Formatting page ...
KIMMINS HIGH SCHOOL PANCHGANI Preliminary Examination Nov. - 2020 SUB MATHEMATICS Std- X Marks - 80 Date - 23/11/2020 Time 2 Hr.30min. 1) 2) 3) 4) 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 is the time allowed for writing the answers. This paper consists of four printed pages. 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 loss of marks. The figure(s), if any, given in this Paper are not to the scale. The intended marks, for questions or parts of questions are given in brackets. [ ] Calculators are not allowed. Mathematical tables are provided. _____________________________________________________________________ Section A (Compulsory) Question 1) (03) a) Find the Value of x and y if. 2 9 7 6 + 5 4 7 10 = 5 22 7 15 b) Sonia had a recurring deposit account in a bank and deposited Rs. 600 per month for 2 years. If the rate of interest was 10% p.a. Find the (03) maturity amount. c) Cards being numbers 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20 are kept in a bag. A card is down at random from the bag. Find the probability of getting card which is a) Prime number b) number divisible by 4 c) number that is multiple of 6 (04) d) an odd number Question 2) a) The circumference of the base of the cylindrical vessel is 132 cm and height is 25 cm. Find the 1) Radius of the cylinder. 2) Volume of the Cylinder (Use = ) (03) b) Find the value of a when 3x3 + ax2 - 5x + 2 is divided by (x + 2) the remainder is 4 (03) : 2: c) If Y = (04) then show that x = Question 3) a) Solve the following in equation, represent solution set on the number line. -2 + 10x < 13 x + 10 < 24 + 10x, x Z (03) b) Solve x2 + 7x = 7 and give your answer to two decimal places. (03) c) Prove that. ( 1 + cot cosec ) ( 1+tan + sec ) = 2 (04) Question 4) 1) The ratio of 6th and 14th terms of AP is 2:5. Find the ratio of (03) 1) 4th and 19th term 2) the sum of first 5 terms and the sum of first 12 terms. 2) The median of the following observations 11, 12, 14, (x 2), (x + 4), (x + 9), 32, 38, 47 arranged in ascending order is 24. Find the value of x and hence find the mean. (03) 3) ABCD is a cycIic quadrilateral in the circle with centre O. OD ll BC. DAB = 550, Find i) BCD, ii) BOD, iii) OBD, iv) BDC Section- B (Attempt Any four Questions) Question 5) a) Given a line segment AB joining the points A(-4, 6) and B(8, -3). Find ration in which AB is divided by y axis. Find the coordinates of the point of intersection. (03) : 3: 2) If A = 2 5 3 0 ,B= 7 1 4 1 0 and C = Find AC + B2 10 C 7 1 4 (03) 3) Use a graph paper for this question. (Take 2 cm = 1 unit on both axes) ABCD is a quadrilateral whose vertices are A(2,2), B(2,-2), C(0,-1) and (04) D(0,1) i) Reflect ABCD on y axis and name it as A B C D ii) Write down the coordinates of A and B iii) Name two points which are invariant. iv) Name polygon A B CD Question 6) a) In PQR, MN is parallel to QR and = (03) i) Find ii) Prove that OMN ~ ORQ iii) A( OMN) : A( ORQ) 2) Priyanka has a recurring deposit account of Rs. 100/- per month at 10% per annum. If she gets Rs. 550 as interest at time of maturity Find time. (03) 3) A cylindrical pillar 4 cm high is surmounted by a coneof diameter 60 cm and height 40 cm. Find the cost of painting the pillar at Rs. 10 per m2 ( = 3.14) (04) Question 7) a) Rs. 7500 were divided equally among a certain number of children. Had there been 20 less children, each would have received Rs. 100 more. Find the original number of children. (04) b) A survey regarding height (in cm) of 60 boys belonging to class 10 of a school was conducted. (03) : 4: Ht(cm) 135-140 140-145 145-150 150-155 155-160 160-165 165-170 No. of 4 8 20 14 7 6 1 boys taking 2 cm = ht of 10 cm on X axis and 2 cm = 10 boys on other axis. Draw an on give. Use graph to estimate . i) the median ii) lower quartile. iii) If 158 cm is considered as the tall Find number of boys in the (06) class who are tall Question 8) (03) 1) Prove that .......... ( + 1) = 1 1+ 2) Point P divides the joining of line segment A(2,5) and B(7,15) in the (03) ratio 2 : 3. i) Find the co-ordinates of P ii) Find equation of a line with gradient -5/3 and passing through P. 3) A market price of a mobile is Rs. 9,000/- and the rate of GST is 12%. A shopkeeper buys it at a discount and sells it to a customer at the marked price. If the shopkeeper pays a GST of Rs. 36/- to the (04) Central Goverment, Find the following. i) Price paid by shopkeeper inclusive of tax. ii) % discount received by shopkeeper. Question 9) 1) If a,b,c are in continued proportion prove that + + + + (03) = 2) The sum of three numbers in an AP is -12 and their product is 36. Find the numbers. (03) : 5: (04) 3) AB is a diameter of semicircle CD AB i) Prove that ADC CDB ii) Find CD if AD = 4.5cm and DB = 8cm Question 10) 1) If the mean of following distribution is 15.5, Find the value of a. (03) Class 0-5 5-10 10-15 20-25 25-30 Frequency 2 7 18 a 5 2) Without solving the following equations. Find the value of P, for which the given equation has equal roots. (03) (P + 6) x2 + (P - 2) x +1 = 0 3) An aero plane at an attitude of 250m observes the angle of depression of two boats on the opposite banks of river to be 450 and 600 respectively. Find the width of the river. Write the answer correct to nearest whole number. (04) Question 11) 1) When Mr. Rao ordered medicines the bill was Rs. 840, which included 12% GST i) What was the price of medicines before tax? ii) How much GST was paid to the Central Government? 2) Using Remainder theorem factories completely 3x3 + 2x2-19x+6 (03) (03) 3) TBP and TCQ are tangent to the circle from T ABP = 650 and ACQ = 400 Find BAC and BTC (04)
|
