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SMT. SULOCHANADEVI SINGHANIA SCHOOL, THANE Clas s Sub. Exam Date Marks Time Total No. of Printed sides 10 Mathematic s Prelim II 08.02.201 6 80 2 hrs. 4 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) Find matrices X and Y such that [ ] 5 2 X+Y= 1 3 [ ] 1 10 and X Y = 5 7 [3] B) Solve the given inequation and represent the solution set on the number line: 1 3x 2 +1< ,x I [3] 5 10 5 C) Use factor theorem to factorise completely: 2x3 + 7x2 9 [4] Question 2 A) On a sum of money, the simple interest for 2 years is Rs. 660, while the compound interest is Rs. 696.30, the rate of interest being the same in both the cases. Find the rate of interest.[ 3 ] B) An article is available for Rs. 1430 inclusive of sales tax at the rate of 10 %. Find its list price. What will be its new selling price if the rate of sales tax changes to 12 % ? [3] C) Determine the ratio in which the line joining ( 0, 7 ) and ( -2, 1 ) is divided by the line 2x + y 2 = 0. [4] Question 3 A) Solve the following quadratic equation and give the answer correct to two 5 significant figures: 2x2 + x 5=0 [3] B) Evaluate without using trigonometrical tables: cot40 +cosec40 2 + cos2 50 tan50 +sec50 + cos 40 [3] C) Marks obtained by 40 students in a short assessment are given below, where a and b are two missing data. Marks 5 6 7 8 9 Number of 6 a 16 13 b students If the mean of the distribution is 7.2, find the value of a and b. [4] Question 4 A) A person invests in a recurring deposit account for two years at 10 % per annum. If the maturity value is 53 800 times the square of the monthly instalment, then calculate the monthly instalment. [3] B) Cards numbered 3, 4, 5, 6, , 20, 21, 22 are put in a box and mixed thoroughly. One person draws a card from the box at random. Find the probability that the number on the card is i) a prime number less than 12 ii) a number divisible by 5 and 10 iii) a perfect cube [ 3 ] C) The given figure shows a circle inscribed in a square of side 14 cm. A, B, C and D are the centres of equal circular arcs. Find the area of the shaded region. [4] SECTION B (Attempt any four complete questions from this section) Question 5 A) A shopkeeper gets a discount at the time of purchasing an article. The list price of the article is Rs. 3000. He sells the article to the customer at the listed price. If the rate of tax is 8 % and the shopkeeper pays a VAT of Rs. 24, find : i) the rate of discount ii) total price paid by the shopkeeper. [3] B) Prove the identity: 1 cosA sin A = 1+cosA 1+cosA [3] C) Without solving the following quadratic equation, find the values of m for which the given equation has real and equal roots: x2 + 2mx + m 2x + 5 = 0 [4] Question 6 A) Draw an isosceles ABC in which base BC = 6 cm and the altitude from vertex to the base is 4 cm. Draw its inscribed circle. [3] B) If P = [ ] , Q = [ ] , find the value of x 2 6 3 9 is null matrix of order 3 x y 2 and y such that PQ 2 X 2. [3] C) A page from the Saving Bank Account passbook of Mr. Ajay is given below: Date Particulars Withdrawals ( in Deposits ( in Balance ( in ( 2005 ) Rs.) Rs. ) Rs. ) Feb 9 By cash 2000 2000 March 10 By cash 1100 3100 April 21 To cheque 800 2300 April26 By cash 700 3000 May 12 To cheque 700 2300 June 13 By cash 400 2700 July 9 By cash 500 3200 August 10 By cash 600 3800 August 29 To cheque 200 3600 th Ajay closes the account on 30 September, 2005. He receives Rs. 3694 on closing the account. Find the rate of interest given by the bank. [4] Question 7 A) How many spherical lead shots each 4.2 cm in diameter can be obtained from a rectangular solid of lead with dimensions 66 cm X 42 cm X 21 cm. [3] B) ABCD is a cyclic quadrilateral. The tangent at B meets DC produced at F and DA produced at E. If BED = 45 BAE = 100 and BFC = 50 , , find i) CAB ii) ABC iii) BDC [3] C) The angle of elevation of the top of an unfinished tower at a point distant 120m from its base is 45 . How much higher the tower must be raised that its angle of elevation at the same point may be 60 . [4] Question 8 A) What point on the Y-axis is equidistant from the points A( 12, 3 ) and B( -5, 10 ). [3] B) When the fare of a certain journey by an airliner was increased in the ratio 5 : 7, the cost of the ticket for the journey became Rs. 1421. Find the increase in the fare. [3] C) In the given figure, ABC is a triangle with EDB = ACB. Prove that ABC EBD. If BE = 6 cm, EC = 4 cm, BD = 5 cm and area of i) length of AB BED = 9 cm2, calculate : ii) area of ABC. [4] Question 9 A) Solve for x, using properties of proportion: 1+x+x2 62(1+x) = 2 1 x+x 63(1 x) [4] B) Using a graph paper, draw an ogive for the following distribution which shows the monthly income of workers : Monthly income ( in 6 7 7 8 8 9 9 10 11 12 thousand rupees) 10 11 12 13 Number of workers 40 68 86 120 90 40 26 Take 2 cm = Rs. 1000 on one axis and 2 cm = 50 employees on the other, to estimate: i) the median income ii) the number of employees whose income exceeds Rs. 11800 iii) the lower quartile. [6] Question 10 A) The population of a town increases at the annual rate of 10 %. If the present population is 242000, find its population 2 years ago. [3] B) If ( x 9 ) : ( 3 x + 6 ) is the duplicate ratio of 4 : 9, find the value of x. [3] C) A two digit number is such that the product of its digits is 12. When 36 is added to this number, the digits interchange their places. Find the number. [4] Question 11 A) A dividend of 9 % was declared on Rs. 100 shares selling at a certain price. If the rate of return is 7 %, calculate: i) the market value of the share ii) the amount to be invested to obtain an annual dividend of Rs. 630 [3] B) Using ruler and compasses construct an isosceles 5 cm, AB = AC and BAC = 90 ABC in which BC = . Locate the point P such that : i) P is equidistant from BC and AC ii) P is equidistant from B and C. Measure PB. [3] C) Use graph paper and plot the points A ( 8 , 2) and B ( 6 , 4 ). These two points are the vertices of a figure which is symmetrical about the lines x = 6 and y = 2. Complete the figure on the graph. Write down the geometrical name of the figure. Also find its area. [4] ALL THE BEST ***************
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