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CBSE Class 10 Pre Board 2020 : Mathematics - Prelim 1 (Delhi Public School (DPS), Jammu)

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DELHI PUBLIC SCHOOL JAMMU ASSIGNMENT PREBOARD -1st Class: X Sub: Maths Q1. The product of the HCF and LCM of the smallest prime number and the smallest composite number is (1) (a) 2 (b) 4 (c) 6 (d) 8 Q2. How many prime factors are there in prime factorization of 5005? (1) (a) Q3. 4 (c) 6 (d) 7 2 (b) 2 (c) 3 3 (d) 2 -3 Product of all the zeroes of the cubic polynomial 3x3 5x2+ 8x 12 is (1) (a) Q5. (b) If one zero of 2x2 3x + k is reciprocal of the other , then the value of K is (1) (a) Q4. 2 8 (b) 3 2 (c) 3 5 3 (d) 4 The pair of linear equations 3x + 4y + 5 = 0 and 12x + 16y + 15 = 0 have (1) Q6. (a) Unique solution (c) Exactly two solutions (b) (d) Many solution No solution] If absicca of a point is zero , then it lies on (1) (a) x axis (b) y axis (c) I Quadrant (d) III Quadrant Q7. The midpoint of the line segment AB is the point ( 0,4) . if the are ( -2,3) , then the coordinates of A are (1) Q8. (a) (2,5) (b) (-2,-5 ) (c) (2,9) (d) (-2, 11) Choose the correct option 2 tan 30 0 1+ 2 30 coordinates of B (1) = (a) sin 600 (b) cos 600 (c) tan 600 (d) sin 300 Q9. The angle of elevations of sun , when shadow of a pole h meters high is meter long is (1) (a) Q10. 600 300 (b) ` (c) 450 (d) 3 150 If in PQR xy QR . Px = x 2 , xq = 3x , py = x+2 and yr = 9x , then the value of x is (1) (a) 1 (b) 2 (c) 3 (d) 4 P X Y Q11. A ladder is placed Q against a wall such thatRits tool is at a distance of 2.5m from the wall and top reaches 6m above ground. The length of the ladder is (1) (a) Q12. Q13. 6.5cm (b) 5cm (c) 9cm (d) 4cm In the given fig. of if ABC PQR the value of x is (1) (a) 3cm 2.5cm (b) 3.5cm (c) 2.75cm (d) Construction of a cumulative frequency table is useful in determining the (1) (a) Mean (b) median (c) mode (d) Q14. x is The mean of 5 observations x , x+ 2 , x+ 4 , x+ 6 and x + 8 is 11 (1) (a) 4 (c) 11 (d) 6 Q15. For a symetrical distribution, which is correct? (a) mean > mode > median (b) mean < mode < median (c) then the value of (b) 7 (1) mode = (d) all + 2 mean = median = mode Q16. A tangent PQ at a point P if a circle of radius 5 cm meets a line through O at a point Q so that OQ = 12 cm. length PQ is (1) (a) Q17. 12cm (b) 13cm (c) 8.5cm (d) Q20. 119 When the point is inside the circle, how many tangents can be (1) constructed (a) (d) None (b) one (c) two Q18. AB is the diameter and TB is the tangent to the circle. If Q is a point on QA is equal to (1) Q19. the centre a) 2 2 b) 2 + 2 c) 4 2 + 2 d) 2 + 4 2 Choose the correct a) 2 A c) 2 1+ 2 1+ 2 = three TB . then (1) b) -1 d) 2 Choose the correct (1) (1 + tan + sec ) (1 + cot - cosec ) = a) 0 (b) 1 (c) 2 (d) cos A Section B Q21. 10 students of class X took part in a mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz (2) Q22. Find the ratio in which the Line segment joining A (1, -5 ) and B ( -4 , 5) is divided by the x axis . Also find the coordinates of the point of division (2) Q23. Find the area of a rhombus if its vertices are ( 3,0) , ( 4,5) ( -1,4) and (-2 , -1 ) taken in order Or Find the value of : (2) 3 3 Q24. Prove that cos cot +cos + 3 + 3 + 1 = (2) +1 If the angle of elevation of the tops of two statues of height m1 and m2 are 600 and 300 respectively from the mid point of the line segment joining their feet , then find the ratio m1 : m2 (2) Q26. Prove that the parallelogram circumscribing a circle is a rhombus (2) Q25. Q27. Prove that 3 + 2 5 is irrational Q28. Find all the zeroes of 2x4- 3x3+ 6x-2 . If it s two zeroes are 2 and Q29. Solve the pairs of equations by reducing them 10 + Q30. + 2 =4, Evaluate: 15 + - 2 15 sin 35 0 55 0 + 35 0 sin 55 0 2 43 0 47 15 0 25 0 60 0 75 0 65 0 Q31. The shadow of a tower standing on a level ground is found to be 40 m when the sun s altitude is 300 than when it is 600. Find the height of the tower longer Q32. