Formatting page ...
PRELIMINARY EXAM 2 2023-24 Grade: 10 Subject : Mathematics Max.Marks:80 Date: 08/01/24 Dur. : 2 Hours Number of printed pages : 6 SECTION - A (40 Marks) (Attempt all questions from this section) Question 1 (15) Choose the correct answers to the questions from the given option: i) A man deposited 600 per month for 9 months and received 5580 as the maturity value. The interest is _______________. (a) 270 ii) (b) 450 (c) 180 (d) 540 Assertion (A) :- A letter is chosen at random from the word MATHEMATICS , then the probability that it will be a vowel is 4/11. Reason (R) :- The probability of an event P(E) is given by P(E) = Number of favourable outcomes Total number of outcomes a) A is false, R is true iii) (b) 38 3 If A =[ 9 9 (a) [ 3 v) (d) Both are false (c) -55 (d) 2 1 6 ], then =_______________. 3 12 2 ] 3 3 (b) [ 3 2 ] 3 1 (c) [ 3 2 ] 4 9 2 ] (d) [ 3 3 For what value of :- 2, 2 3, and + 4 will be in arithmetic proportion? (a) 4 vi) (c) Both are true If a polynomial 2 3 -1 is divided by ( + 3) , then the remainder is ___________. (a) -4 iv) (b) A is true , R is false (b) -4 (c) 1 (d) -1 The point A ( , ) is invariant about = under reflection. The coordinates of its image is : (a) A ( , ) (b) A ( , ) (c) A ( , ) 1 (d) A ( , ) vii) viii) The three vertices of the scalene triangle are always equidistant from a fixed point. The point is a) Orthocentre b) Incentre c) Circumcentre d) Centroid The ratio of volume of a cone and a cylinder of equal radius and perpendicular height is (a) 2: 3 ix) (b) 3: 2 (c) 1: 2 (d) 1: 3 The solution set for the graph of inequation given below is ___________. (a) {x: -4 < x -1, x R} (b) { -1, -2, -3, -4, x I} (c) {x: -4 x < -1, x R} (d) {x: -4 < x < 1, x R} Assertion (A) :- p(x) = 4x3 x2 + 5x4 + 3x 2 is a polynomial of degree 3. x) Reason (R) :- The highest power of x in the polynomial p(x) is the degree of the polynomial. (a) A is false, R is true xi) (d) Both are false (b) (2x 2) (c) (1x 1) (d) (2x 1) Point P (1,3) divides segment AB In the ratio 2: 3 . Coordinates of A are (-1, 7).The coordinates of B area ____________________. (a) (4, -3) xiii) (c) Both are true 8 2 12 ] X= [ ] . Order of matrix X is, Given [ 1 4 10 (a) (1x 2) xii) (b) A is true , R is false (b) (4, 3) (c) (-4, 3) (d) (-4, -3) O is the centre of the circle. If CD = 4, BC = 2, then the radius of the circle is______________. (a) 2 (b) 6 (c) 3 2 (d) 4 xiv) The modal class of histogram given below is_________. (a) 600 - 700 xv) (b) 700 800 (c) 500 600 (d) 300 - 400 The nth term of an A.P. is 2 1, then its first term and common difference is (a) 2, 4 (b) 3, 6 (c) 1, 2 (d) 2, 1 Question 2 a) Priyanka has a recurring deposit account of Rs. 1000 per month at 10 % p.a. If she gets Rs. 5550 as an interest at the time of maturity , find the total time for which account has held. (4) b) Find the co-ordinates of the points of trisection of the line segment joining (-6,0)) and (0,12)). (4) c) Prove that :- [ cosec A sin A ] [ sec A cos A ] sec2 A = tan A (4) Question 3 a) a) A cylindrical bucket , 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap. (4) b) b) In the given figure, ABCD is a cyclic quadrilateral with centre O. ST is a tangent angle OBD = 250, angle CBT = 300. Find :- a) angle BOD b) angle BAD c) angle BCD d) angle BDC (4) 3 c) Use graph paper for this question: i) The point P(2,-4)is reflected about the line = 0 to get the image Q. Find the coordinates of Q. (5) ii) Point Q is reflected about the line = 0 to get the image R. Find the coordinates of R. iii) Name the figure PQR. iv) Find the area of the figure PQR. Section B ( 40 marks ) (Attempt any four questions from this section) Question 4 a) A manufacturer sells a TV to a dealer for Rs.18000 and the dealer