Star City international school taranagar Pre- board Exam :2020 -21 Class-10th Subject- Maths Time:3h. M. M.80 Section-A Section A has 16 questions of 1 mark each. 1. If xy = 180 and HCF(x, y) = 3, then find the LCM(x, y). OR The decimal representation of 14587/(21 × 54) will terminate after how many decimal places? 2. If the sum of the zeroes of the quadratic polynomial 3x2 -kx+6 is 3, then find the value of k. 3. For what value of k, the pair of linear equations 3x+y=3 and 6x+ky=8 does not have a solution. 4. If 3 chairs and 1 table costs Rs. 1500 and 6 chairs and 1 table costs Rs.2400. Form linear equations to represent this situation. 5. Which term of the A.P. 27, 24, 21,…..is zero? OR In an Arithmetic Progression, if d= - 4, n=7,an=4, then find a. 6. For what values of k, the equation 9x2+6kx+4=0 has equal roots? 7. Find the roots of the equation x2+7x+10=0 8. A die is thrown once. find the probability of getting a prime number 9. If two tangents are inclined at 60˚ are drawn to a circle of radius 3cm then find length of each tangent. 10. In the ∆ABC, D and E are points on side AB and AC respectively such that DE II BC. If AE=2cm, AD=3cm and BD=4.5cm, then find CE. 11. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle. 12. ??? ? + ??? ? = 1, ? = 30° and B is an acute angle, then find the value of B. 13. If x=2sin2Ɵ and y=2cos2Ɵ+1, then find x+y. 14. In a circle of diameter 42cm,if an arc subtends an angle of 60˚ at the centre where π = 22/7, then what will be the length of arc. 15. 12 solid spheres of the same radii are made by melting a solid metallic cylinder of base diameter 2cm and height 16cm. Find the diameter of the each 16. Two players, Sangeeta and Reshma, play a tennis match. It is known that the probability of Sangeeta winning the match is 0.62. What is the probability of Reshma winning the match? Section –B Question numbers 17 to 21 two marks each 17.Find the area of a sector of circle with radius 6 centimetre if angle of the sector is 60⁰ 18.The angle of elevation of the top of a tower from a point on the ground which is 30m away from the foot of the tower is 30⁰ Find the height of the tower. 19.If sinA = cos(A - 26) , find the value of A. 20.The radii of two circles are 97cm and 98cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles. 21.A jar contains 24 marbles some are green and other are blue .If a marble is drawn at random from the jar the probability that it is green is 2 /3. find the number of blue balls in the jar. Section -C Question numbers 22 to 31 3 marks each 22. Find the point on x-axis which is equidistant from the points (2,-2) and (-4,2) OR P (-2, 5) and Q (3, 2) are two points. Find the co-ordinates of the point R on PQ such that PR=2QR 23. Find a quadratic polynomial whose zeroes are 5-3√2 and 5+3√2. 24. Draw a line segment AB of length 9cm. With A and B as centres, draw circles of radius 5cm and 3cm respectively. Construct tangents to each circle from the centre of the other circle. 25. If tanA=3/4, find the value of (1/sinA)+(1/cosA ) OR If √3 sinƟ- cosƟ=0 and 0˚<Ɵ <90˚, find the value of Ɵ 26. How many three digit numbers are divisible by 7? 27.. Prove that 2-√3 is irrational, given that √3 is irrational. 28. If one root of the quadratic equation 3x² +px +4=0 is 2/3, then find the value of p and the other root of the equation. OR The roots α and β of the quadratic equation x²- 5x+ 3(k-1)=0 are such that α-β=1. Find the value k . 29. In an equilateral triangle prove that three times the square of one side is equal to four times the square of one of its altitudes. 30. Prove that:(sinA - 2sin³A)/(2cos³ -cosA) =tanA 31. prove that the angle between the two tangents drawn from an external point to a circle in supplementary to the angle subtended by the line segment joining the point of contact at the centre. Section -D Question numbers 32 to 37 4 marks each 32. The median of the following data is 16. Find the missing frequencies a and b, if the total of the frequencies is 70. Class 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 Frequency 12 a 12 15 b 6 6 4 33. A girl of height 90cm is walking away from the base of a lamp post at a speed of 1.2 metre per second. If the length is 3.6 metre above the ground ,find the length of her shadow after 4 seconds 34. The two palm trees are of equal heights and are standing opposite each other on either side of the river, which is 80 m wide. From a point O between them on the river the angles of elevation of the top of the trees are 60° and 30°, respectively. Find the height of the trees and the distances of the point O from the trees. 35. A well of diameter 3m is dug 14 m deep. the earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4m from an embankment. find the height of the embankment. 36.Aftab tells his daughter seven years ago I was 7 times as old as you were then. Also three years from now I shall be three times as old as you will be. find the present age Aftab and daughter using by graphically method. 37.In a class test the sum of Shefali's marks in mathematics and English is 30. Had she got 2 marks more in mathematics and 3 marks less in English .The product of their marks would have been 210. Find her marks in the two subjects.
