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HASANAT HIGH SCHOOL Preliminary Examination Std : X Mathematics Marks : 80 Date : 22/01/2024 R.T. : 15 mins _______________________________________________________________________________________ Time allowed: 2 Hours 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. __________________________________________________________________________________________________________________________________ Section A (Attempt ALL the questions - 40 Marks) Question 1 Choose the correct answers from the option given below. (Do Not copy the question. Write the correct answers only). (i) [15] The nominal value of a share: (a) remains the same (b) changes from time to time (c) can only be changed by the share holder (d) none of these (ii) Roots of the equation (x - 1)2 - 5(x - 1) - 6 = 0 are: (a) 7, 0 (b) 6, 0 (c) 7, 6 (d) 6, -7 (iii) If (x - 2) is a factor of x2 + 5x + p, then the value of p is: (a) 10 (b) 12 (c) -13 (d) -14 (iv) The common ratio of the GP : -3/4, 1/2, -1/3 , 2/9 is: (a) 2/3 (b) -2/3 1 (c) 3/2 (d) -3/2 (v) 8th term of the AP 5, 8, 11, 38, from the end is : (a) 22 (b)20 (c)17 (d)16 (vi) The reflection of a point P(0,-1) in the x-axis is: (a) (1, 0) (b) (-1, 0) (c) (0, 0) (d) (0, 1) (vii) In the figure, BD and CE intersect each other at P. PBC ~ PDE by: (a) AA similarity (b) SAS similarity (c) SSS similarity (d) RHS similarity (viii) If Himanshu reshaped a cone of height h cm and radius of base r cm into a cylinder, then which of the following options is always correct? (a) Volume of cone = Volume of cylinder (b) Surface area of cone = Surface area of cylinder (c) Radius of cone = Radius of cylinder (d) none of the above (ix) If -1 3 + 4x < 23, x R, then: (a) {-1 x < 5, x R} (b) {-1 < x 5, x R} (c) {-2 x < 5, x R} (d) {-2 < x 5, x R} (x) The probability of drawing a black face card from a deck of 52 playing cards is: (a) 1/12 2 (b) 3/26 (c) 1/2 (d) 1/13 (xi) If M = [1 -2], N = [ 2 1 ], then: the matrix MN is: 1 2 (a) [4 3] (b) [-4 3] (c) [4 -3] (d) [ 4 ] 3 (xii) The mid-point of the line segment joining the points A(-1, 4) and B (-3, -2) is: (a) (-2, -3) (b) (1, 3) (c) (-2, 1) (d) (2, 1) (xiii) In the given figure, O is the center of the circle. If angle ABC = 200, then angle AOC is equal to (a) 20 (b) 40 (c) 60 (d) 10 (xiv) If k be the scale factor of a size transformation, then k > 1 means: (a) enlargement (b) reduction (c) identity transformation (d) none of these (xv) The mode of the given observations 5, 3, 2, 7, 5, 9, 3, 8, 5, is: (a) 3 (b) 5 (c) 9 (d) 2 3 Question 2 [4 + 4 + 4] a) Amit deposits Rs 1600 per month in a bank for 18 months in a recurring deposit account. If he gets Rs 31,080 at the time of maturity, what is the rate of interest p.a.? b) If = = , prove that ax + by + cz = 0 [4] [4] c) A man invests Rs 20,020 in buying shares of nominal value Rs 26 at 10% premium. The dividend on the shares is 15% per annum. Calculate: i. the number of shares he buys ii. the dividend he receives annually iii. the rate of interest he gets on his money Question 3 [4] [4 + 4 + 5] a) A solid cylinder of radius 7 cm and height 14 cm is melted and recast into solid spheres each of radius 3.5 cm. Find the number of spheres formed. [4] b) Find the equation of the line passing through (2, 4) and parallel to the line: a. 3x + 5y - 15 = 0 [4] c) With the help of a graph paper, taking 1 cm = 1 unit along both x and y axis: [5] i. Plot points A (0, 3), B (2, 3), C (3, 0), D (2, -3), E (0, -3). ii. Reflect points B, C and D on the y axis and name them as B , C' and D' respectively iii. Write the co-ordinates of B', C' and D'. iv. Write the equation of line B'D'. v. Name the figure BCDD'C'B B Section B (Attempt any four questions - 40 Marks) Question 4 [3 + 3 + 4] a) A shopkeeper bought an article with market price Rs 1200 from the wholesaler at a discount of 10 % the shopkeeper sells this article to the customer on the market price printed on it if the rate of GST is 6%, then find: i. GST paid by the wholesaler. 