Sample Paper – 2011
Class – X
Subject – Mathematics
Class – X
Subject – Mathematics
SECTION A (40 Marks)
Question 1
(a) Rohan Verma opened a bookshop with some initial investment. In the 1st year he incurred a loss of 10%. However, during the 2nd year he incurred a profit of 20%, which in 3rd year increased to 25%. Calculate his net profit percent for the entire period of 3 years. [4]
(b) Find the circum center of the triangle formed by the points (1,6), (-4,1) and (2,3).
[3]
(c) What must be added to 3x3 + x2 – 22x + 9 so that the result is exactly divisible by 3x2 + 7x – 6. [3]
Question 2
(a) If the points (a,1) , (1,2) and (0,b+1) are collinear show that 1/a+ 1/b =1. [3]
(b) Construct a 2x2 matrix A and B whose elements are Aij = 2i +j and Bij = 3i –2j. Hence find the matrix ABTwhere BT is the transpose matrix of B. [4]
(c) Draw a triangle ABC such that BC =6.3 cm. Angle A =75o and AB = AC. Find a point P such that it is equidistant from B and C. [3]
Question 3
(a) Find the ratio compounded of the reciprocal ratio of 15:28, the sub duplicate ratio of 36:49 and triplicate ratio of 5:4. [3]
(b) If 3 £ a £ 9 and 2 £ b £ 5, find the minimum and maximum value of [3]
2b+a |
3a+b |
(c) If cos2A – sin2A = tan2B. Prove that cos2B – sin2B = tan2A. [4]
Question 4
(a) A rectangular courtyard of size 5.04x3.57 is to be paved exactly with circular tiles, all of the same size. What is the radius of the tiles? Also find the remaining area of the courtyard, which is not paved with tiles. [4]
(b) Calculate the mean, median and mode of the following data: 9,0,3,2,8,5,5,2,7,1.
(c) Jay goes to mobile store to purchase a mobile costing Rs. 6000. The rate of VAT is 10%. He tells the shopkeeper to reduce the price of the mobile to such an extent that he has to pay Rs 6050 inclusive of VAT. Find the percentage reduction needed in the price of the mobile. [3]
Section B (40 Marks)
Attempt any four questions from this section
Question 5
(a) Solve 3x2 – 8x +2 = 0 correct to 2 decimal places. [4]
(b) A die is thrown once. What is the probability of getting prime numbers. [3]
(c) Eight points A1,A2,A3,…. Divides the circumference of the circle in 8 equal arcs. A1 and A5, A3 and A6 are joined. Find the measure of acute angle at the intersection of line segments A1A5 and A3A6. [3]
Question 6
(a) The angry Arjuna carried some arrows for fighting with Bhishma. With half the arrows, he cut down the arrows thrown by Bhishma on him and with six other arrows he killed the charioteer. With one arrow each he knocked down the chariot, flag and the bow of Bhishma respectively. Finally, with one more than four times the square root of arrows he laid Bhishma unconscious on an arrow bed. Find the total number of arrows Arjuna had. [4]
(b) A( -3, 4), B(3, -1) and C( -2, 4) are the vertices of a triangle ABC. Find the length of line segment AP, where point P lies on side BC, such that BP : PC = 2 : 3.
[3]
(c) ABCD is a cyclic quadrilateral in which ÐA = (x + y + 10)o, ÐB = (y + 20)o, ÐC = (x + y – 30)o and ÐD = (x + y)o. Find x and y. [3]
Question 7
(a) The marks of 200 students in a test were recorded as follows:
Marks % | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 | 60-69 | 70-79 | 80-89 |
No. of students | 7 | 11 | 20 | 46 | 57 | 37 | 15 | 7 |
Draw the Ogive and use it to find –
(i) the median and
(ii) the number of students who score more than 35% marks. [6]
(b) A spherical drop of soap water of radius 1cm is blown into a bubble of outer radius 20 cm. Find approximately the thickness of the bubble. Leave your answer in fraction.
[4]
Question 8
(a) The point P (a, b) is first reflected in the origin and then reflected in the x- axis to the point P’ (3, - 4). Find the values of “a” and “b”. Also find the co-ordinates of P”, when P is reflected in the line x =y. [4]
(b) Two right ∆s ABC and DBC are drawn on the same hypotenuse BC and on the same side of BC. If AC and DB intersect at P, prove that AP x PC = BP x PD.
[3]
(c) Sejal Agarwal deposits Rs.1500 per month in a recurring deposit scheme of a bank for 9 months. If she gets Rs.675 as interest at the time of maturity, find the rate of interest and maturity value of the deposits. [3]
Question 9
(a) Use ruler and compasses to answer this question, show all construction lines and arcs clearly.
(i) Construct triangle ABC such that AB = BC = 7cm and BC = 5 cm.
(ii) Draw a circle with center A and radius 3 cm, let the circle cut AD at Q.
(iii) Construct another circle to touch the circle with center A externally at Q, and pass through Band C. [6]
(b) The equation of line is y = 3x – 5. Write down the slope of this line and the intercept made by it on the Y-axis. Hence or otherwise, write down the equation of a line which is parallel to this line and which passes through the point (0, 5). [4]
Question 10
(a) Rohan Nagpal has 60 shares of nominal value Rs.100 and he decided to sell them when they are at a premium of 60%. He invests the proceeds in shares of nominal value Rs.50.
Calculate (i) the sale proceeds,
(ii) the number of shares he buys and
(iii) his annual dividend from these shares. [3]
(b) Write equation to line –
(i) Passing through (-1, 3) and parallel to the line 2x + 3y = 7. (ii) Passing through (2, -5) and perpendicular to the line 3x – 4y = 7. [3]
(c) From the top of a building 30m high the angle of depression of a stone X on the side of the road was α. The angle of depression of another stone Y, in line with the line joining the base of the building and X is β. If α and β are complementary angles find the distance between the two stones. [4]
Question 11
(a) Two parallel chords of a circle are 12 cm and 9 cm in length. If the diameter of the circle is 15 cm, find the distance between the chords where they lie on – (i) the same side of the centre, (ii) opposite side of the centre. [3]
(b) Find the remainder when f(x) = x4 – 4x3 + 3x2 + 1 is divided by (x+2). [3]
(c) Calculate the mean mark using step deviation method for the following data:
Mark | 0-9 | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 |
Frequency | 4 | 6 | 12 | 6 | 7 | 5 |
Also state (i) the median class, (ii) the modal class. [
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