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MATHEMATICS (Two and half hours) Prelim 1- Examination 2023-24 Max Marks: 80 _______________________________________________________________________________________ The time given at the head of this Paper is the time allowed for writing the answers. Class: X 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 [15] (i) A shopkeeper buys an article from the wholesaler for 2000 and sells to the customer at a profit of 10%. If the rate of GST is 12 % then the GST paid by shopkeeper to the government is __________ (a) 240 (ii) 12 ] 6 (c) {0,1,2,3 } (d) { -8, -9, -10 } (b) 27 (c) 37 (d) -27 (b) [ 12 ] 4 7 (c) [ ] 4 8 (d) [ ] 8 The point (0,8) is invariant under reflection in_______ (a) the origin (vii) (b) {0,1,2,3,4,5,6} 2 5 If A = [ ] , = [ ] and C = 2A + B , then matrix C is : 0 3 (a) [ (v) (d) 24 What is the remainder when ( ) = 6 3 3 2 8 + 7 ( 2): (a) -37 (iv) (c) 200 If x , then the solution set of the inequation -x > -7 is (a) {8,9,10 } (iii) (b) 120 (b) x-axis (c) y-axis (d) both x and y axes The median of the grouped frequency distribution is found graphically by drawing: (a) a linear graph (b) a histogram (c) a frequency polygon (d) a cumulative frequency curve ____________________________________________________________________________________ This paper consists of 6 printed pages. (viii) + is equal to________ 1 (ix) (a) (b) 2 + 2 (c) (d) + In the adjoining figure, O is the centre of the circle then the value of x is _______ (a) 18 (b) 20 (c) 24 (d) 36 (x) The centroid of the triangle whose vertices are (p, 7), ( 8, 6) and (5, q) is (0 , 3), hence value of p and q is _____ (xi) (a) p = 3 , q = 10 (b) p = 10 , q = 3 (c) p = 0 , q = 3 (d) p = -3 , q = -10 1 The mean proportional between 2 and 128 is (a) 64 (xii) (b) 32 (c) 16 (d) 8 A die is rolled 1 A : probability of even prime number is 6 1 B : probability of perfect square number is 6 1 C : probability of perfect cube is 6 Which of the below statement is valid? (a) A , B and C are true. (b) A , B and C are false. (c) A and C are true , B is false. (d) A and B are true , C is false. (xiii) The 15th term from the last of the A.P. 7, 10, 13, ,130 is (a) 49 (b) 85 (c) 88 (d) 110 ____________________________________________________________________________________ This paper consists of 6 printed pages. (xiv) Nita deposited 100 per month for 12 months in a bank s recurring deposit account. If the bank pays interest at a rate of 9% p.a., then calculate interest earned by her. (a) 58.5 (xv) (b) 50.58 (c) 58.50 (d) 58.05 The locus of a point which is equidistant from two given points is______________ (a) perpendicular bisector of the segment joining two points. (b) parallel to given line. (c) a circle (d) angle bisector. Question 2 (i) Alpha buys following items from the shop: [4] Calculate the total amount paid by Alpha including GST: (ii) Item Quantity Rates ( ) GST Rates Water Bottle 1 150 18% Bag 1 3500 12% Chips 5 30 per packet 5% Using componendo and dividend, find the value of x, when: 3 + 3 341 = 3 2 + 1 91 2 3 ] , find x and y so that 2 = + 1 2 (iii) If A = [ (i) An aeroplane left 30 minutes later than its schedule time, and in order to reach its [4] [4] Question 3 [4] destination 1500 km away in time, it has to increase its speed by 250 km/h from its usual speed. Determine its usual speed. (ii) In what ratio does the x axis intersect the join of A(-3 , 2) and B (9 , -4)? Find the coordinate of point of intersection. ____________________________________________________________________________________ This paper consists of 6 printed pages. [4] (iii) Use graph sheet for this question. [5] Plot A(2,1) , B (5 , 5) and C (8 , 1). (a) Reflect A and C in x axis to get A and C (b) Write the coordinates of A and C (c) Give the geometrical name for the figure ABCC A . (d) Write the equation of the line of symmetry. (e) Find the perimeter of the above figure. SECTION B (Attempt any 4 questions from