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MOCK EXAMINATION 3 2017 MATHEMATICS 1 hrs. 2 Grade: 10 Time: 2 Date: 13th April, 2017 Max. Marks: 80 [The time stated above is the time allowed for writing the examination. In addition, the first 15 minutes will be the time given for reading the question paper.] INSTRUCTIONS 1. Answer all Questions from Section A and any FOUR Questions from section B. 2. All working, including rough work, should be done on the same sheet and adjacent to answer. 3. The intended marks for Questions or parts of questions are given in brackets [ ]. SECTION A [40 Marks] Question 1 [3 + 3 + 4] a) On a certain sum of money, the difference between the compound interest for a year, payable half yearly and the simple interest for a year is Rs.180. Find the sum lent out, the rate of interest in both the cases being 10% per annum. b) Cards marked with numbers 3, 4, 5, .50 are placed in a box and mixed thoroughly. One card is then drawn at random from the box. Find the probability that the number on the card is : i. Divisible by 7 ii. A prime number less than 25 iii. A number, which is a perfect square. c) Find the value of a and b such that (x + 1) and (x 3) are factors of x 3 - 3x2 + ax - b. Question 2 [3 + 3 + 4] Page 1 of 6 a) Given A= b) If y = [ 2 3 0 1 ] ,B= [ 1 k 0 5 ] find the value of k such that AB = BA. a+ 3 b+ a 3 b , show that 3by2 - 2ay + 3b = 0. . .. a+ 3 b a 3 b ............................... c) In the given figure, ABCD is a rectangle and AB = 21cm. inside the rectangle, two semicircles are drawn with P and Q as centres touching the sides AB and CD respectively. If the diameter of the smaller circle is equal to the radius of the bigger circle, find the area of the 22 unshaded portion. Take = . 7 Question 3 [3 + 3 + 4] a) Solve: 3x2 5x + 1 = 0, giving your answer, correct to two decimal places. b) Without using trigonometrical tables, evaluate: 2 tan 37 5 sin 28 sec 62 + + sin2 36 cos2 54 . cot 53 ( ) c) The internal and external diameter of a hollow hemispherical vessel are 14 cm and 21 cm respectively. The cost of silver plating of 1 cm 2 of the surface is Re. 0.40. Find the total cost of silver plating the vessel all over. (Use = 3.14). Question 4 [3 + 3 + 4] a) Solve and graph the inequation: 2x 5 5x + 4 11 ; x I b) Find the equation of the line parallel to the line 3x 5y = 7 and passing through the point which divides the line segment joining the points A( 3, 3) and B(2, 7) in the ratio 2 : 3. c) In the given diagram, ED || BC. If AD : DC = 2 : 3, find i. ED : BC ii. Area of EMD : area of CMB Section B [40 Marks] Page 2 of 6 (Answer any four Questions) Question 5 [3 + 3 + 4] a) A shopkeeper buys an article at a discount of 30% and pays sales tax at the rate of 6%. The shopkeeper sells the article to a customer at 10% discount on the list price and charges sales tax at the same rate. The list price of the article is 3000. Find i. The price inclusive of sales tax paid by the shopkeeper. ii. The price paid by the consumer. iii. The VAT paid by the shopkeeper. b) The marks of 18 students in a science test were as follows: 10, 12, 6, 2, 9, 15, 18, 13, 12, 13, 7, 14, 19, 12, 5, 7, 11, 9 Calculate: (i) The Mean (ii) The Median (iii) The Mode. c) Use graph paper for the question. Use 1 cm = 1 unit on both axes. Plot the points A (4, 5) and B (2, 6) and C(2,-3). (i) A is the image of A when reflected in the line x = 0. Write down the coordinates of A and plot it on the graph paper. (ii) A is the image of A when reflected in the origin. Write the co-ordinates of A . (iii) Write co-ordinates of A the reflection of A the line y = 0. (iv) Assign the special name to the figure ABCA . Hence, find its area. Question 6 [3 + 3 + 4] a) In the adjoining figure, AB is a diameter of the circle with centre O and AT is tangent to the circle. If ADC= 20 , find (i) ABD (ii) BOC. 1 tan 2 b) Prove the identity = tan2 . 