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FRIENDS' ACADEMY TERM II Marks:80 Grade: 10 Time:3 h Subject : Mathematics Date : 16/12/2024 reading first 10 minutes. This time is to be spent in the during write to allowed be not will You the question paper. - Section 'A' and Section 'B'. The question paper has 2Sections SECTION A (Answer all questions from this section) [15] Question 1 questions from the given options. Choose the correct answer to the the correct answers only.) (Do not copy the question, write days he had to pay Rs.7080 including 18% GST. 2 for hotel a in stayed Mukherjee Mr. (i) When accommodation?: What is the tariff of the hotel for a day of (a) Rs.6000 (b) Rs.2000 (c) Rs. 3000 (d) Rs. 5000 1 then the value of sin is: +, ( ) If0 is theacute angle and sin =cos8 8 5 (c) 3 (a) (b) 4 (d) 3 4 3 shares (ii) What is the dividend due at the end of a year on 250 of Rs. 50 each, if the half yearly dividend is 4% of the value of the shares? (a) 1000 (c) 3000 (b) 2000 (d) 4000 (iv) If-3<-4x +5and x e W, then the solution set is : (a) {....3,-2,-1,0,1,2,3,... (b) {1,2} (c) {0, 1, 2 } (d) (2, 3, 4, 5} (v) The ratio of the glass is 6 (a) 120 T cm then diameter glass is 3:5. If the to the height of aBorosil cylindrical In the given figure,, if (vii) centre quadratic equation (a) 3x whose roots are 13x + 10 =0 (b) 3x2 + 13x + 10 = 0 The scale factor 3x -2 3 and 5 is: (c) 3x' + 13x - 10 = 0 (d) 3x'-13x- 10 = 0 of and the actual height plcture is 18 cm thena picture her actual height is If 3x - 5y = 2x + y then the value of (a) 16 (a) 3x + 3y = 6 (b) 5x + 10y = 10 of Sonia is 20 cm: 1.6 m. If her helght in the (c) 1.78 m fd) 1.44 m X-6y is *+6y Which of the following lines cut the x- the origin ? (c) 12 (d) not defined axis and y- axis at equal distances from (c) - x+y=1 (d) 10x+ 5y = 5 If x + ax + bx -6 has a factor x +3 then a + bis: (a) 1 (b) -1 (xii) 18 TN of the circle, then the value of x is. -(b) 0 (xi) (d) The (b) 2.25 m (x) 30 T (c) 180 (d) 240 (a) 14.4 m (ix) (c) D Ois the (a) 15o (b) 20 (vii) (c) 2 (d) -2 If the order of matrices AandBare m xn andpxqrespectively, then Which of the following is true for the product BA? (a) m =p (c) n=p (b) m=q diar curved surface area of cylinder is: (b) 60 T (vi) actual (d) n=q common difference is If the sum of p terms of an A.P. is ap' + bp then it's (c) a +h (a) a (d) (b) 3a +b 2 (xiv) 2 2 end of the G.P 27'9'3 The fourth term from the 2a 162 is : (c) 6 2 (d) 3 (a) 18 (b) 2 = 0is of the line 2x- 2V3y - /3 equation the of intercept (xv) The y1 (c) 2 (a) (d) v3 -1 (b) 2 [12] Question 2 If y = () (p+1)/8+ (p-1)3 (p+1)/8- (p-1)/3 (4] find the value of y -3py' + 3y - p. listed price. A at the rate of 5% on its GST of inclusive 4410 of an article is Rs. that after charging GST, the price so The price listed the ( ) discount on customer asks the dealer for a as listed price. selling price willbe same [4] deal. (a) What is the list price? discount which the dealer must allow for the of (b) What is the amount water [4 same radius. Volume of the of cylinder a and hemisphere 2618 cm below Atest tube consists of a 2849 to fill the tube to a level 2 water of cm (ii) required to fillthe tube is 3 cm and 3 length of the cylindrical part. the and tube the of radius the top.Find the [13] Question 3 () [4] incircle. = 90 , Find the radius of ABC Z cm 12 = BC cm, InA ABC, AB =5 5 cm B 12 cm 1 (ii) (ii) Prove that: 1+ sinA 1+cos4 1 2 1 |+cosecA =2 [4] the angle river. from a boat 5 m above water, There is a coconut tree on the bank of a of depression of reflcction of tree top is the