4 [3] ii. Amount paid by the customer to buy the item. b) Find the sum of first 8 terms of the GP 1/3, 1/6, 1/12 . [3] c) The histogram alongside represents the scores obtained by 25 students in a Mathematics mental test. Use the data to: [4] i. Frame a frequency distribution table. ii. To calculate mean. iii. To determine the Modal class. Question 5 [3 + 3 + 4] a) Given [ 8 2 12 ]X=[ ] 1 5 10 [3] Write down i. the order of matrix X ii. the matrix X. b) In the map of a rectangular plot of land, the length = 2.5 cm and breadth = 1.4 cm. If the scale is 1:10000, find the area of the plot in m . [3] c) Find the value of k if 4x3 2x2 + kx + 5 leaves remainder -10 when divided [4] by 2x+1 Question 6 [3 + 3 + 4] a) Determine whether the line through (-2, 3) and (4, 1) is perpendicular to the line: 3x = y + 1. Does the line 3x = y + 1 bisect the line joining (-2, 3) and (4, 1)? b) Show that tan + sin tan sin = + 1 1 . [3] [3] c) The first term of an AP is 2 and the last term is 50. If the sum of all these terms is 442, find its common difference. [4] 5 Question 7 [3 + 3 + 4] a) A box consists of 4 red, 5 black and 6 white balls. One ball is drawn out at random. [3] Find the probability that the ball drawn is: (i) black (ii) red or white b) Draw a line segment AB = 3 cm. Draw the locus of a point P and Q which moves at a distance of 5 cm from AB and also, equidistant from A and B. [3] c) In the figure, O is the centre of the circumcircle of XYZ. Tangents at X and Y intersect at T. Given [4] XTY = 80 and XOZ = 140 , calculate the value of ZXY. Question 8 [3 + 3 + 4] a) Solve the inequation 2x - 5 2 < + 3 2 3 + 11 2 , . Represent the solution set on a number line. [3] b) The mean of the following distribution is 49. Find the missing frequency a. Class [3] 0-20 20-40 40-60 60-80 80-100 Frequency 15 20 30 a 10 c) In the figure, ABCD is a parallelogram. E is the point on CD. AE intersects BD at O. EF || CB. Find the following ratios, if DF: FB=3:1. [4] a. ar( DFE): ar( DBC) b. ar( OFE): ar( ODA) c. ar( DFE): ar(trap.EFBC) Question 9 [4 + 6] a) An aeroplane travelled a distance of 400 km at an average speed of x km/h. On return journey, the speed was increased by 40 km/h. Write down an expression for the time taken for 6 i. the onward journey ii. the return journeys If the return journey took 30 minutes less than the onward journey, write down an equation in x and find its value. [4] b) The following table shows the distribution of marks in Mathematics: [6] Marks (less than) No. of Students 10 7 20 28 30 54 40 71 50 84 60 105 70 147 80 180 With the help of a graph paper, taking 2 cm = 10 units along one axis and 2 cm = 10 units along the other axis, draw an ogive for the above distribution and use it to find the: i. Median ii. number of students who scored distinction marks (75% and above) iii. number of students, who passed the examination if pass marks is 35%. Question 10 [3 + 3 + 4] a) Using properties of proportion, find x : y if 3 + 12 6 2 + 8 = 3 + 27 9 2 + 27 [3] b) Draw a circle of radius 3 cm. Take a point P outside it. Without using the centre, draw two tangents to the circle from point P, 5 cm from the centre. [3] c) Two poles AB and PQ are standing opposite each other on either side of a road 200 m wide. From a point R between them on the road, the angles of elevation of the top of the poles AB and PQ are 45 and 40 respectively. If height of AB = 80 m, find the height of PQ correct to the nearest metre. [4] 7
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