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Ronal Acade1t/ Boyal Arademy PRE-BOARD EXAMINATION CLASS- X SUBJECT- MATHEMATICS SESSION: - 2022-2023 TIME-2; HOURS F.M.-80 Answer to this paper must be written on the paper provided separately The All working You will not be allowed to write during first 15 minutes This time is to be spent in reading the question paper answers. time given at the head of this paper is the time allowedfor writingthe B. Section questions from from Section A and any four Atempt all the questions including rough work. must be clearl shown, and must be done on thesame sheet as the rest ofthe answer. Omission of essentialworking will result in loss of marks. orpartsofquestions The intended marks for questions are given in brackets. Mathematical tables are provided. SECTIONA [ 40 Marks (Attempt all questions from this Section.) [15 Question 1 Choose the (1 If the answers correct 111)When is a root ofthe equation x 6 2x + (-4 by the of an (a) 2 Which (b) A.P. is given by Tn (b) 6 ofthe following point is = = (d) 2), rate of GST is 4 then remainder is (d) 35 the values 7). - of a b (d) -3,-9 3,-9 (4n 2250, the is 0, the value ofk is 3 (c) -3,9 owner (d) 18% 10 - " 2 ) = 2 2 ) . then find (a) 3,9 term (c) x 2 is divided by (x + (c) 36 -36 + x (b) A= Thenh - k x - 13 2 (b) 1 (a) 24 (1i) given options: from the of an article is 25,000 and CGST paid (c) 15% b) 10% (a) 9% (a) (1 questions cost (1)I f - If to the Find its first term (d) 3 (c)-3 invariant with respect to the line y = - 2? (d) (2,5) (3,-2) (b) (-3,2) (c) (2,-1)16cm. Then the curved surface area of cylinder is: 7cm and its height is The diameter of a cylinder is C 352 cm (d) 304 cm2 200 cm2 (c) (b) 132 cm (a) (a) (vi) (v) In the In the adjoining figure, 3 cm. 2CDA. If AC 8 cm and AD adjoining figure, = LACB = = What is the value of BD? (a) 8 cmn (b) 3 cm (c) 18 cm (d) cm B (1X) -21- 3x<8, r E The solution set for the following 1ncar incquation 1s (b) x-2<x <1,x e R (a)f-2,-1,0,1} (x)If the probability of winning game is (d)2, -1. 0. (c)1, 0, 1, 2 1; What is the probability of the losing it? 1 (a) (b) X1) If matrix A is of order 3 a) 32 11 (d) (c) 2 and matrix B is of order 2 x 2 then the matrix AB is of o (b) 31 (c) 2x3 (d) ITurn over 1x3 (Xi1) The y-axis divdes the line-segment joining the points (- 4, 5) and (3, -7) internally in the ratio (a)2 7 (x11) (b)3:7 In the given figure, if zDAB If p - 1,4p - 3,3p (a) 2 (xV) - 1 (d)3:4 60 and 2ABD = (b) 50 (a) 60 (xIv) (c)4:3 = 30 then LACB is equal to : (c) 70 (d) 90 are in AP, then p is equal to (b) A60 (c) 4 (d) 3 A die is tossed twice then the probability of getting a sum of 7 is 16 A) 36 36 6 uestion: 2 1) Mr. iupta opened a recurring deposit account in a bank. He deposited At the time of maturity he got 2,500 per month for two years. 67,500. Find: (a) The total interest earned by Mr. Gupta (b) The rate of interest per annum 4 (11) Ifqis the mean proportional between p and r show that: pqr (p + q + r)' = (pq + qr + pr)* [4] (11) Prove that sec A .cosecA = tan A +cot A + 2 4 Question 3 (1) A right circular cone of radius 4 cm and height 5 cm contains some water up to a height of2.5 cm. Find the radius of the surface of the water level. If some lead shots of radius 0.5 cm are dropped into the cone, the water rises to the top. Find the number of lead shots. 