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VIBGYOR HIGH First Term Examination 2020-2021 MATHEMATICS Grade: X Max. Marks : 80 Date : 24/09/2020 Time Allowed : 2 hours INSTRUCTIONS: Answers to this paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this paper is the time allowed for writing the answers. Attempt all questions from Section A and any four question from Section B The intended marks for the questions or parts of questions are given alongside the questions. All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer. Omission of essential working will result in the loss of marks. Geometrical figures to be constructed wherever applicable. For geometry, figures are to be copied to the answer script. _________________________________________________________________________ SECTION A (40 marks) (Attempt all questions) Q.1 a) a b Find the third proportion to and b a b) How many terms of the A.P. 27, 24, 21 should be taken so that their sum is a 2 b2 . zero? c) [3] [3] 5 0 1 If Matrix A , B= and 3A M = 2B; 6 4 3 i) Write the order of matrix M ii) Find matrix M [4] 1 Q.2 a) Manohar has a cumulative deposit account in a finance company for 1 1 years 2 at 9% per annum. If he gets ` 15426 at the time of maturity, how much per month has been invested by Manohar? [3] b) Solve the following equation using formula: 4 11x 3 x 2 [3] c) Calculate the ratio in which the line joining A(-4, 2) and B(3, 6) is divided by point P(x, 3). Also find x. [4] Q.3 ma 2 +nc 2 = mb 2 +nd 2 a 4 +c 4 a) If a: b:: c : d, show that [3] b) Solve the following inequation and write the solution set: b 4 +d 4 [3] 13x 5 < 15x + 4 < 7x + 12, x R Represent the solution on a real number line. c) Use short-cut method to find the mean of the monthly wages of a certain number of workers. Monthly [4] 90-110 110-130 130-150 150-170 170-190 4 6 4 8 18 Wages(`) No. of workers Q.4 a) Using ruler and compass, construct a regular hexagon ABCDEF of side 5 cm. Hence construct circle circumscribing the hexagon. 2 [3] b) A shopkeeper sells an article for ` 1770 with GST 18%. A customer willing to buy this article, asks the shopkeeper to reduce the price of the article so that he pays only ` 1888 including GST. If the shop keeper agrees for this, how much reduction will the shopkeeper give? c) [3] In the given figure, PQL and PRM are two tangents to the circle with centre O at point Q and R respectively. If S is a point on the circle such that SQL = 50 L and SRM = 60 Find the reflex QOR . 50 .O S [4] Q P 60 R M SECTION B (40 marks) (Attempt any 4 questions) Q.5 a) In an A.P, the sum of its first n terms is 6n n 2 . Find the 25th term. b) A solid sphere and solid hemisphere have the same total surface area. Find the ratio of their volumes. c) [3] [3] In a trapezium ABCD, AB is parallel to DC and DC = 2AB. EF drawn parallel to AB cuts AD in F and BC in E such that 4BE = 3EC. Diagonal DB intersects FE at point G. Prove that : 7EF = 10AB [4] A F B E G 3 D C Q.6 a) Using a graph paper draw a histogram for the given distribution showing the number of runs scored by 60 batsmen. Estimate the mode of the data: b) Runs Scored No. of Batsmen 3000 4000 4 4000-5000 18 5000-6000 9 6000-7000 7 7000-8000 8 8000-9000 4 9000-10000 10 [3] A retailer purchases fans worth ` 15000 from the wholesaler and sells it to a consumer at 10% profit. If the transactions are intrastate and the rate of GST is 12%, then calculate the GST paid by the retailer. c) [3] Using a ruler and a compass draw a line segment AB = 6cm. construct a circle with AB as the diameter. Mark a point P at a distance of 5cm from the midpoint of AB. Construct two tangents from the point P to the circle which has AB as the diameter. Measure the length of each tangent. [4] In the figure, DBC= 58 . BD is a diameter of the circle. Calculate: [3] Q.7 a) i) BDC ii) BEC iii) BAC A D B C E b) Find the values of k for which the following equation has equal roots x 2 2kx 7 k 12 0 [3] 4 c) Using a graph paper plot quadrilateral ABCD whose vertices are A(2, 2), B(2, -2), C(0, -1) and D(0, 1) (Take 2cm = 1unit along both axes) i) Reflect quadrilateral ABCD on the y-axis and name it as A'B'CD. ii) Name two points which are invariant under the above reflection. iii) Name the type of polygon obtained by the above reflection. iv) Find the area of A'B'CD. [4] Q.8 a) A bag contains 6 black, 5 white and 9 green balls. One ball is drawn at random. What is the probability that the ball drawn is b) i) Not green ii) Either white or green iii) Neither white nor green [3] In the given figure PQ is a tangent to the circle at A. AB and AD are bisectors of o CAQ and PAC respectively. IF BAQ = 30 , prove that: i) BD is a diameter of the circle. ii) ABC is an isosceles triangle [3] C D B P c) 1 1 If A = , B= 2 1 Q A x 1 2 2 2 4 1 and A B (A+B) , find the value of x. 5 [4] Q.9 a) Point A (4, -1) is reflected as A' in y-axis. Point B on reflection in x-axis is mapped as B'(-2, 5). b) i) Write the coordinates of A' and B. ii) Find the coordinates of the mid-point of line segment A'B. [3] B In the given figure AB = 9cm, PA = 7.5cm and PC = 5cm. Chords AD and BC intersect at P i) Prove that PAB ~ PCD ii) Find the length of CD iii) Find Area of PAB : Area of PCD D P A [3] C x 3 x 341 , using properties of proportion find x 3x 2 1 91 3 c) If [4] Q.10 a) From a circular cylinder of diameter 10 cm and height 12 cm, a conical cavity of the same base radius and of the same height is hollowed out. Find the volume of the remaining solid. ( 3.14 ) b) [4] The marks obtained (out of 100) by 400 students in an examination are given below: [6] Marks obtained No. of Students 0-10 10 10-20 20 20-30 22 30-40 40 40-50 54 50-60 76 60-70 80 70-80 58 80-90 28 90-100 12 6 Using a graph paper, draw an ogive for the above distribution. Use your ogive to estimate: i) the median ii) the number of students who obtained more than 80% marks in the examination. iii) the number of students who did not pass, if the pass percentage was 35 marks. Q.11 a) Find the values of x, which satisfy the inequation: 1 2x 5 2, x W. Graph the solution set on the number line. 2 3 6 [3] b) How many whole numbers, each divisible by 7, lie between 200 and 500? [3] c) By increasing the speed of a car by 10 km/hr, the time of journey for a distance 2 of 72 km is reduced by 36 minutes. Find the original speed of the car. ***** 7 [4]
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