angle of elevation of the top of the tree is 45" and 60 . Find the height of the tree, pu os a es 7 tio SECTION B i) (Attempt any fourquestions from this Section) Question 4 (3] 8 15 Find the matrixP if PQ =R. (i) IfQ = ( ) 1: 2. its 20"termis to term (3] 10t" The sum of first six terms of an A.P. is 63. The ratio of its R= |19 -15| Calculate the first and 15" terms. (ii) In the given figure, Z ABC =Z BDC. a) b) c) Prove that A ABC ~AADB. of AB. IF AC= 9cm and CD =7 cm, find the length Find area of AABC: A ADB [4) C 9 cm 7cm [10] Question 5 (i) 16550 deposit scheme and receives Rs. recurring a in month every [3] Shivangi deposited Rs. 500 the bank. by given interest of rate Calculate the at the end of 2% years. (ii) y axis at B. The segment AB meets x axis at A and line the figure, In the given and B. A 2:3,find the coordinates of ratio the in it divides AB (i) of the water is poured. If the radius some cm, 15 radius Into a hemisphere bowl of of water in the bowl. water is 9 cm. Find the depth point P(-3,4) on [3) B surface of [4] [10] Question 6 (i) 80 and the remaining in 6%, Rs. at sold shares 100 Rs. 5%, Kalyaniinvests Rs. 9000 partly in invested dividend is Rs. 480, find the amount annual total the If 70. Rs. 50 shares at Rs. [3] in each. (ii) transporting. The 6000. Ten were damaged during Rs. for bought were vases flower Some glass than what was 1200 by selling each for Rs. 60 more Rs. of profit total a for sold were remaining [3] paid for. Find the number of vases bought. cormmon ratia is If the respectively. 640 the seris G.P. are 10, 40, ofterms of last term ofa the number ath 6" andthe term, common ratio and the first positive, find (10) of Rs. 120 shopkeeper pays GST Question7 paid by the its MP. The calculate the price for Rs. 7200at B oil edible %, 5 shopkeeper sellssome GST charged throughout is A Government. If the inclusive oftax. tothe (3] oil edible polynomial. shopkeeper for the factorise the given Provethat (2x-1 (ii) and 2x'+x'- 13x+6 of factor a ) is state about What can you (ii) hence y = mx + withequations lines of set a C,when (c) m = 0 mis same a) [4] (d) c=0 b) c is same [10] Calculate the actual map. 1:50,000. the cm on of of length 4.6 drawn to a scale line a is by map represented A kilometers. (i) representing the airportrunway is giving your answer in An the map on area (a) runway, the Calculate (3] length of the airport is 3.5 km. the of centimeters. actual area (b) The answer in square your the airport, giving depression of 2 cars on of angle the Find the which is 96 m high, spire tan y = church and a of x = top tan the where 4 (ii) From church are x and y (3] the of side road on the same Question 8 distance between the cars. a (ii) Calculate the measures of C cif==. anglesmarked a, b and 2 3 R M (4] Question 9 (i) timesthe 3 Find the 20" term of an A.P. whose third term is 7 and the seventh term cxceeds third term by 2. Also find nth term. (i) From the given graph, prove that AAOB ~A DOC. Find 5 area of A AOB area ofA DOC + 2 3 B (ii) Solve and give your answer correct to 3 significant figures (x-1) -3x +4 =0 [10] Question 10 (i) [4] In the given semicircle with centre O, tangent drawn at point Dmeets AB produced at C. Given DBA, Z C, Z BDC. [3] 2 DAB= 28 , Calculate A Solve fory: (ii) (ii) Y+2 y-1 y-3 y-4 28 0/ [3] State giving reasons whether following statements are True or False. Here a, b, c, d are real numbers and c 0. a If a>b, then a -c>b-c. c) If a< b, then ac <bc. If a >b, then ->. b) d) If a- c<b-d, then a +d<b + c. c [4]
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