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Wednesday, July 28, 2010

optional mathmetics

Joint Examination Board
PABSON, Bhaktapur
Second Term Exam - 2066
Class: X Time: 3 hrs. F.M: 100
Subject: Opt.Maths P.M: 40



Group A [ (2+2) x 8 = 32]

1. a. If f = {(2,4) , (1,8), (0,0)} and g = {(4,0), (0,5),(8,3)}, show the function of g by an arrow diagram and find it in order pair form.

b. State remainder theorem. When x3 + kx2 + 3x + 4 is divided by x - 2, then the remainder is 18. Find the value of K.

2. a. The AM of two numbers P and 8 is 5, find their geometric mean.

b. If the inverse of the matrix is find the values of m and n.
3. a. Which matrix pre multiplies to the matrix gives (10 16)?

b. If the lines A1x + B1y + C1 =0 and A2x + B2y+ C2= 0 are perpendicular to each other , prove that A1A2 + B1B2 = 0.

4. a. Find the separate equations represented by the equation x2 - y2 + 2y - 1 = 0.

b. Find the centre and radius of the circle x2 + y2 - 20y+ 75 = 0.

5. a. Prove that:

b. If , find the value of Sin .

6. a. Prove that: Cos 1050 + Sin 1050 =

b. Solve:


7. a. If and , find the value of p.

b. The position vector of A is and the position vector of B is . If , find the position vector of the point P.

8. a. The translation followed by the translation gives the translation
, what are the values of a and b?

b. If A = , state the transformation represented by A2. Also find the image of point M (2,3) using A2.


Group B (17 x 4 = 68)

9. If f(x) = 4x + 5, g(x) = 3x + k and gf -1(9) = 5, find the value of K.

10. Solve : x3 - 4x2 - 7x + 10 = 0.

11. The product of three numbers of a G.P is 216 and their sum is 19. Find the numbers.

12. Find the maximum value of P = 2x + 3y under constraints
, x+y 0 , y 2.

13. Solve by matrix method; x = 2y - 1 and 2x = y.

14. Find the equation of the straight line passing through the mid point of the
segment joining the points A(2,-4) and B( 2,4) and parallel to the line
3x - 2y - 4 = 0.

15. Find the single equation of a pair of straight lines passing through the origin
and perpendicular to the pair of lines represented by x2 - 5 xy + 4y2 = 0.

16. Find the equation of the circle which touches the x-axis at a point (3,0) and
passing through the point (1,2).

17. Prove that:

18. If A+B+C = prove that;
Cos(B+C-A) +Cos(C+A-B) +Cos (A+B-C) = 1 + 4 Cos A. Cos B. Cos C.

19. Solve: Tan A + Tan3A + Tan A.Tan3A =

20. The shadow of a tower on the ground is found to be 45 m longer when the
sun's altitude is 450 than when it is 600. Find the height of the tower.

21. Prove by vector method that the diagonals of a rhombus intersect at right
angle.

22. A triangle with vertices A(1,2) , B(4,-1) and C (2,5) is reflected in the line
x=5 then rotated through 90+ about origin. Find the final image. Also draw
on the graph paper.

23. Find 2 x 2 transformation matrix which transform the rectangle
into the unit square.

24. Calculate mean deviation from the median and its coefficient from the given
data.

X: 20 18 16 14 12 10 8 6
f: 2 4 9 18 27 25 14 1

25. Calculate standard deviation from the given data:

Class 0-10 10-20 20-30 30-40 40-50 50-60
Frequency 4 6 10 20 6 4


Best of Luck !

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