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ICSE Class X Prelims 2020 : Mathematics (The Bishop's Co - Ed. School, Kalyaninagar, Pune)

3 pages, 47 questions, 10 questions with responses, 10 total responses,

Jatin Patil
The Bishop's School, Camp, Pune

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THE BISHOP S CO-ED. SCHOOL, KALYANI NAGAR - PUNE SECOND PRELIMINARY EXAMINATION (2019-2020) MATHEMATICS CLASS: 10 TOTAL MARKS: 80 READING TIME: 15 MINUTES WRITING TIME: 2 HOURS DATE: 02-12-2019 Answer 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 ( ). SECTION A (40 MARKS) Answer all questions from this section Question 1: (a) Solve the following inequation and represent it on a number line 1 1 2 2 -5 - x 1 - 3x 3 - x, x R (3) 2 (b) Amit deposits 1,600 per month in a bank for one and a half year in a recurring deposit account. If he gets 31,080 at the time of maturity, what is the rate of interest per annum? (3) (c) The mean of the following distribution is 49. Find the missing frequency 'a' (4) Class interval 0-20 20-40 40-60 60-80 Frequency 15 20 30 a 80-100 10 Question 2: (a) Find a if the polynomials ax3 + 3x2 - 9 and 2x3 + 4x + a, leave the same remainder when divided by x + 3. Hence find the remainder. (3) 2 2 2 2 (b) Prove that tan + cot + 2 = sec . cosec (3) (c) A manufacturer sells a TV to a dealer for 18,000 and the dealer sells it to a customer at a profit of 1,500.If the sales are intra-state and rate of GST is 12%,find: i) the amount of GST paid by the dealer to the State Government. ii) the amount of GST received by Central Government. iii)amount paid by the customer for purchasing the TV (4) Question 3: (a) For what value of n, are nth terms of two A.Ps 63,65,67,......and 3,10,17,.....are equal? Also find that term. (3) (b) Find the ratio in which the line joining (-2,5) and (-5,-6) is divided by the line y =-3. Hence find the point of intersection. (3) (c) Suresh invested equally in two companies A and B. 100 shares of company A are available at 10% premium and it pays 8% dividend whereas 50 shares of company B are available at 12% discount and it pays 7% dividend. If the total income from both the companies is 1340,find how much, in all does he invest? (4) Page 1 of 3 Question 4: (a) If 6 is the mean proportion between the two numbers x and y and 48 is the third proportional to x and y, find the two numbers. (3) (b) A building is in the form of a right circular cylinder surmounted by a hemisphere 19 dome and contains 41 21 m3 of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building. = 22 7 (3) (c) Use a graph paper for this question. (i) Plot point P (-1,3) and reflect it in the line parallel to Y-axis at a distance 2 units to the right of Y-axis on to the point P'. (ii) Plot Q' (-3,-2),the image of Q, reflected in origin (iii) Plot and write the co-ordinates of P' and Q (iv) Write the equation of P'Q (4) SECTION B (40 MARKS) Answer any 4 questions from this section Question 5: (a)Cards marked with all 2-digit numbers are placed in a box and are mixed thoroughly. One card is drawn at random. Find the probability that the number on the card is i) divisible by 10 ii) a perfect square iii) a prime number less than 25. (3) (b) Prove that(cosecA cotA)2= 1 cosA (3) 1+cosA (c) In the given figure, i) prove that ACE ~ DBE ii) If DB = 4.5 cm, BE = 3cm, and CE = 4cm, find AC iii )Find area ACE: area DBE (4) Question 6: (a)The points (1,1) (9,3) (11,8) and (3,6) are the vertices of a quadrilateral. Show that the diagonals bisect each other. Hence classify the quadrilateral. (3) (b) If -5 is a root of the quadratic equation 2x2 + p x - 15 = 0 and the quadratic equation p(x2 + x ) + k = 0 has equal and real roots, find the value of k. (3) o (c) Construct a triangle ABC,AB = 5.4cm,BC = 6.6cm and ABC = 105 . Locate a point P outside the triangle such that BAP = 75o and BP = CP. Measure the length of BP. (4) Question 7: (a) The tangent at the point C on the circle meets the diameter AB produced at P. If CP = y and BP =x, then prove that the radius of the circle is y2 x2 2x (3) (b) The eighth term of an AP is half of its second term and 11thterm exceeds one third of fourth term by 1.Find the 15th term. (3) (c) A metal pipe has a inner diameter of 5cm.The pipe is 2 mm thick all around. Find the weight in nearest kilograms, of 2 metres of the pipe if 1 cm3 of the metal weighs 7.7 grams.( = 3.14) (4) Question 8: (a) ABC is inscribed in the circle. O is the centre of the circle. Tangent AT is parallel to OP. Prove that OBCP is cyclic quadrilateral Page 2 of 3 (3) (b) On a map drawn to a scale of 1: 40,000, a rectangular plot of land, ABCD has the following measurements. AB = 6cm and BC = 8cm. Calculate i) the diagonal distance of the plot in km. ii)the area of the plot in square kilometre. (3) (c) Construct a ABC in which AB = 4.5cm, BC=7cm and median AM = 4cm. Inscribe a circle in it and record its radius. Question 9: (a) If 5a+3b 5a 3b =2 1 8 ;find i) a3 +b3 a3 b3 ii) 2a2 3b2 3b2 (4) using properties of proportion. (3) (b) AB is a tangent to the circle with centre O, at Q. If PSQ = 38o, PQR =110o ,find QPR, PQA, RQB (3) (c) A man on the deck of a ship is 10m above water level. He observes that the angle of elevation of the top of the cliff is 45o and the angle of depression of its base is 20o. Calculate i) the distance of the cliff from the ship ii) the height of the cliff correct to the nearest metre (4) Question 10: 1 2 (a)Find matrix D such that AD = A, given A = [ ] ;State the specific name of 3 4 the matrix obtained . (3) 7 th (b) The fourth term of a G.P is 16 and the term is 128. Find the first term, common ratio and sum of first 7 terms. (3) (c) Find the equation of a line that contains the point of intersection of 2x - 5y =4 and 3x - 2y = -16 and is parallel to the line 3x - y = 9. (4) Question 11: (a) In a mango grove, the trees are planted in horizontal and vertical rows. There are 6 trees more in each horizontal row than in vertical row. If there are 720 trees altogether, find the number of trees in each horizontal row. (4) (b) The daily wages of 80 workers on a construction site are given below. Wages in ` No. of workers 30 - 40 40 - 50 50 - 60 60 -70 70 -80 80 - 90 90 - 100 100-110 6 10 15 19 12 8 6 4 Draw an ogive and estimate i) the median wage ii) upper quartile wage iii) number of workers getting more than 75 and less than 105 (6) ---------------------------------------------------------------------------------------------- Page 3 of 3

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