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SMT. SULOCHANADEVI SINGHANIA SCHOOL, THANE Class Sub. Exam Date Marks Time Total No. of Printed sides 10 Mathematics Prelim II 31.01.2017 80 2 hrs. 5 General Instructions: 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. 5. Mathematical tables are provided. SECTION A (40 Marks) Attempt all questions from this section. Question 1 a. A shopkeeper sold an article for Rs. 7500 to a customer excluding sales tax of 12%. If the shopkeeper pays a VAT of Rs.180, calculate the price at which the shopkeeper purchased. [3] b. A = B = M = . If BA = M2 find the value of a and b. [3] c. Find the equation of a line passing through the point (3,1) and its x-intercept is double the y-intercept. Find the area of AOB , A and B are the points where the line intersects the X and Y axis respectively. [4] Question 2. a. On a certain sum of money invested at 4% p.a. compounded annually, the difference between the interest for the third year and the interest for the first year is. Rs 24.48. Find the sum. [3] b. Solve the following quadratic equation and give your answer correct to 2 significant figures: = 1. c. Solve using properties of proportion : [3] = 4 [4] Question 3. a. Neeta has cumulative deposit account in a bank where she deposits Rs.800 per month and gets Rs. 15198 as maturity value. If the rate of inetrest is 7% p.a., find the time for which the account was held. [3] b. Evaluate the following without using trigonometric tables. : tan2 47 - cosec243 + sec60 sin30 [3] c. Using ruler and compass only, i) construct a ABC with AB = 3.5 cm, BC = 6 cm and ABC =120 . ii) construct a circle with BC a diameter. iii) Find a point P on the circle which is equidistant from AB and BC. iv) Measure CP [4] Question 4 a. The mean of 2, 12, 4, 9,5 and 16 is a. The median of 12, a-1,16, 3, a, 4 is b. Find the value of a and b. [3] b. If x2 -8x +15 is a factor of x3 ax2 + 31`x b. find the value of a and b. [3] c. TP and TR are tangents to the circle with centre O. If POQ = 150 and PTR = 50 . Find i) TPR ii) QPR iii) PQR. [4] SECTION B (Attempt any four complete questions from this section) Question 5 a. Solve and represent the solution on the number line : 2y 3 <y +1 4y + 7, y Z. [ 3 ] b. In the given figure ABC is right angled at A. AD BC. i) Prove ADB CDA ii) If BD =18cm, CD =8cm , find AD iii) Find area of ADB : area of CDA . [3] c. Sunil sold x shares of Rs.100 paying 15% dividend at a premium of 60% and invested the proceeds in shares of nominal value Rs.50 quoted at a 4% discount, paying 18% dividend .If his income increases by Rs.900, find the value of x. [4] Question 6. a. If the duplicate ratio of x : y is (x-a) : (y a), find a in terms of x and y. [3] b. Prove the following : [3] = c. The pass book page of Mr. Rohit is given below. The interest received at the end of December 06 is Rs 377.40. Complete the entries in the balance column and find the rate % p.a. [4] Date( in 2006 ) January 1 March 7 March 1`0 July 17 October 5 December 19 Particulars B/F By cheque By cash To self By cheque To cheque Debit (in Rs.) Credit (in Rs.) Balance (in Rs.) 7500 1875 625 3250 2160 1340 Question 7. a. A (1 , 4) , B (3,2) and C (7,5) are the vertices of ABC. Find the equation of a line through the centroid and parallel to AB. [3] b. If - 5 is the root of the quadratic equation x2 + mx - 5 = 0. Find the value of m. Also find the value of k if x2 +mx + k = 0 has equal roots. [3] c. The following is the frequency distribution of marks obtained by 60 students of a class. If the mean marks is 66, find the value of m and n. [4] Marks 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 100 No. of 8 7 m 15 5 n 7 students Question 8. a. A 10 m high pole is fixed on the top of a tower. The angle of elevation of the top of the pole as observed from a point P on the ground is 60 . The angle of depression of the point P from the top of the tower is 45 . Find the height of the tower to the nearest meter. [4] b. The following table shows the marks of 120 students in an examination. Marks 30 - 40 40 -50 50 - 60 60 - 70 70 - 80 80 - 90 No. of students 1 3 11 21 43 32 Draw an ogive to estimate the following : [6] 90 100 9 i) Median marks ii) Inter quartile range iii) the highest mark scored by the lower 30% students of the class. Question 9 a. From a pack of 52 cards, all even numbered red cards and all black cards are removed and well shuffled. A card is drawn at random, what is the probability of the card drawn is : i) A multiple of 5 ii) A face card iii) A factor of 8 [3] b. ABC is an isoscels triangle circumscribed by a circle. If AB = AC = 10cm, BC =12 cm, find the diameter of the circle. [3] c. An hemispherical bowl of diameter 16.8 cm is filled with water up to the brim. when two equal solid cones are dropped in it, one-third of the water in the bowl over flows. If the height of the cone is 25.2 cm, find the radius of the cone. [4] Question 10 a. If A = B = and AB m I = Find the value of m. [ 3 ] b. A model of a ship is made to a scale of 1 : 200. [3] i) If the length of the ship is 800 m calculate the length of the model ii) If the volume of the model is 200 litres, calculate the volume of the ship in cubic meters. c. An aeroplane departed 40 minutes late due to the bad weathe. In order to reach its destination 1600 km away on time, it had to increase its speed by 400 km/hr from its usual speed x km/hr. Find the value of x. [4] Question 11 a. A customer bought an article for Rs. 748 which included a discount of 15% on the marked price and a sales tax of 10% on the discounted price. Find the marked price of the article. [3] b. In the given figure O is the centre of the semicircle with radius 5cm and DOC = 90 . Find the area of the shaded region. (use = 3.14) [3] c. Plot A ( 4 ,4 ), B ( 4, -6 ), C ( 8, 0) in a graph paper using a scale of 2cm = 2 units on both the axes . Reflect A , B , C on the y axis and name it as A , B and C respectively and plot it. i) Give a geometrical name for the figure ACBB C A . ii) Find the area of the above figure. iii) Write the coordinates of two invariant points P and Q on the line of symmetry. [ 4 ] ********************************
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