sells it to a consumer at a profit of Rs.1500. If the sales are intra state and the rate of GST IS 12 % , find: (3) i) the amount of GST paid by the dealer to the State Government. ii) the amount of GST received by the Central Government. iii) the amount that the consumer pays for the TV. b) Solve the following quadratic equation and give your answer correct to two significant figures 18/ = 6 (3) c) Use a graph paper for this question. The daily pocket expenses of 200 students in a school are given below: (4) Pocket 0-5 expenses ( in Rs.) No. of 10 students (frequency) 5-10 10-15 15-20 20-25 25-30 30-35 35-40 14 28 42 50 30 14 12 Draw a histogram representing the above distribution and estimate the mode from the graph. Question 5 a) If 4 [ 1 2 ] M = 6I, 1 (3) where M is a matrix and I is a unit matrix of order 2 x 2. Find the matrix M. b) Find the sum of the series :- 2 + 6 + 18 + 54 + + 4374. (3) c) If 2x3 + ax2 + bx - 2 has a factor (x+2) and leaves a remainder 7 when divided by 2x-3, find the values of a and b. With these values of a and b, factorize the given polynomial completely. (4) 4 Question 6 a) ABCD is a rhombus. The coordinates of A and C are (3, 6) and (-1, 2) respectively. Write down the equation of diagonal BD. (3) b) Find the sum of first 51 terms of an Arithmetic progression, whose second and third term are 14 and 18 respectively. (3) 0 c) Construct a triangle ABP such that AB = 5 cm, BP = 3 cm and angle ABP = 30 . Complete the rhombus ABCD such that P is equidistant from AB and BC. Locate the point Q on the line BP such that Q is equidistant from A and B. (4) Question 7 a) A bag contains 12 balls out of which x are black in colour. If a ball is drawn at random, what is the probability that it will be a black ball? If 6 more black balls are put in the bag the probability of drawing a black ball will be double than that of first case. Find x. (3) b) By purchasing Rs 25 gas shares for Rs 10 each, a man gets 4% profit on his investment. What rate % is company paying. What is his dividend if he buys 60 shares. (3) 0 c) In the figure O is the centre of the circle and SP is a tangent. If SRT =65 , find the value of x, y and z. (4) Question 8 a) Solve the following inequation and represent the solution in the number line. (3) b) The weight of some wrestlers is given in the table below. Using the given data , find the mean weight using step deviation method.:(3) Weight (in kg) No. of wrestlers 40-50 50-60 60-70 70-80 80-90 90-100 2 8 12 14 8 6 5 c) In the given figure, angle PQR and angle PST = 900, PQ = 5 cm and PS = 2 cm. i) Prove that :- PQR ~ PST ii) Find area of PQR : area of quadrilateral SRQT. (4) Question 9 a) A person can row a boat at a speed of 5 km/hr. If he takes 1 hour more to row the boat 5.25 km upstream than to return downstream , find the speed of the stream. (4) b) Wages (Rs) No. of workers 400-450 450-500 500-550 550-600 600-650 650-700 700-750 2 6 12 18 24 13 5 Use a graph to draw an ogive for the above distribution. Use your ogive to find (6) 1. Median wage of the workers. 2. Lower quartile. 3. No. of workers who earn more than Rs. 625 Question 10 a) If y is a mean proportion between x and z, Prove that :- xyz(x+y+z)3 = (xy+yz+zx) 3. (3) b) Using a ruler and compass construct a hexagon of side 4.5 cm. Hence construct a circle circumscribing the hexagon and find its radius. (3) c) An aircraft is flying at a constant height with a speed of 30 km/h. From a point on the ground , the angle of elevation of the aircraft at an instant was observed to be 45 0. After 20 seconds the angle of elevation was observed to be 300. Determine the height at which the aircraft is flying. (use 3 = 1.732) (4) __________________________________________________________________ 6
|
