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SMT. SULOCHANADEVI SINGHANIA SCHOOL, THANE Exam Class Subject Date Marks Time No. of sides Prelims X Maths 16-01-04 80 2 hrs 6 General Instructions: 1. Attempt all questions from Section A. 2. Attempt any four questions from Section B. 3. All working, including rough work, must be clearly shown, and must be done on the same sheet as rest of the answer. 4. Omission of essential working will result in loss of marks. SECTION A (Attempt all questions from this section) Question 1 Choose the correct answer to the question from the given options and write in the separate answer sheet. [15] 1) The centroid of triangle whose vertices are (5, -6), (-2, 3) and (-6, 15) is A) (1, -4) B) (-1, -4) C) (-1, 4) D) (1, 4) 2) 5 2 5 2 + 1 is equal to A) -4 B) 6 C) 4 D) 7 3) The reflection of the point A (5, 0) in the line y = 0 is A) (5, 0) B) (0, 5) C) (-5, 0) D) (0, -5) 4) If nth term of an AP is 13 4 , then the 20th term is A) -67 B) 67 C) 76 D) -76 5) Arjun invests 8800 in buying shares of face value 100 each at a premium of 10%, the number of shares he bought is A) 88 B) 880 C) 80 D) 800 6) The of the line whose equation is 11 5 + 2 = 0 A) 5 11 B) 2 5 C) 11 5 D) 5 2 7) If 6 is the mean proportional between two numbers x and y and 48 is the third proportional to x and y, then the numbers are: A) = 3, = 12 B) = 4, = 9 C) = 6, = 6 D) = 9, = 24 8) The value of k for which the quadratic equation 16 2 + 4 + 9 = 0 has real and equal roots are 1 A) 6, 1 6 B) 36, 36 3 3 4 4 C) , D) 6, 6 (9) If . then the solution set for 5 3 2 + 2, is A) all real numbers less than or equal to 3 B) all real numbers greater than or equal to 3 C) all real numbers less than or equal to (-3) D) all real numbers greater than or equal to (-3) (10) Find the class mark of the modal class for the following distribution: Class Interval Frequency A) 12.5 0-5 5 - 10 10 - 15 15- 20 20 - 25 10 15 12 20 9 B) 20 C) 17.5 D) 22.5 (11) The slope of a line perpendicular to the line passing through the points (2, 5) and (-3, 6) is A) 1 5 B) 5 1 C) 5 D) 5 (12) In the adjoining figure, sides MN, NL and LM of touch a circle at the points A, B and C respectively. If AN=5cm, CL=4cm and CM=6cm, then the perimeter of is A) 15 B) 40 C) 30 D) 60 (13) In the given figure, AB DE, then the length of CD is A) 10/3 cm B) 3.5cm C) 2.5 cm D) 2.7cm (14) If a pole 6m high casts shadow 2 3 long on the ground, then the sun s elevation is A) 30 B) 60 C) 45 2 D) 90 (15) Assertion (A): The curved surface area of cylinder with radius 2 and height 10 is 40 2 . Reason (R): The volume of cone is one third the volume of cylinder. (A) Both Assertion and Reason are true and R is the correct explanation of A. (B) Both Assertion and Reason are true and R is not the correct explanation of A. (C) Assertion is true but Reason is false. (C) Assertion is false but Reason is true. Question 2 A) Prove the following trigonometric identity: + 1 = +1 [4] 1+ sin B) In the adjoining figure, O is the centre of the circle and = 110 . Find : (i) (ii) (iii) C) If = [4] 2 +1+ 2 1 , then using properties of proportion, prove that : 2 +1 2 1 + = [4] Question 3 A) Mr. Joseph opened a recurring deposit account in a bank for 3 years. If the rate of interest is % p.a. and the bank pays 1776 as interest at the time of maturity. Find (i) The monthly deposit (ii) The amount at the time of maturity. [4] B) The surface area of a sphere is 1386 2 . If the sphere is melted and recast into solid cylinders of radius 3.5 and height 6 . Calculate: (i) Radius of the sphere (ii) Number of cylinders recast. [4] C) Use graph paper for this question. [5] (i) Plot A, B, C where A (2,4), B (-2,1), C (5,0) (ii) Reflect points A and B on the x-axis and name them as A' and B'. Write their co-ordinates. (iii) Give a geometrical name to the figure formed by joining the points ABB'A'C. Find its Area. (iv) Name two points from the figure which are invariant on reflection in x-axis. 3 