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BEACONIDGH Mathematics Second Preliminary Examination Grade: X MM:40 Time: 1 Hrs. i th Date: 2s March, 2022 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.) Question 1 Choose the correct answers to the questions from the given options. (Do not copy the question, Write the correct answer only.) [10) 1. . If the lines 2x + 3y = 5 and ax - 6y = 7 are parallel to each other, then the value of a is -1 a. 4 b. 4 1 c. 4 l:t -4 2. Which of the following cannot be the probability of an event? 2 a. 43% b. 5 -c. 2.7. d. 0.35 3. Point P (x, y) is reflected in the x- axis to P' (4, -3). The values of x and y are , a. x= 4 , y = 3 b. x =-4 y =-3 C. X = 4 y=-3 d. x=-4 y= 3 4. The curved surface area of a cone of radius 2r and slant height is I) a. rrrl -b. 2 rrrl c. rrrl d. rrr(r + I) I \ \ l _ ) and ( 4, -4) will be 1 3 5. The centroid of a triangle whose vertices are ( -2, ) < a. (0, 0) 1 b. (1, -1) 4 c. (1, 0) d. ( i ,~1) 1 6. Two chords AB and CD of a circle intersect externally at CD= 7cm and AP= 12cm, then AB is , a. 2cm cosec2 A 7. 1+ cot 2 A b. 4cm b. I:. eosec A elevation of the sun is b. 30 _p. .../3 cotA times that of its height, then the angle of 80 Weights of 40 oranges were recorded as below 85-90 90-95 95-100 100-105 105-110 Weight limit of class is c. 45 d. 1 8. If the length of the shadow of a tower is 9. '---,.. ,'7 c. 6cm d. none of these = a. O a. 15 point P. If PC= 5cm, to~ p 10 No of ~nges " a. 85 1b. 90 12 12 lo J I..-\.. 2--'1:- c.95 4 :> 2 The-lower the median v- 0 d.100 10. In the figure, If O is the centre of the circle, then the value of x is: a.55 b. 250 , C. 125 d. 70 Section B (attempt any 3 out of 5) Question 2 a. The mid-point of the line segment joining(~. 4) and ( -2, 2b) is (1, 2a +1 ). Find the values of a and b. - [2] b. In the given figure, AB is the diameter, L AOC = 11 o0 , [2] Find LBDC ( ' c. Prove the following sinA (3) +. 1-cotA cosA 1-tanA =cosA+sinA ._ I"' d. Use a graph to answer the following qu_estions i. Plot P (3, 1) and Q ( 0,5). Reflect in the origin to ii. Reflect P in y-axis to get R a ' ~ a . ,1.::,.. (3) iii. Give a name to PQRQ' Question 3 a. A lot of 20 bulbs contains 4 defective bulbs. One bulb is drawn at [2] rand9111 from the lot. What is the probability that the bulb is : i. Defective ii. Not defective 1 b. Prove that: 1-sinA + 1 2 - -=2sec A 1+ sin A (21 [3} c. The mean of the following distribution is 52. Find the value of p. Marks obtained Noof students 10-20 20-30 5 3 30-40 40-50 50-60 p 4 2 60-70 70-80 6 13 d. A bird is perched on the top of a tree 20m high and its angle of elevation from a point on the ground is 45 The bird flies off horizontally straight from the observer and in 10 sec the angle of elevation of the bird reduces to 30 Find the speed of the bird rounded to one decimal place. (3] . . Question4 8 a. The points A (2, 3) , B (3,5) and C ( -1, -1) are the verttces of triangle ABc. 2 Find the equation of the altitude of the triangle through A. [ 1 b. In the given figure , the angle d elevation from a point P to the top d a tower QR , 50 m high is 6Cf and that of tower PT from a point a is 3d'. Fmd the height of the tower PT , correct to the nearest metre. [2] c. In the given figure, AC is tangent to circle at point B. L FBA =5d' and L EDF =30 . [3] Fmd (a)L FOB (b)LEBF (c)LEFB C B A d. Draw a histogram to the following distribution and hence find the made. [3J Height 145 - 155 155 - 165 165 - 175 175- 185 175 - 195 5 35 25 15 20 (cm) Noof persons Question 5 a. M and N are two points on the~~ and >:-axis respectively. P(3,2) divides the line segment MN in the ratio 2 : 3. Find the coordinates of M and N. [2] b. In a pencil box, there are 36 red pencils and some green pencils. When a pencil is taken out from this pencil box, the probability of getting a green pencil is 11Find the number of green pencils in the box. [2] 20 c. A cylindrical jug of radius 8 cm Qnd height 1O cm is filled with orange juice. It is then poured into small conical cups of radius 2 cm and height 6 cm. Find the number of cups that can be filled. [3] d. Monthly lncomc (Rs) 6000 7000 8000 Noof employees 20 4S 9000 9000 10000 10000 JIOOO 65 90 60 8000 7000 Monthly income of a group of 280 employees in a company is given below: Using a graph paper, draw an ogive for the above distribution. Use your ogive to estimate the median. [3] Question 6. a. Find the equation of a line with x - intercept -3 and passing through the point ~.~ b. In the given figure O is the centre of the incircle of quadrilateral ABCD. If PD 36an. CD 44cm BC 15 an, fi~ the 1~ .... - " o radius of the cirde. [2] ~,_ / 'If i- ,I ,t O ~, , }<,. ?;,t. _, , t- ,~/ B 0.. \', -~"-::,..4.A_,,:. "l- "-:!C -,scr,1- c. The following table shows marks secured by 140 students in an examination. Calculate the mean marks. [3] Marks 0-10 No of studenb 20 10-20 20-J0 30-40 40-50 24 40 36 d. The given solid figure is a cylinder sunnounted by a cone. The diameter of the base of the cylinder is 6 an. The height of the cone is 4cm and the total height ottile sorld is 25an. Find the curved surface area of the solid rounded to the nearest whole number. ( Take 1T = 3.14) [3] 20 25cm ---{ 1 rr _j __ V' ' '-' I..
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