Title cbjemapu02.pdf ✅

Page 1 NODIA Sample Paper 02 CBSE Mathematics Class 10 Click the Following Button to See the Free MS/Solutions Sample Paper 02 Class- X Exam - 2023-24 Mathematics - Standard Time Allowed: 3 Hours Maximum Marks : 80 General Instructions : 1. This Question Paper has 5 Sections A-E. 2. Section A has 20 MCQs carrying 1 mark each 3. Section B has 5 questions carrying 02 marks each. 4. Section C has 6 questions carrying 03 marks each. 5. Section D has 4 questions carrying 05 marks each. 6. Section E has 3 case based integrated units of assessment (04 marks each) with sub-parts. 7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and 2 Questions of 2 marks has been provided. 8. Draw neat figures wherever required. Take 7 22 π = wherever required if not stated. Section - A Section A consists of 20 questions of 1 mark each. 1. A letter of English alphabet is chosen at random, what is the probability that the letter so chosen is a consonant? (a) 26 5 (b) 26 21 (c) 13 2 (d) 13 7 2. What is the HCF of smallest primer number and the smallest composite number? (a) 2 (b) 4 (c) 6 (d) 8 3. If A^ h 5 2, , B^ h 2 2 , - and C t ^ h -2, are the vertices of a right angled triangle with +B = 90o, then the value of t will be (a) 1 (b) 2 (c) 3 (d) 4 4. The sum and product of zeroes of a quadratic polynomial are 6 and 9 respectively. The quadratic polynomial will be (a) x x9 6 2 + − (b) x x6 9 2 + + (c) x x6 9 2 − + (d) x x6 9 2 + − 5. Half the perimeter of a rectangular garden, whose length is 4 m more then its width, is 36 m. The dimensions of garden will be (a) 20 m by 16 m (b) 36 m by 10 m (c) 16 m by 30 m (d) 20 m by 16 m 6. The quadratic equation x x 5 0 2 + − = has (a) two distinct real roots (b) two equal real roots (c) no real roots (d) more than 2 real roots 7. Which of the following equations has 2 as a root? (a) x x4 5 0 2 − + = (b) x x3 12 0 2 + − = (c) 2 7 x x 6 0 2 − + = (d) 3 6 x x 2 0 2 − − =
Page 2 NODIA Sample Paper 02 CBSE Mathematics Class 10 Click the Following Button to See the Free MS/Solutions 8. What happens to value of cos θ when θ increases from 0o to 90o. (a) cos θ decreases from 1 to 0. (b) cos θ increases from 0 to 1. (c) cos θ increases from 2 1 to 1 (d) cos θ decreases from 1 to 2 1 9. The times, in seconds, taken by 150 athletes to run a 110 m hurdle race are tabulated below Class 13.8-14 14-14.2 14.2-14.4 14.4-14.6 14.6-14.8 14.8-15 Frequency 2 4 5 71 48 20 The number of athletes who completed the race in less than 14.6 second is : (a) 11 (b) 71 (c) 82 (d) 130 10. For what value of k , the pair of linear equations kx − 4 3 y = , 6 1 x y − 2 9 = has an infinite number of solutions ? (a) k = 2 (b) k ! 2 (c) k ! 3 (d) k = 4 11. The top of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30c with the horizontal, then the length of the wire is (a) 12 m (b) 10 m (c) 8 m (d) 6 m 12. Which term of an AP, 21, 42, 63, 84, ... is 210? (a) 9th (b) 10th (c) 11th (d) 12th 13. The perimeters of two similar triangles TABC and TPQR are 35 cm and 45 cm respectively, then the ratio of the areas of the two triangles is ......... (a) 9 2 (b) 9 7 (c) 81 49 (d) 4 3 14. ? tan tan cot cot 1 1 2 2 2 2 θ θ θ θ + + + = (a) 1 (b) 2 tan2 θ (c) 2 cot 2 θ (d) 2 sec2 θ 15. It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would be (a) 10 m (b) 15 m (c) 20 m (d) 24 m 16. If two solid hemispheres of same base radius r are joined together along their bases, then curved surface area of this new solid is (a) 4 r2 π (b) 6 r2 π (c) 3 r2 π (d) 8 r2 π 17. If zeroes of the polynomial x x4 2a 2 + + are a and , a 2 then the value of a is (a) 1 (b) 2 (c) 3 (d) 4 18. If radii of two concentric circles are 4 cm and 5 cm, then the length of each of one circle which is tangent to the other circle, is (a) 3 cm (b) 6 cm (c) 9 cm (d) 1 cm
Page 3 NODIA Sample Paper 02 CBSE Mathematics Class 10 Click the Following Button to See the Free MS/Solutions In the question number 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correction option. 19. Assertion : Pair of linear equations : 9 3 x y + + 12 = 0,8 6 x y + + 24 = 0 have infinitely many solutions. Reason : Pair of linear equations a x1 1 + + b y c1 = 0 0 and a x2 2 + + b y c2 = have infinitely many solutions, if a a b b c c 2 1 2 1 2 = = 1 (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. 20. Assertion : If nth term of an AP is 7 4 - n, then its common differences is -4. Reason : Common difference of an AP is given by d a = n n +1 − a . (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. If two positive integers p and q are written as p a b 2 3 = and q a b, 3 = where a and b are prime numbers than verify LCM H ( , p q) ( # CF q q, ) = pq 22. If the nth term of an AP -1 4, , 9 1, , 4 ..... is 129. Find the value of n. O Write the nth term of the AP , , ,..... m m m m 1 1 + +1 2m 23. If the mid-point of the line segment joining the points A( , 3 4) and B k( , 6) is P x( , y) and x y + − 10 = 0, find the value of k . 24. In figure, AP, AQ and BC are tangents of the circle with centre O. If AB = 5 cm, AC = 6 cm and BC = 4 cm, then what is the length of AP? O Two chords AB and CD of a circle intersect at E such that AE = 2 4. cm, BE = 3 2. cm and CE = 1 6. cm. What is the length of DE ?