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LOKHANDWALA FOUNDATION SCHOOL PRELIMINARY EXAMINATION-(2020-21) SUBJECT :MATHEMATICS Date :25 /01/21 Duration:2 Hrs. Grade: 10 Max. Marks: 80 ____________________________________________________________________________________________ General Instructions:-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 of the answer. Omission of essential working will result in the loss of marks. The intended marks for questions or parts of questions are given in brackets ( ). The paper consists of 4 printed sides. ____________________________________________________________________________________________ SECTION A (40 MARKS) (Attempt all questions) Question.1 a) Mrs. Roy opened a Recurring Deposit Account in a bank. She deposited 2500 per month for two years. At the time of maturity, she received 67500. Find (i)Total interest earned by her. (ii)Rate of interest per annum. b) If A = [ ] and B = [ ] , find the value of 3A - 2B + I , where I is the identity matrix. c) Given that A = {x : 3 < 2x 1 < 9, x R} and B = {x : 11 3x + 2 23, x Represent A and B on number lines. Also, write A (3) (3) R} . B. Question.2 a) KLMN is a quadrilateral , PQ is a tangent to the circle at K. If LN is a diameter of the circle, KLN= 30 and MNL= 60 , find (i) QKN (ii) PKL (iii) MLN (4) (3) b) Manufacturer sold a TV set to the wholesaler for 7000. Wholesaler sold it to the trader at a profit of 1000. If the trader sold it to the customer at a profit of 1500, find (i)Total GST at the rate of 5% collected by State Govt. (ii) Amount that the customer paid for the TV set. (3) c) In the adjoining figure, MN ll QR, PM : MQ = 5 : 4. Find: (i)MN : QR (ii)area( MON) : area( ROQ) (4) Question.3 a) Solve the equation 3x x 7 = 0 and give your answer correct to two decimal places. b) Using factor theorem, show that (x + 4) is a factor of 2x + 9x + x 12. Hence, factorize the given expression completely. (3) (3) P.T.O Grade : 10 SUBJECT: MATHEMATICS Page: 2 c) Following distribution shows no. of wickets taken by bowlers in one - day cricket matches. Find the mean no. of wickets using step- deviation method. Also, round off your answer to the nearest integer. (4) No. of wickets 20 - 40 40 - 60 60 - 80 80 - 100 100 - 120 120 - 140 No. of bowlers 7 5 16 12 2 3 Question.4 a) If 7x 15y = 4x + y , find the value of using properties of proportion. (3) b) Write the equation of line whose gradient is 3/2 and which passes through point P where P divides the line segment joining A(-2,6) and B (3,-4) in the ratio 2 : 3. (3) c) In an Arithmetic Progression of 50 terms, the sum of its first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the AP. (4) SECTION B (40 MARKS) (Attempt any four questions) Question.5 a) In the adjoining figure, AB and CD are the lines 2x y + 6 = 0 and x 2y = 4 respectively. Using given figure, (i)Write the coordinates of points A, B ,C and D. (ii)Also, write the equation of BD. (3) b) Find the value of k for which the equation kx(x 2) + 6 = 0 has real and equal roots. (3) c) Plot the points A(-1,0) and B(4,3) on graph paper. (i)Reflect A in Y- axis and B in X- axis to get images A and B respectively. (ii) Write the coordinates of A and B . (iii) Name the geometrical figure ABA B . (iv) Also, find its area. (4) Question.6 a) If a, b, c and d are in proportion, prove that = . (3) b) Prove that the points A(-2,-1), B(1,0), C(4,3) and D(1,2) are the vertices of parallelogram ABCD. (3) c) Volume of conical tent is 1232 cu. m and area of its base is 154 sq.m. Calculate : (i)Radius of floor. (ii)Height of tent. (iii)Length of canvas required to cover this conical tent if its width is 2m. (4) P.T.O Grade : 10 SUBJECT: MATHEMATICS Page: 3 Question.7 a) In the adjoining figure, ABDC is a quadrilateral with CAD = 25 , ABC= 50 and ACB= 35 . Calculate : (i) CBD (ii) DAB (iii) ADB (3) b) Mean of 1,7,5,3,4 and 4 is m . The numbers 3,2,4,2,3,3 and p have mean m - 1 and median q. Find the values of p and q. - c) Prove that = (3) - (4) Question.8 a) A conical vessel whose internal radius is 12 cm and height 50 cm full of liquid. The contents are then emptied into a cylindrical vessel with internal radius 10 cm. Find the height to which liquid rises in the cylindrical vessel. b) Let A be a matrix such that [ ] .A=[ (3) ] (i)State the order of matrix A. (ii) Find the matrix A. (3) c) Two objects C and D are located on the same side of tower AB. When observed from the top B of the tower, their angles of depression are 45 and 60 respectively. Find the distance between the objects if the height of tower is 180 m. Give your answer correct to the nearest metre. (4) Question.9 a) If 8 times eighth term of an AP is equal to 13 times thirteenth term, find the value of 21st term of the same AP. (3) b) P(3,4) , Q(7,-2) and R(-2,-1) are the vertices of PQR. Write down the equation of median of the triangle through vertex Q. (3) c) In winter, a train travels a distance of 264 km at a certain speed. In summer, it travels 8 km/hr faster and takes 22 minutes less than in winter. Find its speed in winter. (4) Question.10 a) Marked price of a mobile is 9000 and rate of GST is 12% . A shopkeeper buys it at a discount and sells it to customer at the marked price. If the shopkeeper pays a GST of 72 to Government, find (i)Price paid by shopkeeper inclusive of tax. (ii)% age of discount received by the shopkeeper. (4) b) Using graph paper, draw an ogive for the following distribution of weights of 200 students in kg. Wt. in kg No. of students 40-45 5 45-50 17 50-55 22 55-60 45 60-65 51 65-70 31 70-75 20 75-80 9 P.T.O Grade : 10 SUBJECT: MATHEMATICS Use your ogive to answer the following : (i)Median weight (ii)Weight above which the heaviest 30% of the students fall. (iii)No. of students who are underweight if 56 kg is considered as standard weight. Page: 4 (6) Question.11 a) Identical cards are marked 1 to 100. When a card is drawn at random, what is the probability that it is (i) a multiple of 2 and 3? (ii)a prime number containing the digit 9 ? (iii)a number in which one digit is twice the other? (3) b) In the given figure, TBP and TCQ are tangents to the circle from T. If ABP = 65 , ACQ = 40 , find the measures of BAC and BTC. (3) c) The daily pocket money of some students in a class are given below. Pocket money in 0-50 50-100 100-150 150-200 200-250 No. of students 8 10 24 18 6 On a graph paper, draw a histogram for the above distribution and estimate modal expenses. (Take 2cm = 4 students along Y- axis and 2cm = 50 rupees along X- axis.) NOTE: KINDLY REFER THE LOG PAGES ATTACHED BELOW. (4)
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