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VIBGYOR HIGH SEMESTER 2 - PRELIMINARY EXAMINATION 2021-2022 MATHEMATICS Grade: X Max. Marks: 40 Time Allowed: hours Date: 17/02/2022 Maximum Marks: 40 Time allowed: One and a half hours Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 10 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 three questions from Section B. The intended marks for questions or parts of questions are given in brackets []. SECTION A (Attempt all questions from this Section.) [10x1=10] Question 1 Choose the correct answer s to the questions from the given options. (Do not copy the question, Write the correct answer only.) (i) The image of the point P under reflection in the is (5,-2) . Write the coordinates of P. (a) (5,2) (b) (-5,-2) (c) (5,-2) (d) (-5,2) 1 [1] (ii) AB is a chord of the circle and AOC is its diameter such [1] that ACB=50 . If AT is the tangent to the circle at the point A, then BAT is equal to (a) 65 (b) 60 (c) 50 (d) 40 (iii) How many bags of grain can be stored in a cuboid granary [1] 12m 6m 5m, if each bag occupies a space of 0.96 cu. metre? (a) 750 (b) 75 (c) 1500 (d) 375 (iv) Find the mid-point of the line segment joining the points: [1] (-6, 7) and (3, 5) 3 (a) ( 2, 6) 7 (b) ( 2, 3) 3 (c) ( 2, 5) 5 (d) ( 2, 6) (v) ( 2 1) 2 is equal to = (a) cos (b) 0 2 [1] (c) sin (d) 1 (vi) The mean of the numbers 6, , 7, and 14 is 8. Express in [1] terms of . (a) 13 - (b) 13 + (c) 3 - (d) 10 - (vii) Find the value of a if the straight lines 5x 2y 9 = 0 and [1] ay + 2x 11 = 0 are perpendicular to each other. (a) 5 4 (b) 5 (c) 5 1 (d) 5 (viii) Find the height of the cone whose slant height is 17cm and [1] radius of the base is 8cm. (a) 15cm (b) 15.5cm (c) 16cm (d) 14.5cm (ix) The following data have been arranged in ascending order. If [1] their median is 63, find the value of x. 34, 37, 53, 55, x, x + 2, 77, 83, 89 and 100. (a) 63 (b) 61 (c) 60 (d) 62 (x) In a single throw of a die, find the probability of getting a number greater than 4. 2 (a) 3 1 (b) 6 (c) 1 3 3 [1] 1 (d) 5 SECTION B (Attempt any three questions from this Section.) Question 2 (i) In what ratio does the point P(2,-5) divide the line segment [2] joining A(-3,5) and B(4,-9)? (ii) A bag contains 4 white balls and some red balls. If the 2 [2] probability of drawing a white ball from the bag is , find the 5 number of red balls in the bag. (iii) In the given figure, O is the centre of the circle. Tangents at A [3] and B meet at C. If ACO = 30 , find: (i) BCO (ii) AOB (iii) APB (iv) From a point P on the ground, the angle of elevation of the top of a tower is 30o and that of the top of the flag-staff fixed on the 4 [3] top of the tower is 60o. If the length of the flag-staff is 5 m, find the height of the tower. (Use =1.732) Question 3 (i) [2] In the given figure, Find length of BC : (ii) If the volumes of the two cones are in the ratio of 1:4 and their [2] diameters are in the ratio of 4:5, find the ratio of their heights. (iii) (iv) Prove that + ( 1) ( +1) [3] = 2 2 Use graph paper for this question, take 2 cm=10 marks along [3] one axis and 2 cm = 10 students along the other axis. Draw the ogive for the following data which gives the marks and number of students. Also estimate the median marks. Marks 0-10 10-20 20-30 30-40 40-50 Students 6 21 16 32 10 Question 4 (i) A,B and C have co-ordinates (0, -3),(4,4) and (8,0) respectively. [2] Find the equation of the line through A and perpendicular to BC. (ii) (iii) [2] Find mean of the following distribution: Class 1-3 3-5 5-7 7-9 Frequency 9 22 27 17 A patient in a hospital is given a soup daily in a cylindrical bowl of diameter 7cm. If the bowl is filled with soup to a height of 5 [3] 4cm, how much soup the hospital has to prepare daily to serve 250 patients? Give your answer in liters. (iv) The triangle ABC, where A is (2, 6), B is (-3, 5) and C is (4, 7), [3] is reflected in the y-axis to triangle A'B'C'. Triangle A'B'C' is then reflected in the origin to triangle A''B''C''. (i) Write down the co-ordinates of A'', B'' and C''. (ii) Write down a single transformation that maps triangle ABC onto triangle A''B''C''. Question 5 (i) In the given figure, AE and BC intersect each other at point D. [2] If CDE=90 , AB = 5 cm, BD = 4 cm and CD = 9 cm, find AE. (ii) Prove: [2] (iii) 1 + sin = sec + tan 1 The line 4x - 3y + 12 = 0 meets the x-axis at A. Write the co- [3] ordinates of A. Determine the equation of the line through (2,-1) and parallel to 4x - 3y + 12 = 0. (iv) Use graph paper for this question. Estimate the mode of the given distribution by plotting a histogram. [Take 2 cm = 10 marks along one axis and 2 cm = 5 students along the other axis] Class 140-145 145-150 150-155 155-160 160-165 8 12 18 10 5 interval Frequency 6 [3] Question 6 (i) Cards marked with numbers 11, 12, 13, 14, ................. 50 are well shuffled and a card is drawn at random. Find the probability [2] that the number on the card drawn is : a. a prime number less than 40 b. divisible by 7. (ii) One end of the diameter of a circle is (-2, 5). Find the [2] co-ordinates of the other end of it, if the centre of the circle is (2, -1). (iii) A person standing on the bank of a river observes that the [3] angle of elevation of the top of a tree standing on the opposite bank is 60 . When he moves 40 metres away from the bank, he finds the angle of elevation to be 30 . Find the height of the tree and the width of the river. (iv) If the mean of the following distribution 54, find the value of p: Class: Frequency: 0 20 20 40 40 60 60 80 80 100 7 p 10 ***** 7 9 13 [3]
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