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ARYA VIDYA MANDIR, BANDRA WEST PRE-PRELIM REVIEW JANUARY 2021 STD: X MATHS Marks: 80 Date: 19-01-2021 MATHEMATICS 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 from Section B All working including rough wok 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 [ ]. This paper consists of six printed pages. ______________________________________________________________________________________ Section A I - 40 marks (Attempt all questions from this section) Question 1: a) Ram has a cumulative deposit account in a post-office. He deposits Rs. 500 per month for 4 years. If at the end of maturity period she gets Rs. 28410, find the rate of interest paid by the post -office. b) Find: BA [3] [3] Sec 60o cos 90o A= cot 45o 0 B= -3 tan 45o sin 90o -4 sin 30o 3 sin 90o Prove c) Factorise the following: 2x4 + x3 14x2 19x - 6 using Factor theorem. [4] Question 2: a) If A = {x: 11x 5 > 7x + 3, x R} and Q = {x: 18x 9 15 + 12x, x R}; Find the range of the set A B and represent it on the number line. [3] b) In an A.P. the first term is 25, nth term is -17 and the sum of n terms is 132. Find n and the common difference. [3] Prove c) Prove: cos A 1 tan A + sin2 A sin A cos A = sin A + cos A [4] ..2 -2Cont. Std. X Mathematics Pre-Prelim Review January, 2021 Question 3: a + b + c + d = a b + c - d, Prove that: a+b c d a b c+d a) If a=c b d [3] b) Find the value of k for which the given equation has equal roots. Also, find the roots. 2kx2 40x + 25 = 0 [3] c) Use a graph paper to solve this question. (Take 1cm = 1 unit on both the axes). Plot P (3, 2) and Q (-3, -2) on the graph paper. From P and Q, draw perpendiculars PM and QN on the x axis. (i) Name the image of P on reflection in the origin. (ii) Assign the special name to the geometrical figure PMQN and its area. (iii) Write the coordinates of the point to which M is mapped on reflection (a) x axis (b) y axis (c) origin. [4] Question 4: a) A black die and a white die are thrown at the same time. What is the probability? (i) That the sum of the two numbers that turn up is 8? (ii) That the sum of the numbers appearing on the top of the dice is a prime number. [3] b) If the coordinates of the mid-points of the sides of a triangle are (1,1), (2, -3) and (3,4). Find its centroid. [3] c) The marked price of an article is Rs.18000. A wholesaler sells it to a dealer at 20% discount. The dealer further sells to a customer at a discount of 10% on the marked price. If the rate of GST at each stage is 18%, find the amount of tax (under GST) paid by the dealer to the Government. [4] Section B (40 marks) Attempt any FOUR questions from this section Question 5 a) 4x3 12x2 + cx + d has x 3 as a factor and when it is divided by x + 2, leaves a remainder -75. Find the value of c and d. [3] b) If a cos + b sin = m and a sin - b cos = n, prove that a2 + b2 = m2 + n2 [3] ..3 -3Cont. Std. X Mathematics Pre-Prelim Review January, 2021 c) In the given figure BAC= 700, DBA = 350 BD is the diameter. Find the measure of: (i) Angle DAC (ii) Angle ACB [4] Question 6 a) Solve the quadratic equation: x2 10x = 6 correct to 2 decimal places. [3] b) If the radius of the base of a cone is halved, keeping the height same, what is the ratio of the volume of the reduced cone to that of the original cone? [3] In ABC, AB = 8 cm, AC = 10 cm and B = 900. P and Q are points on the sides AB and AC respectively such that PQ = 2 cm and PQA = 900, find: (i) Area of AQP (ii) Area of quadrilateral PBCQ : Area of ABC [4] c) Question 7 a) The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is [4] 600. At a point Y, 40 m vertically above X, the angle of elevation is 450. Find the height of the tower PQ and the distance XQ. ..4 -4Cont. Std. X Mathematics Pre-Prelim Review January, 2021 b) Using a graph paper, draw an ogive for the following distribution which shows a record of weight in kilograms of 200 students: Weight (kg) 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 Frequency 5 17 22 45 51 31 20 9 [6] Use your ogive to estimate the following: (i) The percentage of students weighing 55kg or more. (ii) The weight above which the heaviest 30% of the students. (iii) The number of students who are (a) under-weight and (b) over-weight, If 55-70 kg is considered as standard weight. Question 8 a) Find the equation of a line passing through the point (-2,3) and having x-intercept [3] 4 units b) `1 4 2 3 Solve the inequation -2 + 2x 4 3 + 2x, x W. Graph the solution set on the [3] number line. c) A bag contains 12 balls out of which x are white. (i) (ii) [4] If one ball is drawn at random, what is the probability that it will be a white ball? If 6 more white balls are put in the bag, the probability of drawing a white ball will be double than that in (i). Find x. ..5 -5Cont. Std. X Mathematics Pre-Prelim Review January, 2021 a) b) c) Question 9 In the given figure, O is the centre of the circle, = 1500, = 510. Find the measure of: (i) (ii) [3] The sum of first n term of an A.P. is 5n2 8n. Find the A.P. and hence its 15th term. [3] The side of a square exceeds the side of another square by 4 cm and the sum of the areas of the two squares is 400 sq. cm. Find the dimensions of the squares. [4] Question 10 a) ABC is a triangle in which = 900, AN BC, BC = 12 cm and AC = 5 cm. Find the ratio of the areas of and . b) If A = [ 9 1 ] 5 3 and B = [ [3] [3] 1 5 ], 7 11 Find a matrix X such that 3A + 5B 2X = 0 c) If x = 2 + 2 + 2 2 2 + 2 2 2 , show that: b2 x2 - 2a2x + b2 = 0 [4] 6 -6Cont. Std. X Mathematics Pre-Prelim Review January, 2021 Question 11 a) The mean of the following frequency table is 50. But the frequencies f 1 and f2 in class 20-40 and 60-80 are missing. Find the missing frequencies. Class Frequency 0-20 20-40 40-60 60-80 80-100 Total 17 f1 32 f2 19 120 [3] b) Find the point of intersection of the lines: 4x + 3y =1 and 3x y + 9 = 0. If this point lies on the line (2k-1) x 2y = 4; find the value of k. [3] c) A tent is of the shape of a right circular cylinder up to a height of 3 metres and them becomes a right circular cone with a maximum height of 13.5 metres above the ground. Calculate the cost of painting the inner side of the tent at the rate of Rs.2 per square metre, if the radius of the base is 14 metres. [4] ----------THE END----------
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