4] (i) If co-ordinates of two points A and B are (-3, 4) and (2, -1), Find (a) The cquation of AB (b) The co-ordinates of the point where the line AB intersects the y-axis. (1) Use graph paper for this question. (Take 2 cm = I unit along both [4 x-axis and y-axis.) Plot the points O(0,0), A(-4,4), B(-3,0) and C(0, -3) (a) Reflect points A and B on the y-axis and nanme them A' and B' respectively. Write down their co-ordinates. (b) Name the figure OABCB'A (c) State the line of symmetry of this figure. SECTION B | 40 Marks (Attempt any four questions from this Section.) yuestion 4 (1) The printed price of an article is t60,000. A wholesaler allows a discournt of 20% to a shopkeeper. The shopkeeper sells the article to a customer at the printed price. GST is charged at the rate of 5% at every stage. Find: a) The cost to the shopkeeper inclusive of GST b) GST paid by the shopkeeper to the government 2 1) Solve (11) Draw 18 x - 6. Find answer correct to two = 13 significant figures. histogram to represent the following data: Class mark 24 32 16 Frequency 8 12 48 56 64 18 | 25 19 10 40 15 14 Question 5 (i) Matrix Find the value of x and y (i) In the given fig, AB = AC and 2ADC = , [1+2[3]-4 if = CD 38 Calculate. (a) 2ABC (b) LBEC. (i)Ifxs ********** axi + bx + + 6 has x 2 - by - 3, find x 3 . as 38 B a factor and leaves a remainder 3 when divided [3 D [4 the value of a and b. Question 6 find Point A and B have co-ordinates (7, -3) and ( 1,9) respectively, (i) (a) the slope of AB. the line segment AB, (b) the equation of perpendicular bisector of : [3] 1sin 6 1-sin 4 tan sec 6 Prove that 1-sin 1+sin6 3 - (i1) (i1) In an arithmetic progression ten times of its 10th term is equal to thirty times of its 30th term. [4] Find its 40th term. Question 7 (i) A pair of die is rolled. Find the probability of getting a) doublets b)sum is 6 [3] c)sum is at least 10 (1) is melted and recast into solid of a solid metallic sphere is 1256 cm. It 8 cm. Calculate circular cones ofradius 2.5 cm and height The total area (a) The radius of the solid (b) The number (ii) PT is a tangent sphere of cones recast. (t to the circle right = 13 3.14) at T. LABC = 70 , 70 B ACB 5 0 Calculate . ** P (a) 2CBT (b) 2BAT 4 (c) LAPT Question 8 3 (1) Solve the inequation 2 s -2+ x 4x - 19< , x R also presentthe solution on the 3 numberline (11) If the mean distribution is 25 Class Frequency 0-10 10-20 5 18 20-30 15 L 30-40 40-50 P 6 [3 Then find p. (i) ABC is a right angled triangle with 2ABC = 90 . D is any point on AB and DE is perpendicular to AC. Prove that (a) AADE ~ ABCA. (b) If AC 13 cm, BC 5 cm and AE =4 cm. Find DE and AD. (c) Find area of AADE : area of quadrilateral BCED. D [4] B uestion 9 (i) A plane left 30 minutes later than the schedule time and in order to reach its destination 1500 km away in time, it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed. 4] (i1) Use graph paper for this question. The table given below shows the monthly wages ofsome factory workers. (i) Using the table, calculate the cumulative frequencies of workers (i1) Draw a cumulative frequency curve. (iii) Find median. Use 2 cm = { 500, starting the origin at |Wages (in T)| 6500-7000 Frequency 10 7000-7500 6500 on x-axis, and 2 cm = 10 workers on the y-axis. 7500-8000 L 18 22 8000-8500 | 8500-9000 L 25 L 17 9000-9500 L 10 6] 9500-10000 L 88 uestion 10 (i) Find x from the equation : a+X+va2-x2 [3] atx-Va2-2 ii)Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon [3 (i) A man on acliff observes a boat, at an angle of depression 30 , which is sailing towards the shore to the point immedietely beneath him. Three minutes later, the angle of depression of the boat is found to be 60 . Assuming that the boat sails at a uniform speed, determine (a) how much more time it will take to reach the shore ? (b) the speed of the boat in metre per second, if the height of the cliff is 500 m A 4)
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