this Section.) Question 4 (i) Zaheeda deposits a certain sum of money, every month in a recurring deposit [3] account for 2 years. If she receives 37,875 at the time of maturity and the rate of interest is 5 %, find the monthly deposit. (ii) Find two numbers such that the mean proportional between them is 28 and the [3] third proportional to them is 224. (iii) In the adjoining figure, D is a point on BC [4] such that ABD = CAD. If AB = 5cm , AC = 3cm and AD = 4cm, find: (a) BC (b) DC (c) ( ) ( ) Question 5 (i) A man invests 3,072 in a company paying 5% per annum, when its 10 share [3] can be bought for 16 each. Find : (a) his annual income; (b) his percentage income on his investment. (ii) Determine the AP whose fifth term is 19 and the difference of 8th term from the thirteenth term is 20. ____________________________________________________________________________________ This paper consists of 6 printed pages. [3] (iii) If 2 3 + 2 + 2 has a factor ( + 2) and leaves a remainder 7 when divided by (2 3) , find the values of a and b. With these values of a and b, factorize the given polynomial completely. [4] (i) Solve the following inequation, write the solution set and represent it on the real [3] Question 6 number line : 2 < 3 2 5 , (ii) Find 4 numbers in GP such that the third number is greater than the first by 12 and [3] the second number is greater than the fourth by 24. (iii) Water flows through a circular pipe of radius 3.5 cm at 12 km/h into a [4] cylindrical tank of radius 7m and height 25 m. Find the depth of water in the tank after 15 minutes. Question 7 4 = 3 + 8 meets y axis at A. Find: (i) [5] (a) the coordinates of A. (b) the equation of a line AB perpendicular to 4 = 3 + 8 and passing through A. (c) the coordinates of B. (ii) The following table shows the distribution of heights of a group of 200 factory [5] workers. Take a scale of 2cm = 5cm of height and 2cm = 20 workers. Height (in cm) 145 150 150 155 155 160 160 165 165 170 No. of workers 6 12 20 46 57 170 175 175 180 37 180 - 185 15 7 Draw Ogive and estimate the following: (a) the median height (b) the height above which the tallest 25% of workers fall Question 8 (i) Solve the following quadratic equation and give your answer correct to two significant figures: (ii) 1 2 [3] 2 11 + 1 = 0 The median of the following numbers, arranged in ascending order, is 25. Find x: 11 , 13 , 15 , 19 , x + 2 , x + 4 , 30 , 35 , 39 , 46. ____________________________________________________________________________________ This paper consists of 6 printed pages. [3] (iii) Prove that : 1 + 1 = 1 + [4] (i) A box contains cards bearing numbers from 6 to 70. If one card is drawn at random [3] Question 9 from the box, find the probability that it bears (a) a prime number (b) perfect cubes (c) a number divisible by 2 and 5. (ii) Find the value of k if the roots are real and equal. 9 2 + + 1 = 0 [3] (iii) Find mean using assumed mean method: [4] Marks Obtained less than 20 less than 30 less than 40 less than 50 less than 60 less than 70 less than 80 less than 90 No. of students 16 21 35 52 58 78 94 100 Question 10 (i) An aeroplane, at an altitude of 250 m, observes the angles of depression of two [3] boats on the opposite banks of a river to be 45 and 60 respectively. Find the width of the river. Write the answer correct to the nearest whole number. (ii) The daily wages of 30 employees in an establishment are distributed as follows: [3] Find modal wages and modal class. Wages (in ) No. of employees (iii) 0 10 10 20 20 30 30 40 40 50 50 60 1 8 10 5 4 2 By using ruler and compasses only, construct an isosceles triangle ABC in which BC = 5 cm, AB = AC and = 90 . Locate the point P such that (a) P is equidistant from the sides BC and AC. (b) P is equidistant from the points B and C. ____________________________________________________________________________________ This paper consists of 6 printed pages. [4]
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