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PRELIMINARY EXAMINATION II (2020-21) SUBJECT: MATHEMATICS Grade: X Date :11/01/2021 Time: 3 hours Total Marks: 80 General Instructions: 1. This question paper contains two parts A and B. 2. Both Part A and Part B have internal choices. Part A: 1. It consists of three sections- I and II. 2. Section I has 16 questions of 1 mark each. Internal choice is provided in 5 questions. 3. Section II has 4 questions on case study. Each case study has 5 case-based sub-parts. An examinee is to attempt any 4 out of 5 sub-parts. Part B: 1. Question No 21 to 26 are Very short answer Type questions of 2 mark each, 2. Question No 27 to 33 are Short Answer Type questions of 3 marks each 3. Question No 34 to 36 are Long Answer Type questions of 5 marks each. 4. Internal choice is provided in 2 questions of 2 marks, 2 questions of 3 marks and 1 question of 5 marks. Q.No PART A Marks Section-I Section I has 16 questions of 1 mark each. Internal choice is provided in 5 questions. 1) Show that 13/3125 has terminating decimal expansion 1 2) If the sum of zeros of the quadratic polynomial 3x2+kx-5 is 4, then find the value of k. 1 3) For what value of k, the pair of linear equations 2x + 3y = 7 and 5x + ky = 9 has a unique solution? 1 4) If ab = 1050 and LCM of a and b is 70, then find the HCF (a,b) 1 5) Is 301 a term of 5,11,17,23,......? 1 6) Find the value of p for which the equation px2 - 8x + 4 = 0 has two equal roots 1 7) Write a quadratic polynomial whose sum of zeros is 6 and product is 9. 1 8) The angle between the tangent and the radius drawn at the point of contact is ______ 1 9) Area of a sector is of the area of the circle. Find the degree measure of its minor arc. 1 10) If the mid-point of the line segment joining the points P(6 , b-2) and Q(-2 , 4 ) is (2 , -3 ), find the value of b. 1 11) A rectangular sheet of paper 44cm x 18cm is rolled along its length and a cylinder is formed. Find the volume of the cylinder thus formed. [ use = 22/7 ] 12) In fig. M= N = 46 , express x in terms of a, b and c, where a, b and c are lengths of LM, MN and NK respectively. 1 13) If radii of two concentric circles are 3 cm and 6 cm, then the length of each chord of one circle which is tangent to the other circle is ___ 1 14) The areas of two similar triangles are respectively 54 cm2 and 90 cm2 . The ratio of their corresponding sides is _______. 1 15) Evaluate: (sin30 + cos30 ) (sin60 + cos60 ) 1 16) Two dice are thrown simultaneously. Find the probability of getting a total of 4. 1 1 Section - II Case study based questions are compulsory. Attempt any four sub parts of each question. Each subpart carries 1 mark 17) 4 Points A and B are on opposite edges of a pond as shown in figure. To find the distance between the two points, Joe makes a right angled triangle using rope connecting B with another point C at a distance of 12m, connecting C to point D at a distance of 40m from point C and then connecting D to point A which is at a distance of 30m from D such that a) Which property of geometry will be used to find the distance AC? ADC = 90 0 b) What is the distance AC? c) Which of the following does not form a Pythagorean triplet? a) (7,24,25) b) (15,8,17) c) (5,12,13) d) (21,20,28) d) Find the length AB. e) Find the length of the rope used. 18) In a village, a group of people complained for an electric fault in their area. On their complaint, an electrician reached the village to repair an electric fault on a pole of height 5m. She needs to reach a point 1.3m below the top of the pole to undertake the repair work. She used ladder, inclined at an angle of to the horizontal (such that cos = 0.5) to reach the required position. a) Find the angle of elevation . b) Find the length BD. c) Find the length of the ladder. (take 3 = 1.73) d) How far from the foot of the pole should she place the foot of the ladder? e) If the height of pole and distance BD is doubled, then what will be the length of the ladder. 4 19) 4 The figure shows a bridge with hanging wires showing a mathematical shape. Answer the questions given belowa) Name the shape of the hanging wires ? a) Linear b) Spiral c) Parabola d) Ellipse b) What will be the expression of the polynomial shown in the figure ? a) y= ax + b b) y = ax2 + bx + c c) y = ax3 + bx2 + cx + d d) None of these c) The hanging wires on the bridge are represented graphically. Zeros of a polynomial can be expressed graphically. Number of zeros of polynomial is equal to number of points where the graph of polynomial a) Intersects x-axis b) Intersects y-axis c) Intersects y-axis or x-axis d) None of the above d) The representation of Hanging wires on the bridge whose sum of the zeroes is -3 and product of the zeroes is 5 is e) Graph of a quadratic polynomial is a) straight line b) circle c)parabola d)ellipse 20) An aircraft has 120 passenger seats. The number of seats occupied during 100 flights are given in the following table : a) i) What is the class width? a) 5 b) 10 c) 4 d) 100 b) What is the modal class? a) 100-104 b) 104-108 c) 108-112 d) 112-116 What is the median class? a) 100-104 b) 104-108 c) 108-112 d) 112-116 c) d) What is the upper limit of the second class interval? 4 a) 100 e) b) 104 c) 108 d) 112 Cummulative frequency helps in calculation of a) Mean b) Median c) Mode d) All of these Part B All questions are compulsory. In case of internal choices, attempt anyone. 21) A merchant has 120 ltrs and 180 ltrs of two kinds of oil. He wants to sell oil by filling the two 2 kinds of oil in tins of equal volumes. What is the greatest of such a tin? 22) Circumference of the edge of a hemispherical bowl is 132cm. Find the capacity of the bowl. 2 23) Find a quadratic polynomial whose zeros are 6 - 5 2 and 6 + 5 2 2 24) If the point A (2, 4) is equidistant from P (3, 8) and Q ( 10, y), find the values of y. 2 25) The centre of a circle is (2a, a 7). Find the values of a if the circle passes through the point 2 (11, 9) and has diameter 10 2 units. 26) Determine the volume of the remaining portion of a cube of edge 4.2cm after the largest right 2 circular cone is cut from it. 27) Prove that 3 + 5 is an irrational number. 3 28) Given that -3 and m are the roots of the quadratic equation kx2+5x - 3 = 0. Find the value of m and of k 3 29) P and Q are any points on sides AB and AC respectively of Prove A( 30) ABC. 3 APQ) : A( ABC) = (AP AQ) : (AB AC) A pilot in an aeroplane observes that Vashi bridge is one side of the plane and Bandra-Worli sea-link is on the opposite side. The angle of depression of Vashi bridge and Worli Sea-link are 60 and 30 respectively. If the aeroplane is at a height of 5500 3 at that time. What is the distance between Vashi bridge and Worli sea-link? 3 31) Find the values of x and y if the median for the following data is 31. 3 32) If 3tan2 + 4 3tan + 3 = 0 determine the possible values of acute angle . 3 33) A medical camp was held in a school to impart health education and the importance of exercise 3 to children. During this camp, a medical check of 35 students was done and their weights were recorded as follows: Compute the modal weight. 34) Prove that the intercept of a tangent of a circle made by two parallel tangents of the same circle 5 subtends a right angle at the centre. 35) ABC is a right triangle, right angled at C. Let BC = a, CA = b, AB = c and let p be the length of the perpendicular frm C on AB. Prove that : 36) 1) cp=ab 5 2) 1/p2 = 1/a2 + 1/b2 A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream. 5
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