Webocreation

Wednesday, July 28, 2010

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


Attempt all the questions
Group A [ (2+2) x 8 = 32]

Q.1 a. If the range of the function f(x) = is 14, find its domain.


b. Arrange the surds , , in ascending order in
magnitude.

Q.2 a. If the polynomials P(x) = x3 + kx2 + 5x+ 6 and
Q(x) = x3 + x2 - rx + 6 are equal, find the value of k and r.

b. Define diagonal matrix with an example.

Q.3 a. If the distance between two points A (a,1) and B( -3, 4) is 5
units, find the value of a.

b. The mid point of the line joining the points, A(3,4) and B(x,y) is ( 2,3), find the coordinates of B.

Q.4 a. From the given figure, find the slope of AB and slope of AC.

b. Find the equation of the line PQ from the figure.






Q.5 a. If 40g is taken from 1000. Find the remainder in circular measure.

b. Prove that: = Sec A - Tan A


Q.6 a. If , find the numerical value of Sec .

b. Prove that:

Q.7 a. Find the value of :


b. The magnitude of is 5 units, find the value of x.

Q.8 a. If find the vector such
that

b. Find the image of P(2,3) under the lines
(a) x = 0 and ( b) x-3=0


Group B [ 17 x 4 = 68]


Q.9 If f(x) = x2 + 4x + 5 then for what value of x , f(x) ¬= f(x+1)?

Q.10 Solve :


Q.11 Simplify: + -


Q.12 Find x, y, z and w if = +


Q.13 If the point P(x,y) is equidistant from the points A (a+b, b-a) and B(a-b, a+b), prove that ay = bx.

Q.14 The line joinig the points (6,9) and (-6, -9) is trisected . Find the coordinates of the points of trisection.

Q.15 Find the equation of the locus of the point which moves so that the sum of the square of its distances from the points (-3, 0) and (3,0) is 9 units.

Q.16 Prove that by geometrically , where the symbols have their ususal meanings.

Q.17 Find the equation of the straight line, which passes through the point (2, -3) and makes an intercept on the y -axis twice as long as that on x - axis.

Q.18 Find the equation of the striaght lines bisecting the co-ordinate axes.
Q.19 One angle of a triangle is of right angle. The difference between remaining two angles is 300, find the angles of a triangle in circular measure.

Q.20 Prove that:

Q.21 If find the value of

Q.22 If find the value of x.

Q.23 The vector from A(1,1) to B(2,4) is such that it equals where C is (2,-1). Find the coordinates of the point D.


Q.24 The vertices of ABC are A(0,2) , B(3,4) and C(-1,3). Find the image of A'B'C' under the reflection line y=2. Also draw on the graph paper.


Q.25 PQR having vertices P(3,2), Q (6,1) and R(3,2) is rotated 270+ about origin. Find the coordinates of P' , Q' and R'. Also draw on the graph paper.


Best of Luck !

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 gof 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 seperate equations represented by the eauation 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
in to 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

1 comment: