MATHEMATICS MC 17 M 1 1

Transcription

1 MATHEMATIS M 17 M 1 1

2 M 17 M - 1 SETION I (40 Marks) (All questions in this section are compulsory) Question 1 (a) Solve the following inequation and graph the solution set on the number line x 3 < x + 3x + 5, x R Mr. Khan deposited Rs.150 per month in a bank for 8 months under the Recurring Deposit Scheme. What will be the maturity value of his deposits, if the rate of interest is 8% per annum and interest is calculated at the end of every month? Using the properties of proportion, solve the following equation : x + 4 x 1 x 4 x 1 = 4 Question (a) In what ratio is the line joining the points A(4, 3) and B ( 10, 4) divided by the x-axis? Also find the co-ordinates of the point of intersection of line AB and the x-axis. Let A = and B = and AX = B where X is a matrix 1. Find the order of the matrix X. Find matrix X Evaluate : 50 ( n 1). n 1 Question 3 (a) 45 solid cones of radius 5 cm and slant height 13 cm are recast in a single solid sphere. If there is no loss of metal, find the radius of the sphere. Solve the equation x 1 x places. = 7. Write your answer correct to two decimal In the figure given along side ABED is A a cyclic quadrilateral. B (i) Prove that BE ~ DA (ii) If AB = 6cm, B = 4cm, E = 5 cm, then find DE E (iii) If A (BE) = 10 cm, find A(AD). D M 17 M 1

3 MT EDUARE LTD. X - ISE (Mathematics) Question 4 (a) Determine the A.P. whose third term is 16 and the 7 th term exceeds the 5 th term by 1. If the polynomials x 3 + ax + 3x 5 and x 3 + x 4x + a leave the same remainder when divided by x, find the value of a. A manufacturing company M sells a computer to distributer D for `,000. The distributer D sells it to a retailer R at a profit of ` 400 and the retailer sells it to a consumer at a profit of ` If the rate of sales tax under VAT is 10%, find : (i) the amount paid by the consumer (ii) the amount of tax received by the state government. SETION II (40 Marks) (Attempt any four complete questions in this section) Question 5 (a) Without using Trigonometrical tables evaluate : sec17º tan 68º + cos 44º + cos 46º cosec 73º cot º A ABD is a cyclic quadrilateral. P is a tangent at. x DP = 40º and DA = 65º. D z B Find angles marked as x, y and z. y P 40º 65º Find the mode of the following distribution by drawing a histogram. Also write the modal class. Daily wages (in `) No. of workers Question 6 (a) From a pack of 5 cards, a black jack, a red queen and two black kings fell down. A card was then drawn from the remaining pack at random. Find the probability that the card is : (i) a black card (ii) a king (iii) a red queen Write the equation of a line parallel to x y + 8 = 0 and passing through the point (1, ). M 17 M 1 3

4 X - ISE (Mathematics) MT EDUARE LTD. In the figure given alongside, ST is parallel to QR, PQ = 8 cm, PS = cm and PR = 10 cm. alculate : 1. the length of TR S P T. Ar Ar PST PQR Q R Question 7 (a) Prove the identity : 3 cosa cos A 3 = cot A sin A sina If A = evaluate A 3A + I where I is a unit matrix of order. onstruct a triangle AB in which B = 7 cm, AB A = 1 cm and AB = 45º. onstruct the locus of all points inside AB, which are equidistant from B and and also equidistant from A and B. Question 8 (a) Mr. Ravi reduces the number of employees in his factory in the ratio 7 : 5 and increases their wages in the ratio 8 : 13. In what ratio, the wages bill is increased or decreased? Using Short-cut method, find the mean of the following distribution. lass interval No. of workers cm A ladder has rungs 5 cm apart (shown in the adjoining figure). The rungs decrease uniformly in length from 45 cm at the bottom to 5 cm at the top. If the top and the bottom rungs are 1 m apart, what is the length of the wood required for the rungs? 1 m 5 cm Question 9 (a) In the adjoining figure, AD = BD, E is mid-point of BD and F is mid-point of A and E BH. Prove that (i) DF BH (ii) AH = 3AF. B E D A F G H 4 M 17 M 1

5 MT EDUARE LTD. X - ISE (Mathematics) Sum of two natural numbers is 8 and the difference of their reciprocals is. Find the numbers. 15 onstruct a triangle AB in which base B = 6 cm, AB = 5.5 cm and AB = 10º. (i) onstruct a circle circumscribing the triangle AB. (ii) Draw cyclic quadrilateral ABD so that D is equidistant from B and. Question 10 (a) The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of nd hour, 4th hour and nth hour? Raj invests ` 6000 in 10%, ` 10 shares at ` 1. He sells the shares when the price rises to ` 30 and invests the proceeds in 15% ` 100 shares at ` 15. alculate : 1. sales proceeds. number of ` 15 shares he buys 3. the change in his annual income from dividend. From the top of a hill, the angles of depression of two consecutive kilometer stones, due east are found to be 30 0 and 45 0 respectively. Find the distance of the two stones from the foot of the hill. Question 11 (a) Use graph paper for this question. (i) Plot the points A(3, 5) and B(, 4). Use 1 cm = 1 unit on both the axes. (ii) A is the image of A when reflected in the x-axis. Write down the co-ordinates of A and plot it on the graph paper. (iii) B is the image of B when reflected in the y-axis followed by reflection in the origin. Write down the co-ordinates of B and plot it on the graph paper. (iv) Write down the geometrical name of the figure AABB and find its area. Marks obtained by 00 students in an examination are given below : Marks No. of Students Draw an ogive for the given distribution taking cm = 0 marks on one axis and cm = 0 students on the other axis, using the graph, determine : (i) The median marks. (ii) The number of students who failed if minimum marks required to pass is 40. (iii) If scoring 85 and more marks is considered as grade one find the number of students who secured grade one in the examination. (iv) The upper quartile. [6] M 17 M 1 5