CBSE Class 10 Mathematics Exam Paper PDF

Paper Contributed By SP LEARNING SOLUTIONS SOLUTIONS, Gubbi Mathematics Exam [ NCERT Based] CBSE Class 10...

Paper Contributed By SP LEARNING SOLUTIONS SOLUTIONS, Gubbi Mathematics Exam [ NCERT Based] CBSE Class 10 Time: 90m 80 Marks 1. The lines represented by the pair of linear equations x + 2y = 8 and 2x + 4y = 10 are (a)) intersecting each other ((b) perpendicular to each other1 1 x 20 = 20 (c)) coincident ((d) parallel to each other 2. Sum of the zeroes of the polynomial p ( x ) = x2 – 2x – 8 is……. (a) – 8 (b)) 2 (c) ( –2 (d) ( 8 3. If tan θ = 1, then the value of sec θ is……….. is a) (b) √33 ( √2 (c) 2 (d) ( √ √ 4. In ∆ ABC, AB = 3 units, BC = 1 unit, AC = 2 units and ∟ACB ACB = θ, then value of ‘θ’is (a) 0° (b)) 60° (c) ( ) 45° (d) ( 90° 5. The HCF and LCM of two numbers are 4 and 60 respectively. If one of the numbers is 12, then the other number is ….. a)) 30 b) 20 c)) 45 d) 56 𝟏 √𝟑 6. If sin A = , cos A = , thenthe value of tan A is…………. 𝟐 𝟐 a) b) c) d) √ √ 7. On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps? (a) 2540 (b)2560 (c)2650 (d)2520 8. Find the quadratic polynomial whose zeros are -3 and 4. (a) x2 - 7x – 12 (b) x2 + x + 12 (c) x2 – x – 12. (d) x2 + 3x – 4 9. Which of the following equations has no real roots? (a) x2 – 4x +3√2 = 0 (b) x2 + 4x - 3√2 = 0 (c) x2 – 4x -3√2 = 0 (d) 3x2 + 4√3 x + 4 = 0 10. The roots of ax2 + bx + c = 0, a ≠ 0 are real and unequal. Which of these is true about the value of discriminant, D? (a) D < 0 (b) D > 0 (c) D = 0 (d) D ≤ 0 11.Two APs have the same common difference. The first term of one of these is –1 and that of the other is – 8. Then the difference between their 4th terms is……. (a) 7 (b)) 8 (c)) 9 (d) ( 10 www.cbseguess.com Page 1  Paper Contributed By SP LEARNING SOLUTIONS SOLUTIONS, Gubbi 12. If the numbers n – 2, 4n – 1 and 5n + 2 are in AP, then the value of n is ………… (a) 3 (b)) 4 c)) 1 d) 2 13. If ∆ABC~∆PQR, AB =6.5 cm ,PQ = 10.4cm. Perimeter of ∆ABC is 60 cm , then the perimeter of ∆PQR is (a) 100cm (b) 60cm (c) 96 cm (d) none 14. XY is drawn parallel to the base BC of a ∆ABC cutting ting AB at X and AC at Y. If AB = 4 BX and YC =2cm, then AY is…………. (a) 2cm (b) 4cm (c) 6 cm (d) 8c 8cm 15. The coordinates of a point A, where AB is the diameter of a circle, whose ccenter is (2, -3) 3) and B (1,4) is…………… a. (10, 3) b. (3, (3,-10) c. (-3,10) 3,10) d. ((-3,-10) 16. The points (–4,4, 0), (4, 0) and (0, 3) are the vertices of a ………….. (a) right triangle (b) isosceles triangle (c) equilateral triangle (d) scalene triangle 17. If sin θ + cos θ = √2,2, then tan θ + cot θ = (a)1 (b) 2 (c) 3 (d) 4 18. = …………… (a) sec2 A (b) -1 (c) cot2A (d) tan2A 19. Assertion (A): The polynomial f(x) = x2- 2x + 2 has two real zeros. Reason (R): A quadratic polynomial can have at most two real zeroes. 20. Assertion(A): The equation 9x2 + 3kx + 4 = 0 has equal roots for k = 9. Reason (R): If discriminant 'D' of a quadratic equation is equal to zero, then roots of equation are real and equal. 21. Prove that 3 + √22 is an irrational number. number 2 x 5 = 10 22. Solve the given pair of linear equations by Elimination method : 2x + y = 8 and 3x – y = 7. 23. Prove that: =. 24.Find the coordinates of the point which divides the linesegment joining the points (4, – 3) and (8, 5) in theratio 3 : 1 internally. 25. ‘D’ is a point on the side BC of a ∆ ABC such that∟ADC = ∟BAC BAC. Then prove 2 that AC = BC. CD.33 x 6 = 18 26.Age of mother is twice the square of age of her son. After8 years mother’s age is 4 years more than the thrice ofage of her son. Find their present ages. [OR] www.cbseguess.com Page 2  Paper Contributed By SP LEARNING SOLUTIONS SOLUTIONS, Gubbi The sum of a two -digit digit number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number, how many such numbers are there. 27. Prove that √3 is an Irrational ational number. 