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G.D.SOMANI MEMORIAL SCHOOL PRELIM EXAMS SUB: MATHEMATICS MARKS:80 DATE: 21/01/2021 TIME:2%HRS. Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this Paper isthe timeallowedforwritingtheanswers. Attempt all questions from Section A and any four questions from Section B. All working, including rough work, must be clearly shown and must be done on the same sheet as the rest e the answer. Omission ofessential working will result in the loss of marks. The intended marks for questions or parts of questions are given in brackets I Mathematical tables are provided. SECTION - A [40 Marks] (Attempt all questions from this Section) Question: 1 [a] Solve the following inequation, write the solution set and represent it on the 3 real number line. 2 [b] s 2, xEl Find the value of k, for which the equation 3x- 6x + k = 0 has distinct and real roots. 41 Mr. Tripathi bought some items as per the details given below: MRP (in Rs) for each item Number of items Discount % | CGST % 200 125 20 32 35 25 Calculate: the total amount of GST paid. il the total bill amount including GST paid by Mr. Tripathi. Question:2 Use factor theorem to factorise 3x + 2x* - 19x + 6 completely. [al [b] cl A bag contains 4 green, 12 red and x yellow balls. Express the probability of getting a yellow ball in terms of x. When a ball is drawn at random, the probability of getting a yellow ball is double that of a green ball. Find: the number of yellow bals. the probablity of getting a red bal. Mis the mid-point ofthe line segment Joining the points A(-3, 7) and B (9, -1). Find the co-ordinates of point M. Further, if R(2, 2) divides the line segment joining M and the origin in the ratio p: q, find the ratio p:q. (3] (3 4 (This paper consists of5 printed pages & one blank page) GDS/STD.x /MATHEMATICS... contd. 2 Question:3 a) IfA-O B1-cosec?6 01 C[2 c21 Find the matrix X such that A+ B +2X = C [bl In the 3 adjoining figure, PQRS is a cyclic quadrilateral. LQPS 73 , LPQS = 55 and PSR 82 . Calculate: il4QRSii] 4RQS The volume of a 73 ii) 4PRQ conical tent is 1232m* and the area of the floor is 55 154m 4 Calculate: the radius of the base. the height of the tent. ii the length of canvas required to cover the tent if the width is 2m. iv the cost of the canvas at the rate of Rs.24 per metre. Question: 4 al Mr. Peter opened a recurring deposit account with a bank and deposited Rs.250 per month. If the rate of interest is 12% per annum and the bank pays Rs. 10665 on maturity, find the time for which he held the account. sin 2sin3 0 tan 6 [b] Prove that Ic The marks obtained by 19 students of a class are given below: 2cos3 0 - cos 6 27, 36, 22, 31, 25, 26, 35, 24, 37 32, 29, 28, 36, 35, 27, 26, 32, 35 and 28. Find: i) the median the inter-quartile range i the mode. 3 4) GDS/STD.x /MATHEMATICS... contd. 3: SECTION - B [40 Marks] (Attempt four questions from this Section) Question:5 la A In the adjoining figure, D LEDB =LACB, Provethat: AABCAEBD. If BE 6cm, EC = 4cm,BD = Scm and the area of A BED = 9cm, calculate: t h e length of AB. B E C the area of AABC. [b] Find the equation of the line through the intersection of lines 2x- y =1 and 3x +2y -9 and making an angle 30 with positive direction ofx- axis. Ic f , ,find 4 XY Question:6 The maturity value of a recurring account is lal Rs. 11364 in 4 years. If the monthly deposit is Rs.200, find the rate of interest. [b] Divide 96 into four parts which are in AP and the ratio between product of their means to product oftheir extremes is 15 :7. c 3 [3 From a solid cylinder of height 30cm and radius 7cm, a conical cavity of height 24cm and of base radius 7cm is drilled out. Find the volume and total surface area of the remaining solid. Question: 7 iven |M 61, where Mis a matrix and I is unit matrix oforder 2 x2. [3 State the order of matrix M. Find the matrlix M. [b 6 is the mean proportional between two numbers x and y and 48 is the third proportional of x and y. Find the numbers. [3 GDS/STD.x /MATHEMATICS...contd. c In the 4 adjoining figure, 14) PA and PB are tangents at the points A and B respectively of a circle with centre O.Q and R A points are on the circle.If LAPB = 70 , find O Q LARB [il [ii [iv] LAQB LAOB LOAB Question:8 al A shopkeeper buys an article for Rs.800 from a wholesaler at a discount of 20% on the list price. He marks up the list price by 10% and sells it at Rs.1155 which includes GST on the marked-up price. Find: the rate of GST. [il [b] the profit percentage for the shopkeeper. When the polynomial x* 2x - 5ax 7 is divided by x-1, the remainder is A and when the polynomial x+ax - 12x + 16 is divided by x +2, the remainder is B. [cl Find the value of 'a' if 2A + B = 0. Use graph paper for this question. (Take 2cm = 1 unit along both x and y-axis). 13 [4] ABCD is a quadrilateral whose vertices are A(2, 2), B(2,-2), C(O,-1) and D{0, 1). Reflect quadrilateral ABCD in the y-axis and name it as A'B'CD. Write down the co-ordinates of A' and B'. ii Name two points which are invariant under the above reflection. [iv] Name the polygon A'B'CD. Question:9 la If the 8h term of an AP is 37 and 15th term is 15 more than 12h term, find the AP. Also, find the sum of first 20 terms of this AP. b] Solve x - 8x = -5 and give your answer correct to three significant [3 figures. 1 +(sec A- tan A ) c (3 Prove that Cosec A (sec A - tan A) 2 tan A 4 GDS/STD.X /MATHEMATICS... contd. 5: Question: 10 Use Graph paper for this question. lal In a collection of funds for flood hit victims, 200 people in a colony contributed some money. The following table shows the distribution. Contribution 500-600 in Re.) I6] 600-700 700-800 800-900 900-1 1000 1000-1100 1100-1200 1200-1300 12 16 34 40 36 28 14 Number of people 1400-1500 1300-1400 6 Taking 2cm = Rs.100 along one axis and 2cm = 20 people along the other axis, draw an ogive of the above distribution. Use the graph to estimate the following: the median. the lower quartile. ii) if the top 10% of the contributors were to attend a programme, find the lowest contribution which qualify a contributor to attend the programme. [b] When a building under construction was observed from a point 120 m from its base, the angle of elevation of the top was 30. After its completion when it was again observed from the same point, the angle changes to 60. How much higher was the building raised, from the time it was first observed ? Give your answer to the nearest metre. 4 Question: 11 [a] Anamika bought some pens for Rs. 360. When the price of each was reduced by Rs.3, she could buy 6 more pens for the same cost of Rs.360. Find the original [b) cost of the pen. (3 Find the mean of the following frequency distribution: (3 Class interval 12.5-17.5 17.5-22.5 22.5-27.5 2 22 19 Frequency c 27.5-32.532.5-37.5 14 In the adjoining figure, D D and E are two points on the side AB such that AD BE. if DP || BC and EQ|| AC,then using basic proportionality theorem and its converse, prove that PQ|| AB. *** B 3 4]
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