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GOLDCREST HIGH, VASHI COMPREHENSIVE ASSESSMENT [2020-21] Roll No._______ Name :________________ Sub: Mathematics Grade: 10 MM : 80 Time : 2 Hours 30 minutes Date : 25.01.2021 __________________________________________________________________________ GENERAL INSTRUCTIONS First 15 minutes are for reading of questions. All questions to be answered on- the SECTION I (40answer Marks)sheets. On the First page of your write your Name, Class/Sec, Roll Attempt all Answer questionsScript, from this Section. No., Date and Total number of pages used. Also write your Name, Class/Sec, Roll No and Page number on each page. After completing the Answers, click the picture of your answer script and convert it to PDF. Rename the PDF File with your Name_ClassSec_Roll No_Subject Upload the PDF in your Google Classroom. Total no: of questions in the question paper: 11 Total no: of pages for the question paper:6 SECTION I (40 Marks) Attempt all questions from this section. Question 1. a) What must be subtracted from 16x3 8x2 + 4x +7 so that the resulting expression has 2x + 1 as a factor? b) Kangna had a recurring deposit account in a bank and deposited Rs.600 [3] [3] 1 per month for 2 years. If the rate of interest was 10% p.a, find the maturity 2 value of this account. c) Prove that: ( 1 + cot cosec ) ( 1 + tan + sec ) = 2 Question 2. a) Three vertices of a parallelogram ABCD taken in order are A(3,6), B(5,10) and C(3,2). Find: (i) The co-ordinates of the fourth vertex D (ii) Equation of side AB of the parallelogram ABCD. 1 [4] [3] b) The sum of the height and the radius of a solid cylinder is 35 cm and its total surface area is 3080 cm2; find the volume of the cylinder. [3] c) Cards marked with numbers 5,6,7,8, ,100 are well shuffled, and a card is drawn at random. What is the probability that the number on the card is: (i) a perfect square? (ii) divisible by 5? [4] Question 3. a) Solve the equation 4x2 5x 3=0 and give your answer correct to two decimal places. b) In the given figure, AB and DE are perpendicular to A BC. (i) If AB=6cm, DE=4cm and AC=15cm. Calculate CD. (ii) Find the ratio of the area of . B [3] D E C c) From the top of a building 60m high, the angle of depression of the top and bottom of a vertical lamp post are observed to be 30 and 60 respectively. Find: (i) The horizontal distance between the building and lamp post. (ii) The height of the lamp post. Question 4. a) The MRP of an article is Rs 1200. The shopkeeper sells it at Rs 900. If the rate of G.S.T is 12% on the article, calculate the net amount paid by the consumer including G.S.T. b) The sum of the first three terms of an A.P. is 42 and the product of the first and third term is 52. Find the first term and the common difference. c) Find the range of value of x , which satisfy : 4 19 < 3 5 2 2 5 + Graph in each of the following cases, the value of x on the different real number lines when: (i) x (ii) x (iii) x 2 [3] [4] [3] [3] [4] SECTION II (40 Marks) Attempt any four questions from this Section. Question 5. a) A certain number of metallic cones, each of radius 2 cm and height 3 cm are [3] melted and recast into a solid cylinder of diameter 12 cm and height 4 cm. Find the number of cones. b) Three coins are tossed together. Find the probability of getting: [3] i) at least two heads. ii) atmost two heads. iii) all tails. c) In the given figure, AD is the diameter. O is the center [4] of the circle. AD is parallel to BC and = 32 . Find: (i) ( ) ( ) E A D B C Question 6. a) The line through A(-2,3) and B(4,b) is perpendicular to the line 2x 4y = 5. Find the value of b . [3] b) Using properties of proportion, solve for x . [3] +1 +1 1 1 = 4 1 2 3 c) Calculate the mean marks of the following distribution (Using any suitable [4] suitable method): Class Interval 50 55 55 60 60 65 65 70 70 75 75 80 80 85 85 90 Frequency 5 20 10 10 9 6 12 8 Question 7. a) Given: 12 8 2 .X = , Write down: (i) the order of the matrix X 1 4 10 [3] (ii) the matrix X. b) Rs.480 is divided equally among x children. If the number of children were 20 more, then each would have got Rs.12 less. Find x . [3] c) Use graph paper for this question: [4] The points A(2,3), B(4,5) and C(7,2) are the vertices of , (i) Write down the co-ordinates of A , B , C if is the image of , when reflected in the origin. (ii) Write down the co-ordinates of A , B , C if " " " is the image of , when reflected in the x-axis. (iii) Mention the special name of the Quadrilateral BCC B and find its area. 4 Question 8. a) The daily wages of 80 workers in a project are given below. Wages (in Rs.) No of workers. 400-450 2 450-500 500-550 6 550-600 12 [4] 600-650 18 650-700 24 700-750 13 5 Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2cm= Rs50 on x-axis and 2cm=10 workers on y-axis). Use your ogive to estimate: (i) the median wages of the workers. (ii) the lower quartile wage of workers. (iii) the number of workers who earn more than Rs.625 daily. b) Find the sum of the series to 8 terms of an A.P. whose 4th term is 22 and 15th [3] term is 66. c) If 6 is the mean proportion between two numbers x and y and 48 is third [3] proportion to x and y . Find the numbers. Question 9. a) The line through P(5,3) intersects the y-axis at point Q. Y [3] i) Write the slope of the line PQ. P(5,3) X ii) Write the equation of the line PQ. iii) Find the co-ordinates of point Q. O 45 X Q Y b) A bird at a height of 250 m observes the angle of depression of two boats in the opposite banks of river to be 45 and 60 respectively. Find the width of the river. 5 [3] c) Prove that: 1 + 1 = + [4] Question 10. a) In the figure alongside, BD and CD are tangents to the circle at B and C [3] respectively. Point O is the center. Given AB = CB; = 82 ; Calculate: i) BOC ii) BDC C O A O D B b) P = 3 2 3 2 5 ; Q= and R = . If PQ = 3R, 0 8 4 10 6 [3] Find the value of x and y. c) Tanisha has a recurring deposit account for 5 years and deposits Rs 240 per [4] month. If she receives Rs 17694 at the time of maturity, find the rate of interest. Question 11. a) Solve the following inequation and represent it on the number line: [3] 4 12 6 14 4 9; . b) A manufacturer sells a T.V set for Rs 20,000 to a wholesaler, who sells it to a retailor at a profit of 10%. If the rate of GST is 28% at each state, find the net tax payable by the wholesaler to the government. [3] c) A solid is made up of a cone mounted on a cylinder with the same diameter. The base area of the cylinder is 100 sq.cm. and the height of the cylinder is 3 cm. If the volume of the entire solid is 600 cubic cm., find the height of the solid. [4] _____________________x_______________________x_______________________ 6
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