28. Find the zeros of the quadratic polynomial 4x2 – 4x + 1 and verify the relationship between its zeros and coefficients. 2 29. Prove that : (cosec θ – cot θθ) = [OR] Prove that : secA(1–sinA) sinA) (secA + tan A ) = 1 30. The sum of third and seventh terms of an AP is 6 and their product is 8. Find the sum of the first sixteen terms of the AP. [OR] The sum of 4th and 8th terms of an AP is 24 and the sum of 6th and 10th terms is 44. Find the first three terms of the AP. 31.If AD and PM are medians of triangles ABC and PQR respectively where 𝛥ABC ~𝛥 PQR, Prove that = [ OR ] A girl of height 90 cm is walking away from the base of a lamp post at a speed of 1.2m/s, If the lamp is 3.6m above the ground, find the length of her shadow after 4 seconds. 4 x 5 = 20 32. If a Train travels 360 km at a uniform speed. If the speed had been 5km/h more, m it would have taken 1 hour less for the same journey. Find the speed of the train. [OR] A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the sstream. 33. State and prove Basic Proportionality theorem. 34.Find the solution of the given pair of linear equations bygraphical method: 2x + y = 8 and x + y = 5 35. Places A and B are 100km apart on a highway. If one car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours, if they travel towards each other they meet in one hour, what are the speeds of the two cars? [OR] The ratios 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 Rs per month, find their monthly incomes. Case Study Q Questions 3 x 4 = 12 36.The below picture are few natural examples of parabolic shape which is represented www.cbseguess.com Page 3  Paper Contributed By SP LEARNING SOLUTIONS SOLUTIONS, Gubbi by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms. 1. In the standard form of quadratic polynomial, a, b, c are a) All are real numbers. b) All are rational numbers. c) ‘a’ is a non zero real number b and c arereal numbers. d) All are integers. 2. If the roots of the quadratic polynomial are equal, where the discriminantD = – 4ac, then a) D > 0b) D < 0c) D≥ 0 d) D = 0 3. Ifὰ and are the zeroes of the quadratic polynomial 2x2 – x + 8k then k is………. a) 4b) c) d) 2 4. The graph of x2+1=0 a) Intersects x‐axis ‐axis at two distinct points.b)Touches points.b)Tou x‐axis at a point. c) Neither touches nor intersects xx‐axis.d)Either ‐axis.d)Either touches or intersects x‐ axis. 2. Raj and Ajay are very close friends. Both the families decide to go to Ranikhet by their own cars. Raj’s car travels at a speed of x km/h while Ajay’s car travels 5 km/h faster than Raj’s car. Raj took 4 hours more than Ajay to complete journey of 400km. 1. What will be the distance covered by Ajay’s car in two hours? a) 2(x +5)kmb) (x – 5)kmc) 2( x + 10)kmd) (2x + 5)km 2. Which of the following quadratic equation describe the speed of Raj’s car? a) x2- 5 x - 500 = 0b) x2+ 4x - 400 = 0c) x2+ 5x - 500 = 0d) x2- 4x + 400 = 0 www.cbseguess.com Page 4  Paper Contributed By SP LEARNING SOLUTIONS SOLUTIONS, Gubbi 3. What is the speed of Raj’s car? a) 20 km/hourb) 15 km/hourc) 25 km/hour d) 10 km/hour 4. How much time took Ajay to travel 400 km? a) 20 hourb) 40 hour c) 25 hourd) 16 hour 3. Your elder brother wants to buy a car and plans to take loan from a bank for his car. He repays his total loan of Rs 1,18,000 by paying every month starting with the first rst instalment of Rs 1000. If he increases the instalment by Rs 100 every month , answer the following: 1. The amount paid by him in 30th installment is a) 3900b) 3500c) 3700d) 3600 2. The amount paid by him in the 30 installments is a) 37000b) 73500c) 0c) 75300d) 75000 3. What amount does he still have to pay offer 30th installment? a) 45500b) 49000c) 44500d) 54000 4. If total installments are 40 then amount paid in the last installment? a) 4900b) 3900c) 5900d) 9400 www.cbseguess.com Page 5