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CLASS: PRE-FINALEXAI\4INATION-IAN-2016 TIME:2112hrsMARKS:80 SUglgCt: UrtttnpltttCs (40 marks)(Attempt all questions from this section) Section: L A Question:1 Without using trigonometric tables, evaluate Sin2340 + s#so'o + 2tan18otan720 -cot2300 ani factor theorm, factorise the following polynominal U 6 Calculate the area of the shaded region, Takez :'- ,t icircle is equal to 14cm. e if the diameter of the d,_1.l 7 Question:2 (i) Varun inverts a sum of money in RS. 50 shares, paying 1 5% dividend uoted at 20Yo premium. his annual dividend is Rs.600, calculate {i) The number of shares he bought (+n His total investment 3 @ The rate of return on his investment :. If owing points A(q3), B(2,1) and C(5,a) are coilinear rc rs 2464cm2. It is melted and recast into solid right lculate the radius of the sphere e{*"number ion:3 - I 22' 7 12% end bo year frrst Kfuan r of cones recast. . TakelT he repays Rs.8,400 at the end unt of loan outstanding at the beginning of the third year. Find the values of X, which salisfy the inequation-2.1 a;-'{ = Z,*e - 3-, 3 graph the solution set on the number line die has 6 faces marked by the given numbers as shown below: j': o@@o@@ tr"he die is thrown once what is the probability -!D ^ integer greater than of gett\ng(tf apositive integer + ii) the smallest integer Question:4 numbers 6,8,10,12,13, and x axo affanged in an ascending ordeg If the mean of the observations is to the median. find the value of x b. In the figure, b!g-:Sgo. BD is a diarneter of the circle. Calculate irlBDC. (ii Eg E 3 tJse graph paper to answer the following questions (take 2cm:lunit) on both axis. PlottbE points a(-4,2) andB (2,4) Al is the image of A when reflect in the y-oris. Plot it on the graph paper and write the go-ordinates of Al. Bl is the image of B when reflected in the line AA1. Write the co-ordinates of Bl. Write the geometric name of the figure ABAIBI Name a lineof symmetry of the figure formed. g n) {uestion:s , indX,Y ir[? ?1 t;l +3 (.? ] : r?rl 3 Question:6 ;L-- xz+yz find the value fr-vz g) x3+Y3 . (i) X:Y (ii) X3_Y3 of r b. A shopkeeper bought a washing machine at a discount of 20o/o from a wholesaler, the printed price a washing mu"Lirr" being Rs.18,000. The shop keeper sells at to a consumer at a discount of IIYo on the printed price. If the rate of sales tax is 8%, Find (i) The VAT paid by the shop keeper iii) ttt" total amount that the iotsu-". pays for the washing machine. - c. In AAC,IABC :lPS" : 8orn, AC :4cm, AD : 5cm ^ i. Prove that Affitissirnil'u too,Ar,llC F ii" Find tsC and CD iii. Find ,{rea of AACD : Area of IABC ,t prestion no. 7 A AC:5cm. Construct the incircle of the onstruct A egC with BC:6.5cm, AB:5.5cm, . b. -. ----1-------*l 3 of the l2ci6it--\ trianglc. Measure and recotd the Radius The compound interesl, calculated yearly on a1 ertztn sum of money for the second year is Rs.1320 and for the third vear is Rs.1452. C lculate the rate of interest and the original sum of money. 3 I \-.--v \ Cont... -J- in a expenses of 200 students s question)' The daily pocket i Number of students Pocket exPensts ( FrequencY) (inRs') 10 0-5 ' VKa 14 28 42 50 30 5-10 t0-15 15 -20 20 -25 25 -3U 30-35 35-40 l4 t2 q from the graph' distribution and estimate the mode histogram representing the above 3 No. of students b. In the f,rgure given below, !1am;ter *P T1"1::1CD PB:4cm' Find the circle at T' CD:7'Scm, PD:5cm' tA -1rl'u [-1 -1r] *u t: [:1 f]'r*a Question:9 .a. A two digit positive mrmber is such that ih" pt:-11:t iit" ii git JinLrchan ge their pl ace t : I ild'h: ", T:"j :ot b. 'T'3ltJT;l[H#t* lllv ruvuvreJ from the sav i;'oi " ?1""0 4 to of u toit meet at P' PI is a tangent A2 +Ac-5 the number' of its digits is 6' If 9 is added to Q) =seco + 3 cosec 0 05-04-2006 10.000-00 Ifthe interest earned bY v 5 erate ofinterest ' p.t.o -4- Question:10 4xv a. If P:--x+y' b. find the value of p+2x tp+2y P-2x p-Zy The marks obtained bv 100 students in a mathematics test are given below. 0-10 No. of ,students t0-20 20-30 3040 40-50 505,0 60-70 70-80 80-90 90-100 3 Marlcs - 12 l7 23 L4 9 6 5 4 Draw an ogive for the given distribution on a graph sheet. Use a scale of 2cm:lOunits on both axis Use the ogive to estimate the ; (i) median (ii) lower quartile (iii) No of students who obtained more thanSSYo marks in the'test (iv) No. of students who did not pass in the test, If the pass percentage was 35. 6 pestion:11 (a) In the figtre given below , 'o' is the centre of the circle. AB and CD are two chords of the circle OM is perpendicular toAB and ON is perpendicularto CD. e root of the quadraiic equation 2*+ax-6:0 is 2 , find the value of a- Also find the other J aeroplane at an altitude of 25tlm observes the angle of depression of two boats on the osite banks of a river to be 450 and 600 respectively. Find the width of the river. Write the answer correct to the nearest whole number. !****
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