RAW- 3 (X)

1) The price of a TV set inclusive of sales tax of 9% is Rs40221. Find the marked price.   (2)

2) if x: y = 4 : 3, find (5 x + 8y) : (6x - 7y).    (2)

3) Using the remainder theorem, find the remainder when y³- 7y²+ 15y - 19 is divided by y - 3.    (2)

4) Without using tables , evaluate 3 cos 70° cosec20°+ 2cos 65° cosec25°.    (2)

5) State and draw the lous of a point equidistant from the two parallel lines.  (2)

6) In the given figure, the medians QS and RT of a ∆PQR meet at G. Prove that:
a) ∆TGS similar to ∆RGQ
b)!QG = 2GS from (a) above.      (3)

7) Solve the following inequation and graph the solution on the number line:
2 x - 5≤ 5x + 4 < 11, x ∈R.     (3)

8) Given  R={(x,y) ∈ A x A : x = y} and A={0, 1, 2, 3}; find:
a) the list of the elements R.
b) list the domain of R.
c) List the range of R.     (3)

9) Using only a ruler and compass, construct angle ABC=120°, where AB= BC =5 cm. Mark two points P and Q which satisfy the condition that they are equidistant from both BA and BC and are also at a distance of 3cm from the point B.    (3)

10) The marks of 20 students in a test were as follows:
5, 6, 8, 9, 10, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19, 20. Calculate 
a) the mean
b) the median
c)  the mode.     (3)


11) Construct a ∆ABC in which AB = AC = 4 and BC= 3cm. Using a ruler and compasses only , draw the reflection A'BC of ∆ABC. Draw the lines of symmetry of the figure ABA'C.    (3)

12) In the figure, BMD is the segment of a circle with centre O and angle BOD = 90°, BO= OD = 40cm. Find 
a) the area of the shaded figure,
b) the perimeter of the shaded figure.  take π=3.14.      (4)

13) If A= 1   -4 & B= -3    2 & C= 4   0
                4    1           4     0         0   -3 , find 
a) A²
b) BC
c) A²+ BC.        (4)

14) The point A(3, 4) is reflected to A' in the x-axis; and O'clock is the image of O (the origin) when reflected in the AA'. Using graph paper, give 
a) the coordinates of A' and O'.
b) the lengths of the segments AA' and OO'.
c) the perimeter of the quadrilateral AOA'O'.
d) the geometrical name of the figure AOA'O'.      (4)

15) Prove the following identity: 
1/(sinx + cosx)  + 1/(sinx - cosx) = 2sinx/(2 sin²x -1).       (3)

16) In the given figure, AB is the diameter of a circle with centre O. Angle BCD is 130°. Find 
a) angle DBA
b) angle BAD.       (3)

17) Find the equation of a line passing through the point (-4, 6) and having the x-intercept of 8 units.     (4)

15) A man wants to buy 72 shares available at Rs130 (par value of Rs100).
a) how much should he invest?
b) If the dividend is 7.5%, what will be his annual income ?
c) if he wants to increase his annual income by Rs300, how many extra shares should be buy?       (4)

16) Solve graphically the simultaneous equations given below. Take the scale as 2 cm= 1 unit on both the axes.
3x - 2y - 4 = 0; 5x - 2y = 2.       (5)

17) The following table gives the weekly wages of workers in a factory.
 weekly wedges(in Rs)   No. of workers
 150- 155                            5 
 155-160                           20
 160-165                           10 
 165 -170                          10 
 170- 175                           9
 175-180                            6 
 180- 185                         12
 185-190                            8 Calculate 
a) the mean
b) the model class 
c) the number of workers getting weekly wages, below Rs180
d) the number of workers getting Rs165 or more, but less than Rs185 as weekly wages.    (5)

18) Using rule and compass only, construct
a) The triangle ABC in which AB=8cm, BC= 11cm and angle ABC =45°
b) A circle of radius 3cm to touch the arms of angle ACB in (a) above.   (5)

19) A hollow sphere of internal and external diameter 8cm and 16cm respectively, is melted into a cone of base diameter 16cm. Find the height of the cone.   (5)

20) The shadow of a vertical tower AD on level ground is increased by 30m, when the altitude of the sun changes from 45° to 30°, as shown in the given figure.

Find the height of the tower and give your answer correct to 1/10 of a metre.    (4)

20) A man sells an article at 15% above cost price. If he had bought it 10% less than what he paid for it and sold it for Rs140 less, he would have gained 20%. Find the cost price of the article .     (4)

21) a function  f is given by the formula f(x)= 225 - 4x². find f3 such that zero the marks obtained by 242 in the mathematical test given below 0 to 10 10 to 18 22 32 32 52 5262 70 22 728 1282 9692008 draw an Ho jaaye for the given distribution a graph sheet used suitable scale for your side and using estimate the medium the lowercortil the number of students who obtained more than 75% the taste the number of students who did not passing a test in the past percentage was 40 24 3375 are the vertices of find the coordinates of the centroid the equation of the line through G and a parallel to PQ Mr print of the Bank of India aeroplane travel distance of 800 at an average speed of x on the return gen speed was increased by 40 write down the expression for the time taken for the onward journey the return journey if the return journey to 40 minutes less than one word journey write down in equation in X and find its value

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