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SMT. SULOCHANADEVI SINGHANIA SCHOOL, THANE Class Subject Exam Date 10 Mathematics Prelim 30.01.2021 General Instructions: Marks Time 80 2 Hrs. Total No. of printed sides 5 1. Attempt all questions from section A 2. Attempt any 4 complete questions from section B 3. All working, including rough work must be clearly shown and must be done on the same sheet as the rest of the answer. 4. Omission of essential working will result in loss of marks. SECTION A (40 MARKS) Attempt all questions from this section QUESTION 1 A) Solve the following inequation and represent the solution on a real number line 2 1 3 2 6 2 1 , [3] B) Milk from a cylindrical can 30 cm deep and radius 16 cm is poured into cylindrical glasses 4cm in diameter and height 8 cm. Find out how many such glasses can be filled. [3] C) If A = [ 3 2 7 0 ] , B=[ 4 5 2 1 ] and C = [ 3 4 5 ] Find AB 5C + B 6 [4] QUESTION 2 A) Solve and write the answer correct to 3 significant figures: 5 2 3 4 = 0 [3] B) Cards numbered 11, 12, 13, 14, , 28, 29, 30 are put in a box and mixed thoroughly. One card is drawn from the box at random. Find the probability that the number on the card is - i) a prime number ii) a number divisible by 2 and 3 iii) a perfect square. [3] C) ACBD is a quadrilateral in a circle with centre O . If ACB = 1400 . Find : (i) ADB (ii) AOB (iii) OAB . [4] 1 QUESTION 3 A) Find the value of a when the polynomial 2x3 3x2 +ax 5 divided by (2x -3), leaves a remainder 7. B) Prove the following trigonometric identity: 1+ 2 1+ = 1 [3] [3] C) Find the total CGST, total SGST and the amount of bill for the following intra-state transaction of goods/services, if the GST rate is 16%. [4] Product MRP (in Rs.) Discount % Television 12,000 10 Refrigerator 15,000 - Camera 10,000 30 QUESTION 4 A) Which term of the A.P: 23, 44, 65, 86, ... is 212? [3] B) Mr. Kabir deposits a certain sum of money every month in a Recurring Deposit account for 2 years. If the bank pays interest at 10% p.a. and he receives Rs. 66250 as the maturity value, what sum of money did he deposited every month? [3] C) Draw a histogram for the given distribution on a graph sheet taking 2cm= Rs.100 on one axis and 2cm= 10 workers on the other axis and estimate the mode of the following data: [4] Wages (in Rs,) No. of workers 200-300 45 300-400 68 400-500 80 500-600 100 600-700 50 700-800 72 SECTION B (Attempt any four complete questions from this section) QUESTION 5 5 1 2 2 A) In the A.P 4, , 1, , 2, Find the following: i) common difference ii) 20th term iii) sum up to 20 terms. B) If b is the mean proportion between a and c prove that 2 2 + 2 2 2 + 2 = 4 2 [3] [3] C) In the adjoining figure, chords AB and CD are produced to meet at O. [4] i) Prove ODB ~ OAC ii) Given CD = 2 cm, DO = 6 cm, BO = 3 cm, calculate AB. iii) Find Area (Quadrilateral CABD) : Area ( OBD) QUESTION 6 A) Find the ratio in which the line segment joining A (2, -5 ) and B (-3, 10) is divided by y-axis. Also, find the co-ordinates of the point of intersection. [3] B) Prove the following identity: 2 + 2 1 2 = 2 [3] C) If the mean of the following distribution is 30, find the value of a. Marks No. of students 0 - 10 4 10 - 20 a 20 - 30 12 30 - 40 15 40 - 50 7 [4] 50 - 60 4 QUESTION 7 A) In the given ABC, D and E are points on AB and AC respectively. If AD = 5.6cm, AB = 8.4 cm, AE = 3.8 cm and AC = 5.7 cm. i) Show that DE BC. ii) Find the measure of BC if DE = 4.8 cm. [3] B) The co-ordinates of a diameter AB of a circle are (3, 0) and (-5, 6) respectively. CD is another diameter where the co-ordinates of C is (-1, -2). Find the co-ordinates of D, the other end of the diameter. [3] C) Use graph for this question. Take 2 cm = 1 unit on both axes. (i) Plot the following points on your graph sheet: A ( 5, 0 ), B ( 3, 2 ), C ( 3, 4 ), and D ( 0, - 4 ) (ii) Reflect the points A, B and C on the Y axis and name them as A , B and C respectively. (iii) Reflect the point D on the x axis and name it as D (iv) Join the points ABCC B A D and give the geometrical name of the closed figure formed. [4] 3 QUESTION 8 A) Find the value of for which the equation 2 2 + 2 + + 5 = 0 has real and equal roots [3] 4 4 B) If [ ] . A = [ 1 1 8 ] state the order of matrix A and find matrix A. 2 [3] C) The solid right circular cone with slant height 13 cm has a total surface area of 90 cm2. Find the following : (i) radius of the cone (ii) height of the cone (iii) volume of the cone ( take = 3.14) [4] QUESTION 9 A) Find the equation of a straight line passing through the point P ( 3, - 2 ) and Q, where Q is the point of intersection of the lines 4 5 + 7 = 0 and 2 + 3 = 13. [3] B) In the adjoining figure, given ACB = 36 , find the measure of angle x and y . [3] 360 C) A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60o. When he moves 80 m away from the bank, he finds the angle of elevation to be 30o. Find to the nearest meter: (i) the height of the tree (ii) the width of the river. [4] QUESTION 10 A) If the speed of car is reduced by 30 km/hr, it takes 40 minutes more to cover 120 km. Find the original speed of the car. Frame an equation in x and solve it. [4] 4 B) The following data shows the marks scored by a certain number of students in an examination: [6] Marks 0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 - 80 No. of 12 20 30 38 24 16 12 8 students Use a graph sheet by taking 2 cm = 10 marks on one axis and 2 cm = 20 students on the other axis and draw an ogive for the above distribution and estimate the following: (i) (ii) (iii) Median marks scored Upper quartile Find the number of students scoring above 40% marks. QUESTION 11 A) Using factor theorem completely factorise the polynomial 6x3 + 11x2 3x 2. [3] B) Mr. Mohan opens a recurring deposit a bank and deposits Rs.250 per month for a period of 1 1 2 years. If the rate of interest is 12% p.a. find the amount he would receive at the time of maturity. [3] C) Using properties of proportion solve for x, if 3 + 9 2 5 3 9 2 5 ********************** 5 =5 [4]
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