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Villa Theresa High School STD: X Preliminary Examination DATE: 03/01/2023 MARKS: 80 SUBJECT: Mathematics WRITING TIME: 2 Hrs. SECTION I (Attempt all questions from this section) Question 1 Choose the correct alternative from the options given below. [15] i. If the MRP of an article is ` 6,000 and rate of GST is 10% then CGST is `: a. 300 b. 600 c. 1200 d. 60 ii. If the quadratic equation has equal roots, then the value of is a. 0 b. c. d. iii. When is divided by the remainder is 6. Then the value of is a. 4 b. d. c. 32 iv. If A= a. v. If the 7th and the 13th term of a A.P. 34 and 64 respectively then its 18th term is: a. 87 b. 90 c. 89 d. 88 vi. If a point A (5, 0) is reflected in to A (5, 4) then a = a. 0 c. 3 b. vii. ix. { { { { The solution set of the inequation represented on the number line is In a single throw of a dice, probability of getting an odd number less than 8 is a. 0 x. d. 2 In quadrilateral ABCD diagonals AC and BD intersect at O. If AO = 6 cm, BO = 8 cm, CO = 3 cm and DO = 4 cm. then AOB COD by: a. SSS test b. AAA test c. SAS test d. ASA test viii. a. b. c. d. ,B= and A B then is equal to: c. 5 b. d. b. c. The mean proportional between and is a. b. c. 1 d. 1 d. xi. Order of matrix (A x B) is 3 x 2 and order matrix B is 5 x 2, then the order of matrix A is: a. 3 x 5 b. 5 x 3 c. 5 x 2 d. 3 x 2 xii. PT and PQ are tangents to the circle with centre C from an external point P. If PT = 17 cm. The length of PQ is: a. 17 cm b. 12 cm c. 8 cm d. Cannot determine xiii. The radius and height of a cylinder are equal to each other. The cylinder is melted into a sphere of same radius. If the volume of the cylinder is 270 cm3. Then the volume of the sphere is: a. 270 cm3 b. 90 cm3 c. 360 cm3 d. 180 cm3 xiv. In the given figure AB is the diameter, then the value of is a. 30 xv. b. 60 c. 45 d. 150 Jack wants to find the mode from a given data. To find it he will draw a. Frequency b. Ogive c. Histogram d. Bar graph polygon Question 2. i. Saloni deposited ` 150 per month and gets `1236 on maturity under recurring deposit scheme. If the rate of interest is 8% per annum interest calculated at the end of every month. Find the period for which the amount was deposited. [4] ii. If and are in continued proportion prove that: iii. [4] [4] Question 3 i. 3080 cm3 of water is required to fill a cylindrical vessel completely and 2310 of water is required to fill it up to 5 cm below the top. Find: a. Radius of the vessel. b. Height of the vessel. c. Wetted surface area when it is half filled with water. [4] ii. and intercepts of a line AB are both . Point P divides AB. Find: a. The ratio in which P divides AB b. The equation of line through P which is perpendicular to AB. c. The angle made by line AB with axis. [4] iii. Use graph paper for this question. Take 1 cm = 1 unit on both and axis. a. Plot points A (0, 4), B (3, 7), C (6, 4), D (6, 1) and E (0, 5) b. Reflect Points B, C and D in axis to B , C and D respectively. c. Join the points A, B, C, D, E, D , C , B and A. d. Give a geometric name to the figure ABCDED C B . [5] 2 Section B (Attempt any 4 questions from this section) Question 4 i. The following bill shows the GST rates along with marked price of the articles. Find the amount of the bill. BILL Marked Price Rate of GST Articles Cell Phone 25000 18% Blue tooth 15000 28% [3] ii. Solve the following quadratic equation correct to 3 significant figures. A mathematics aptitude test of 50 students was recorded as follows: 50- 60 60-70 70-80 80-90 Marks 4 8 14 19 No. of students iii. [3] 90-100 5 Draw a histogram of the above data and using a graph paper taking 2 cm = 10 marks on one axis and 2 cm = 2 students on the other and locate the mode. [3] Question 5 i. ii. and C . Evaluate: AB 3C B In the given figure: a. Prove that . b. Find AT if TP = 8 cm and AB Let A [3] [3] iii. Factorise the given polynomial completely: [4] Question 6 i. In the given figure line AB meets axis at point A. line through C (2, 10) and D intersects the line AB at right angle at point P. Find: a. Equation of line CD and AB b. Co-ordinates of points E and D. [3] ii. Prove that: +(1+ )= 3 [3] iii. The first and last term of a A.P. are 17 and 350 respectively. If their common difference is 9. a. How many terms are there in the A.P.? b. What is their sum? [4] Question 7 i. A box contains 90 discs numbered from 1 to 90. One disc is selected at random Find the probability that the disc selected is: a. A prime number b. Multiple of 3 or 5 c. Multiple of 3 and 5 [3] ii. The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate: a. Radius of the sphere. b. The number of cones recast. [3] iii. In the given figure ABCD is a cyclic quadrilateral with centre O. ST is a tangent , Find: a. b. c. d. Question 8 i. Solve the following inequation, write the solution set and represent it on the number line [3] ii. Using step deviation method calculate the mean marks of following distribution: 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 Class Interval 5 20 10 10 9 6 12 8 Frequency [3] iii. In the figure given below, AB // EF// CD. If AB 22.5 cm, EP = 7.5 cm, PC =15 cm and DC = 27 cm. Calculate: i. EF ii. AC [4] Question 9 4 i. A trader bought a number of articles for Rs. 900, thirteen articles were found damaged. He sold each of the remaining articles at Rs. 3 more than what he paid for it. He got a profit of Rs. 30 on the whole transaction. Find the number of articles he bought. [4] ii. The daily wages of workers in a project are given below: Wages (in `) No. of workers. 400450 2 450500 6 500550 12 550600 18 600650 24 650700 13 700750 5 Use a graph paper to draw an ogive for the above distribution. (Use a scale 2 cm = `50 on axis and 2 cm = 10 workers on axis). Use your ogive to estimate: a. Median wages of the workers. b. The lower quartile of the workers. c. The number of workers who earns more than ` 625 a day [6] Question 10 i. ii. iii. . Using properties of proportion find: [3] Using ruler and compass draw a circle circumscribing a regular hexagon of side 5cm. also measure the radius the circle. [3] Given A 20 m vertical pole and a vertical tower are on the same level ground in such a way that the angle of elevation of top of the tower as seen from foot of the pole is 60 and the angle of elevation of top of the pole as seen from the foot of the tower is 30 . Find: a. Height of the tower. b. Horizontal distance between the pole and the tower. [4] @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ 5
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