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Prove it Q33. Draw less than and more than ogive on the same graph and find median (3) on graph C .g 0-10 10-20 20-30 30-40 40-50 Frequency 5 10 15 06 04 Q34. Prove that the lengths of tangents drawn from one external point to a equal. (3) circle are Q35. The students of a class are made to stand in rows. If 3 students are extra in a row , there would be 1 row less . If 3 students are less in a row, there would 2 rows more. Find the number of students in the class (4) Q36. The two opposite vertices of a square are ( -1 , 2) and ( 3,2) . find the of the other two vertices (4) coordinates tan tan + cot Q37. If A+ B = 900, then prove that Q38. If tan + sin = m and tan - sin = n , sin sec 2 2 Show that m2 n2 = 4 Q39. The angle of elevation of an aeroplane from a point on the ground is 600. After a flight of 30 seconds, the angle of elevation changes to 300 .If the plane is flying at a constant height of 3600 3 , find the speed of the plane in km / hour (4) Q40. BL and CM are medians of a triangle ABC right angled at A , prove that 4 ( BL2 + CM2) = 5BC2 Q41. If the median of the following frequency distribution is 32.5. find the F1 and F2 (4) Class frequency 0-10 F1 10-20 5 20-30 9 30-40 12 40-50 F2 50-60 3 60-70 2 values of 40 42. Check whether the following statement is true of false. Justify your answer. Every quadratic equation has at least one real root. + 43. Does there exist a quadratic equation whose coefficients are all distinct irrational but both the roots are rationals? Why? 44. Does their exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer. 45. The 51st, 11th and last term of an AP are 0, 8, -1/5 respectively. Find the common difference and the number of terms? 45. Find the 10th term from the end of the AP, 4, 9, 14, , 254. 46. The sum of three numbers in AP is 3 and their product is -35. Find the numbers. 47. If the first and the last terms of an AP are 17 and 350 respectively and the common difference is 9, how many terms are there in the AP? 48. If the 3rd and the 9th term of an AP are 4 and -8 respectively. Which term of this AP is zero. 49. The eighth term of an AP is 131. If its 15th term exceeds its 11th term by 16, find the AP. 50. Find the value of k for which 2k-7, k+5 and 3k+2 are first consecutive terms of an AP. Find the AP. 51. Draw a line segment PQ of length 7cm and divides it internally in the ratio 8:5. Also measure the lengths of two parts so obtained. 52. Draw a line segment AB of length 4cm and divides it internally in the ratio 2:3. Also give the justification for this construction. 53.Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game.? 54.One card is drawn from a well shuffled deck of 52 cards . Find the probability of getting (1) a king of red colour (2) a face card (3)the queen of diamond . 55. A bag contains 5 red balls and some blue balls . if the probability of drawing a blue ball is double that of a red ball determine the number of blue balls in the bag . 56. Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60 degree . 57. Construct a triangle with sides 5 cm 6 cm 7 cm and then other triangle whose sides are 7/5 of the corresponding sides of the first triangle . 58. Sum of the areas of two squares is 468 m sq. if the difference of their perimeters is 24 m,find the sides of two squares 59. Find two consecutives odd positive integers sum of whose squares is 290. 60.A train travels 360km at a uniform speed. If the speed had been 5 kmph more It would have taken 1 hour less for the same journey .Find the speed of the tran.

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