SECTION B (Attempt any four questions from this section) Question 4 A) Solve the following inequation and represent the solution set on the number line. 1 2 5 2 2 3 1 6 , [3] B) The sum of three numbers in an A-P is (-12) and their product is 36 Find the numbers. [3] C) Mr. Rohit went to a department store and buys the following articles. [4] Sr. No Bought Items Price per items Quantity Discount GST 1 A packet of sweets 450 3 - 5% 2 Hair oil 500 2 - 18% 3 Chess board 300 1 10% 12% (i) Find the total amount of the GST Paid. (ii) The total bill amount including GST paid by him. Question 5 A) Determine the ratio in which the line 2 + = 4 divides the line segment joining the points A(2,-2) and B (3,7). [3] B) Construct a with = 6.5 , = 5.5 , = 5 . Construct the incircle of the triangle . Measure and write down the radius of the circle. [3] C) In , such that = 2 , = 6 , = 20 . Find: (i) the length of (ii) Area of Trapezium PQNM : Area of Triangle LPQ [4] Question 6 A) A and B are two points on the opposite banks of a river. Between them in the river, is a boat with a mast of height 20 . Find the width of the river if angles of elevation of the tip of the mast are 38 from the point A and 26 from the point B. The points A and B and the foot of the mast are on the same level. Give your answer to the nearest metre. [5] 4 B) Scores obtained by 120 shooters in a shooting competition are given below. Scores 0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 No. of shooters 5 10 18 23 26 19 11 8 Use a graph paper to draw an ogive for the given distribution taking 2 = 10 scores on one axis and 2 = 20 shooters on the other axis. Use the ogive to estimate: (i) Median (ii) The number of students who obtained more than 60 scores. [5] Question 7 A) Solve the following equation and give your answer correct to three significant figures. 2 3 9 = 0 [3] 3 1 ] then find 2 5 + 7 , where I is an identity matrix of 1 2 order 2 2. [3] B) If = [ C) Deepak bought 4500, 10 shares paying 12% per annum. He sold them when the price rose to 23 and invested the proceeds in 25 shares paying 10% per annum, at 18. Find the change in his annual income. [4] Question 8 A) Construct a triangle ABC with = 5.5 , = 6 , and BAC = 105 . Hence, (i) Construct the locus of points equidistant from and (ii) Construct the locus of points equidistant from B and C (iii) Mark the point which satisfies the above two loci as P. Measure and write the length of PC. [3] B) Cards bearing numbers 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card which is: (i) A prime number. (ii) A number divisible by 4. (iii) A number that is multiple of 6. [3] C) A straight line passes through the points A (2, -4) and B (5, -2). Find: (i) Slope of the line AB (ii) The equation of the line AB (iii) The value of k , if AB passes through the point P (k + 3, k -4 ) [4] Question 9 A) On a map drawn to a scale of 1: 20,000 a rectangular plot of land ABCD has AB = 32cm and BC=24cm. Calculate (i) The diagonal distance of the plot in km. (ii) The area of the plot in square km. [3] 5 B) Find the mean of the following distribution by step deviation method. [3] Class Intervals 20 30 30 40 40 50 50 60 60 70 70 80 Frequency 10 6 8 12 5 9 C) A plane travels a distance of 1600 km at an average speed of / . On the return journey, due to bad weather as the speed was reduced by 40 / , it took 1 hour 20 minutes more than onward journey. Find . [4] Question 10 A) The 5th term of a G.P is 48 and the 8th term is 384. Find its 11th term. [3] B) What must be added to the polynomial 2 3 3 2 8 , so that it leaves a remainder 10 when divided by (2 + 1). [3] C) The following distribution represent the height of the students of a school: Height (in cm) 145 150 150 155 155 160 160 165 165 170 No. of 34 42 25 6 13 students Draw a histogram for the above data using graph paper and hence, find the mode. [4] ************************************** 6
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