the mess.When Swati takes food for 20 days, she has to pay ` 3000 as hostel charges whereas, Mansi who takes food for 25 days pays ` 3500 as hostel charges. Find the fixed charges and the cost of food per day. 3 OR Jamila sold a table and a chair for ` 1050, thereby making a profit of 10% on the table and 25% on the chair. If she had taken a profit of 25% on the table and 10% on the chair, she would have got ` 1065. Find the cost price of each. 29. In the given figure, PA and PB are tangents to the circle from an external point P. CD is another tangent touching the circle at Q. If PA = 12 cm, QC = QD = 3 cm, then find PC + PD. 3 30. Prove that: 1 tan2 θ θ + cot2 θ θ = 1 3 + tan2 1 + cot2 NBSE 2023 6

OR If 7 sin2A + 3 cos2A = 4, show that tan A = 1 . 3 31. One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting 3 (a) Non-face card (b) Black king or Red queen (c) Spade card SECTION-D Section D consists of 4 questions of 5 marks each. 32. A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time, it had to increase its speed by 100 km/h from the usual speed. Find its usual speed. 5 OR Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream. 33. Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides at distinct points, then other two sides are divided in the same ratio. 5 OR In figure, PQ || AB and AQ || CB. Prove that AR2 = PR . CR. 34. Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm standing water is needed? 5 OR In a rain-water harvesting system, the rain-water from a roof of 22 m × 20 m drains into a cylindrical tank having diameter of base 2 m and height 3.5 m. If the tank is full, find the rainfall in cm. NBSE 2023 7 P.T.O.

35. The distribution below gives the marks of 30 students of a class in mathematics. Find the median marks of the students. 5 70–75 Marks 40–45 45–50 50–55 55–60 60–65 65–70 8 6 6 3 2 Number of 2 3 students SECTION-E Case study based questions are compulsory. 36. Case study-1 Pollution—A major problem: One of the major problem that the world is facing today is the environmental pollution. C ommon types of pollution include light, noise, water and air pollution. In a school, students thoughts of planting trees in and around the school to reduce noise pollution and air pollution. Condition I: It was decided that the number of trees that each section of each class will plant be the same as the class in which they are studying, e.g. a section of class I will plant 1 tree, a section of class II will plant 2 trees and so on a section of class XII will plant 12 trees. Condition II: It was decided that the number of trees that each section of each class will plant be the double of the class in which they are studying, e.g. a section of class I will plant 2 trees, a section of class II will plant 4 trees and so on a section of class XII will plant 24 trees. Refer to Condition I: (i) If there are two sections of each class, how many trees will be planted by the students? 1 NBSE 2023 8

(ii) If there are three sections of each class, how many trees will be planted by the students?  1 Refer to Condition II: (iii) If there are two sections of each class, how many trees will be planted by the students? 2 OR I f there are three sections of each class, how many trees will be planted by the students? 37. Case study-2 Student of a school are standing in rows and columns in a playground for a drill practice. A, B, C, D are the positions of four students as shown in the figure. (i) What are the coordinates of A and B respectively? 1 (ii) What are the coordinates of the points C and D respectively? 1 (iii) Find the distance between A and B. 2 OR Find the distance between A and C 38. Case study-3 A satellite flying at a height h is watching the top of the two tallest mountains in Uttarakhand and Karnataka, they are being Nanda Devi (height 7,816 m) and Mullayanagiri (height 1,930 m). The angles of depression from the satellite, to the top of Nanda Devi and Mullayanagiri are 30° and 60° respectively. If the distance between the peaks of two mountains is 1937 km, and the satellite is vertically above the mid-point of the distance between the two mountains. NBSE 2023 9 P.T.O.

(i) Find the distance of the satellite from the top of Nanda Devi. 1 (ii) Find the distance of the satellite from the top of Mullayanagiri. 1 (iii) What is the distance of the satellite from the ground ? 2 OR What is the angle of elevation if a man is standing at a distance of 7816 m away from Nanda Devi? NBSE 2023 10