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Atul Vidyalaya Maths paper 1

4 pages, 32 questions, 32 questions with responses, 74 total responses,

Chirag Kamath
Atul Vidyalaya, Valsad

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ATUL VIDYALAYA THIRD PRELIMINARY EXAMINATION (2014-15) MATHEMATICS STD: X DATE: 06/01/2015 SESSION: I B MM: 80 TIME: 2 hrs GENERAL INSTRUCTION (Two and half hours) Answers to this paper must be written on the paper provided separately. You will NOT 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. This question paper is divided into two sections. Attempt all questions from Section A and any four questions from Section B. The intended marls for questions or parts of questions are given in the brackets [ ]. All working, including rough work , must be clearly shown and should be done on the same sheet as the rest of the answer. Omission of essential working will result in loss of marks. Mathematical tables are provided. SECTION A [40 Marks ] Question 1. (a) Ram purchased a shirt for Rs 300, a cup set for Rs 6700 and a pair of shoes for 1 8 1 2 Rs 1200. Sales tax was charged at the rate of 5%, 8 % & 7 % respectively If the shopkeeper allowed 5% rebate on the bill, what was the amount paid? (b) Find the value of k if ( x k ) is a factor of the polynomial x 3 (k 2 1) x + 2 . Also factorise it further. (c) If 3a + 8b : 3c + 8d = 3a 8b : 3c 8d, then show that a, b, c, d are in proportion. Question 2. 1 1 1 1 = sec tan cos cos sec + tan (a) Prove that: [3] [3] [4] [3] (b) The area enclosed between two concentric circles is 770 sq cm. If the radius of the outer circle is 21 cm. Calculate the radius of the inner circle. [ = 22 ] [3] 7 (c) Point P ( k, m) is reflected in the x-axis to P ( 5, -2). Write down the values of k and m. P is the reflection of P when reflected in the y axis. Write down the co-ordinates of P . Name a single transformation that maps P to P . Question 3. (a) If the mean of the following distribution is 7.5, find the missing frequency f. Variable 5 6 7 8 9 10 11 20 17 f 10 8 6 7 [3] 12 Frequency [4] 6 (b) A rectangular playground has two semicircles along its widths, which also act as diameters. If the sides of the rectangle are 120 m and 21 m, then find the area of the playground. (c) If [m n ] m n [3] = [25] , (i) find all the positive integers m and n (ii) find all the integers m and n Question 4. [4] 1 3 2 (a) Find the nature of the roots of x + 2 x + = 0 and solve it. [3] (b) Find the value of x given that A2 = B [3] Atul Vidyalaya Cont ..on Pg 2 Shaping the Future Page 1 STD: X SUB: MATHEMATICS (c) In the given figure, if ACE = 43 and CAF = 62 , find the values of a, b and c. [4] Section- B(40 Marks) ( Answer any four questions. All the sub questions of a main question should be answered together) Question 5. (a) Entries of pass book of Mrs Rashmi are: Date Particulars Withdrawals (in Deposits (in Rs) Balance Rs) (in Rs) Jan 1 B/ F 5000 5000 Jan 7 By cash 2000 7000 Feb 2 By cash 3000 10000 Feb 17 By cash 5000 5000 Feb 29 By cheque 10000 13000 , If account is closed on 7th April same year, find the money received if rate is 6% (b) The point P is the foot of perpendicular from A ( -5 , 7) to the line whose equation is 2x 3y + 18 = 0. Determine: (i) the equation of line AP (ii) the co-ordinates of P. (c) The marked price of an article is Rs 7500. A shopkeeper sells the article to a consumer at the marked price and charges sales tax at the rate of 7%. If the shopkeeper pays a VAT on Rs 105. Find the price inclusive of sales tax of the article which the shopkeeper paid to wholesaler. Question 6. (a) Mukul invests Rs 9000 in a company paying a dividend of 6% per annum when a share of face value Rs 100 stands at Rs 150. What is his annual income? If he sells 50% of his shares when the price rises to Rs 200, what is his gain in this transaction? (b) 2x + 3y = 12 and px+ y = 7 are parallel to each other, find p DCB. DOE = 42 , where O is the centre. Find (c) In the given figure D [3] [3] [4] [3] [3] [4] C A E 42 O B Question 7. (a) Draw an Ogive and estimate (i) median (ii) lower quartile (iii) upper quartile (iv) inter quartile Marks 30 39 40 - 49 50 - 59 60 - 69 70 - 79 No of students 01 04 10 18 45 [6] 80 - 89 90 - 99 Atul Vidyalaya 32 10 Cont ..on Pg 3 Shaping the Future Page 2 STD: X SUB: MATHEMATICS (b) In the given diagram, calculate the length of CE. Hence find A 8 cm C AED CEB [4] E 6 cm B 10 cm D Question 8. (a) The upper part of tree is broken by wind falls to the ground without being detached. The top of the broken part touches the ground at an angle of 38 30' at a point 6 m from the foot of the tree. Calculate (i) the height at which the tree is broken (ii) the original height of the tree. [3] (b) Mr X deposits Rs 3000 per month in a cummulative bank account for 5 years at the rate of 11% p.a. Find the amount he will receive at the time of maturity. [3] 2 3 y 1 2 x (c) If A = ; B = ; C = find x and y; if A + B = C 3 1 4 4 2 2 [4] Question 9. (a) In an auditorium, seats are arranged in rows and columns. The number of rows was equal to the number of seats in each row. When the number of rows was doubled and the number of seats in each row was reduced by 10. The total no of seats increased by 300. Find: (i) the number of rows in the original arrangement. (ii) the number of seats in the auditorium after re-arrangement. [3] (b) A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm. Find the number of cones thus obtained [3] (c) Find the mean by short cut method. [4] Marks 0 - 10 10 - 20 20 - 30 30 40 40 - 50 50 - 60 60 - 70 Frequency 05 10 15 08 06 10 07 Question 10. (a) Using ruler and compass only draw a circle of radius 4.5 cm. Draw two tangents to this circle so that the angle between the tangents is 60 from external point P. (b) The simple interest on a sum of money for 2 years at 4% per annum is Rs 340. Find (i) the sum of money and (ii) the compound interest on this sum for one year payable half yearly at the same rate. (c) A vessel is in the form of an inverted cone. Its height is 11 cm and the radius of its top, which is open, is 2.5 cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.25 cm, are dropped into the vessel 2/5th of the water flows out. Find the number of lead shots dropped into the vessel Question 11. (a) A and B are born in 1991. What is the probability that both will have (i) the same birthdate (ii) different birth date (b) Find the third proportional to x y y + x and x2 + y2 [3] [3] [4] [3] [3] (c) If the compound interest for two successive years on a sum is Rs 570 and Rs 741, calculate the rate of interest. Atul Vidyalaya Pg 3 [4] Shaping the Future

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