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A.B.V.M. Agrawal Jatiya Kosh s Seth Juggilal Poddar Academy(ICSE) Second Preliminary Examination (2020 21) Sub: Mathematics STD: X Marks: 80 Date: 15/03/2021 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 is the time allowed for writing the answers. 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 intended marks for questions or parts of questions are given in brackets [ ]. Mathematical tables are provided. SECTION A [Attempt all questions from this section] Question 1) a) A retailer buys a T V from a manufacturer for Rs.25000. He marks the price of the TV 20% above his cost price and sells it to a consumer at 10% discount on the marked price. If sales are intra-state and rate of GST is 12% find: [3] i) The marked price of T V. ii) Consumer s cost price of TV inclusive of tax (under GST). iii) GST paid by the retailer to the Central and State Governments. b) Prove that : tan2 + cot 2 + 2 = sec 2 cosec 2 [3] c) From a solid cylinder of height 24cm and radius 7cm, a conical cavity of same radius and height are made. Calculate the volume and surface area of the remaining solid . Page 1 of 6 [4] Question 2) a) Solve the following inequation, and write the solution set: 3( 7) 15 7 > +1 3 [3] , Represent the solution on a real number line. b) AB is a diameter of the semicircle. Chord DC is parallel to AB. = 64 . Find the angles marked , . [3] c) Identical cards are marked with numbers from 10 to 50 and well shuffled. One card is picked up from the set. Find the probability that the number on the card is i) Getting single digit ii) Divisible by 5 iii) Multiples of 3 and 5 iv) With one of the digits 5 [4] Question 3) 8 11 4 5 a) If + = [ ] = [ ] 11 14 3 4 Find the matrices X and Y. b) Solve the following quadratic equation for x and give your answer correct to two significant places: 9 2 + 6 = 4 c) ABCD is a rectangle, AB=12cm and BC=8cm. E is point on BC such that BE=5cm. AE produced meets DC produced at F. i) Prove that ~ . ii) Find the lengths of EF and CF. iii) Find area of : Page 2 of 6 [3] [3] [4] Question 4) a) Soham has a recurring deposit account in HDFC bank for 2 years at 6% p.a. [3] simple interest. If he gets Rs.2400 as interest at the time of maturity, find: i) The monthly installment. ii) The amount at the time of maturity. b) Three consecutive vertices of a parallelogram ABCD are (1,2), (1,0) (4,0). Find the fourth vertex D [3] c) A building under construction was observed from a point P 120m 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 changed to 60 . How much higher was the building raised, from the time it was first observed? Give your answer in nearest metre. [4] SECTION B [Attempt only four questions from this section] Question 5) a) ( 2) is a factor of the expression 3 + 2 + + 6. When this expression divided by ( 3), it leaves the remainder 3. Find the values of a and b . b) The following table gives the pocket money of 200 students. Calculate the mean of the following distribution. Also Calculate the new mean if the pocket money increases by Rs.20 Pocket 100 - 150 200 - 250 300 - 350 400 Money(Rs) 150 200 250 300 350 400 450 No.of Students c) = 10 14 ( +3 )+ ( 3 ) ( +3 ) ( 3 ) 2 28 42 50 30 14 [3] [3] 450 500 12 , then using properties of proportion show that 3 2 + 3 = 0 . Page 3 of 6 [4] Question 6) a) The sum of the first 3 terms of an AP is 42 and the product of the first and third term is 52. Find the first term and the common difference. b) The coordinates of two points E and F are (0,4) (3,7) respectively.Find i) The equation of EF. ii) The coordinates of points where the line EF intersects the x-axis and y-axis. [3] [3] c) A girl fills a cylindrical bucket 32cm in height and 18cm in radius with sand. She empties the bucket on the ground and makes a conical heap of the sand. If the height of the conical heap is 24cm. Find: [4] i) Its radius ii) Its slant height.(Give your answer in two decimal value) Question 7) a) If a, b and c are in continued proportion, prove that: 2 + 2 + 2 = + + + [3] b) In , : = 2: 3. PO is parallel to BC and is extended to Q, so that CQ is parallel to BA. Find : [3] i) ii) : If CQ=6cm, find AP. c) Attempt this question on graph paper. Plot (3,2) (5,4) on the graph paper. Reflect A and B in the x-axis to A ,B . Plot these on the same graph paper. Write down: i) The geometrical name of the figure ABB A . ii) The area of ABB A iii) The image A , when A is reflected in the y-axis. iv) The single transformation that maps A to A . Page 4 of 6 [4] Question 8) a) : sec 1 sec +1 = 1 cos [3] b) Using the Remainder Theorem, factorise completely the following polynomial. [3] 3 3 + 2 2 19 + 6 c) Amrita has a recurring deposit account in bank of Baroda of Rs.2000 per month at the rate of 10%. If she gets Rs.83100 at the time of maturity, find the total time for which the account was held. [4] Question 9) a) Sonam can row a boat at a speed of 5km/h in still water. If it takes her 1 hour more to row the boat 5.25km upstream than to return downstream, find the speed of the stream. b) 100 pupils in a school have weights as tabulated below. [4] [6] Weights(kg) 40-45 45-50 50-55 55-60 60-65 65-70 70-75 No.of Pupils 12 16 30 20 14 5 3 i) ii) iii) iv) Draw an ogive for the above data and from it determine. The median. Lower Quartile The number of pupils who are obese, if weight more than 67kg is considered obese. The percentage of pupils whose weight is less than 47kg. Page 5 of 6 Question 10) a) Determine the A.P . whose third term is 6 and the difference of the eighth term from the thirteenth term is 20. b) Determine the ratio in which the line 2 + 4 = 0 divides the line segments joining the points (2, 2) (3,7) [3] [3] c) = { : 2 5 5 + 4 < 11, } = { : 13 5 < 15 + 4 < 7 + 12, } Find the range of set and represent it on the number line for the following. i) ii) [4] Question 11) a) AB is a diameter of the circle. TS is a tangent to the circle at C and O is the centre. = 48 . Find , [3] b) Find the equation of a line passing through the points ( 1,3) (0,2). Hence, show that the points , (1,1) are collinear. [3] 3 5 c) If = [ ] and 2 5 = , where I is an identity matrix of order 2x2. 4 2 Find the value of scalar factor k. *********END************* Page 6 of 6
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