RAW-2(X)

1) Calculate the compound interest on Rs8000 for 1 year at 12% per annum compound at half yearly.m.  (2)

2) The point P(a, b) reflected in the x-axis to obtain point Q(3,4). Find a and b.   (2)

3) if A= a    3a & B= 2  & C= 5
              b    4b          1          12 with the relation AB= C, then find a and b.    (2)

4) The mean of the number 6, y, 7, x and 14 is 8 . Express y in terms of x.    (2)

5) Given f(x)= x/(x²-1), find f(-1/2).     (2)

6) Solve using the quadric formula , x²- 5x -2=0. Give your answer correct to 3 significant figures.       (3)

7) If (8a + 5b)/(8c + 5d)= (8a - 5b)/(8c - 5d), prove that a/b = c/d.     (3)

8) Find the value of of k, if x - k is a factor of x³- kx²+ x +4.      (3)

9) Solve: 1 < 3x - 3 ≤ 12, x ∈R and mark it on a number line.    (3)

10) Calculate the mean, median and mode of the following numbers: 12, 11, 10, 11, 12, 13, 15, 13.     (3)

11)  In the diagram AB and CD of circle are produced to meet at O. 
Given that CD= 4cm, DO= 12cm and BO=6cm, calculate AB.      (3)

12) If cosA= 4/5 and cos B =24/25, evaluate :
a) cosec²A
B) cotA + cotB.     (4)

13) On a map drawn to a circle of 1: 125000, a triangular plot of land has the following measurements :
PQ= 10cm, QR= 8cm, angle PRQ=90°. Calculate 
a) the actual length of PQ in km.
b) the area of the plot in square kilometres.     (4)

14) AB is a diameter of a circle of radius 36 m. M and N are points on the diameter such that AM= MN= NB. 
Semicircle are drawn with AN and NB as diameter, as shown in the figure. Find:
a) The perimeter of the shaded region.
b) The area of the unshaded region (leave your answer in π form ).   (4)

15) The work done by (2x - 3) men in (3 x + 1) days and the work done by (3x + 1) men in (x+8) days are in the ratio of 11:15. Find the value of x.     (3)

16) If f(x)= (2x -7)/(x+4), find 
a) f(2).
b) f(x³).
c) f(3x +1).

17) Find the mean of the following frequency distribution:
Class interval     frequency 
   00- 30                   3 
   30- 60                   7 
   60- 90                  15
   90- 120                14
 120- 150                 7 
 150- 180                 4       (4)

18) A man invests Rs30800 in buying shares of nominal value Rs56 at 10% premium. The dividend on the shares is 18% per annum. Calculate:
a) The number of shares he buys.
b) The dividend he receives annually.
c) The rate of interest he gets on his money.      (5)

19) Prove that: sinx/(1- cotx) + cosx/(1- tanx)= sinx + cosx.      (5)

20) A straight line passes through the points A(-2,8) and B(10, -4). It interesects the coordinate axes at point E and F. P is the midpoint of the segment EF.
Find :
a) The equation the line.
b) The coordinates of E and F.  
c) The coordinates of the point P.     (5)

21) In an auditorium, seats were 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 15, the total number of seats increased by 400. Find :
a) The number of rows in the original arrangement.
b) The number of seats in the auditorium after rearrangement.    (5)

22) Draw a histogram and hence estimate the mode for the following frequency distribution:
 Class        frequency 
00-20            3 
20-40            8 
40-60           10
60-80            6
80-100          4 
100-120        3               (5)

23) A man standing on the bank of a river observes that the angle of a tree on the opposite bank is 60°. When he moves 40m away from the bank, he finds the angle of elevation to be 30°. Calculate :
a) the width of the river.
b)  The height of the tree.       (5)

24) find a and b, if
A= 3   -2 & B= -4 & C= 2 & D= 2
     -1    4           1          5          b with the relation AB + 4C = 3D.     (4)

25) A vessel is in the form of an inverted cone. its height is 15cm and the diameter of its top which is open, is 5cm. it is filled with water up to the rim. When lead shots, each of which is a sphere of diameter 5 mm are dropped into the vessel , 1/3 of the water flows out. Find the number of lead shots dropped into the vessel .    (4)

26) In the given circle with diameter AB,
find the value of x.    (2)

27) Construct an angle ABC = 45°. Mark a point P on BC such that BP= 5.5cm. construct a circle to touch AB at B and also to pass through P.     (4)

28) Find the value of k for which the lines Kx - 7y+ 5=0  and 6x -2y +9= 0 are perpendicular to each other.     (4)

29) If (a,b) ∈ R, name the kind of relation between a and b if a R b => b R a, i.e., is related to b => b is related to a.
Does R={(a, b)= a < b, a, b ∈N} also show a relation if this kind ? Explain.     (2)

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