1 cot ( ) c) Draw Ogive for the following distribution: Monthly income( ) Number of employees 600 700 40 700 800 68 800 - 900 900 1000 1000 1100 1100 1200 1200 1300 86 120 90 40 26 Find the following: (i) The Median income, (ii) The number of employees whose income exceeds 1180. (iii) The lower and upper quartile (iv) The interquartile range. Question 7 [3 + 3 + 4] Page 3 of 6 a) A man invested 24000 in 8% 100 shares, selling at a discount of 20%. After a year, he sold these shares at 72 each and invested the sale amount in 12% 100 shares selling at a discount of 105. Calculate: i. His original income ii. His new income iii. The increased percentage return on his original income. b) In the adjoining figure, O is the centre of the circle. XOY = 40 , TWX = 120 and XY is parallel to TZ. Find: (i) XYZ (ii) YXZ (iii) TZY c) Mr. Ashok has a saving bank account in Bank of India. His passbook has the following entries: Date Particular Withdrawal( ) Deposit ( ) Balance ( ) April 1, 2008 B/F .. .. 5350.00 April 19 By transfer .. 1500.00 6850.00 August 7 By clearing .. 2707.00 9555.00 August 23 To Cheque 5000.00 .. 4555.00 Sept 25 By cash .. 1200.00 5755.00 Nov 3 By cash ... 750.00 6505.00 Feb 16 To self 2000.00 .. 4505.00 March 5 By cheque .. 3680.00 8185.00 Page 4 of 6 Calculate the interest due to him at the end of the financial year (March 31,2009) at the rate of 4% p.a. Question 8 [5 + 5] a) Using ruler and compasses only, construct a triangle AC in which AB = 5.5 cm, BC = 7 cm and the median through A is 5 cm. also construct circumcircle of the triangle ABC. b) Two pillars of equal heights stand on either side of a roadway, which is 150 m wide. At a point in the roadway between the pillars the elevations of the tops of the pillars are 60 and 30 . Find the height of the pillars and the position of the point. QUESTION 9 [3 + 3 + 4] a) A card is drawn from a pack of well-shuffled deck of 52 cards. Find the probability that the card drawn is (i) A black king (ii) Either a jack or a queen or a king or an ace (iii) Neither a heart nor a king. 1 years and she 2 pays 640 as monthly deposit. Find the amount she gets at the time of maturity, if the rate of interest is 12% per year. b) Mrs. Mathew has a recurring deposit account in a post office for 4 c) P(3,4), Q(7,-2) and R(-2,-1) are the vertices of a PQR. Write down the equation of the median of the triangle, through R. QUESTION 10 [3 + 3 + 4] a) A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number. b) How many lead balls, each of diameter 2 cm, can be made from a sphere whose radius is 8 cm? c) Following is the distribution of earnings of 200 workers in a flour mill. Monthly wages in Number of workers 80 - 100 2 100 120 120 - 140 140 - 160 160 - 180 18 10 8 7 Page 5 of 6 Estimate the Mean earning of the workers. QUESTION 11 [3 + 3 + 4] a) Find the value of k for which the equation has equal roots: kx2 5x + k = 0 b) In the adjoining figure, PQ and PR are tangents to the circle, with centre O. If QPR = 60 , find: (i) PQO, (ii) QOR (iii) OQR c) Construct a triangle ABC with AB = 6cm, ABP = = 5cm. Complete the rectangle ABCD such that: i. P is equidistant from AB and BC, and ii. P is equidistant from A and D. 45 and BP ******************************************************************************************************* Page 6 of 6
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