Optional mathematics question paper 2010
Joint Examination Board
PABSON, Bhaktapur
Pre-send up Examination - 2066
Class: X F.M: 100
Subject: Opt. Maths Time: 3 hrs. P.M: 40
Examinees are required to give their answers in their own words as far as possible. Priority will be given to creative answers in marking rather than the rot learning.
Attempt all the questions:
Group 'A' [8×(2+2)=32]
Q.1 a. If f(x) 2x+3 and fg (x) = 2x + 1, find the function g(x).
b. Define factor theorem. If x - 2 is factor of the polynomial
x2 + kx + 6, find the value of K.
Q.2 a. If 8x + 4, 6x - 2 and 2x - 7 are in A.P., find its second term.
b. If A = and AB= , find the matrix B.
Q.3 a. Define inverse of the matrix. For what value of 'x' the matrix
A = does not exits its inverse?
b. If the lines p1x + n1y+c1 = 0 and p2x + n2y + c2=0 are parallel to each other, prove that .
Q.4 a. Find the separate equations represented by the equation
ab (x2-y2) + (a2-b2) xy = 0.
b. If the radius of the circle x2+y2 - kx - 6y + 1 =0 is 3 units, find the value of k.
Q.5 a. Find the value of Tan 150 in rationalize form without table or
calculator.
b. Prove that :
Q.6. a. Prove that:
b. Solve:
Q.7 a. If and , find the angle between them.
b. In figure, o be the origin if , and
. Find the position vector of the point P.
Q.8 a. R be the rotation through 900 + about origin and T = be the
translation. If the image of M (1, 2) under the combined transformation ROT is M' (5, 7), find the translation T.
b. State the transformation represented by the matrix . Find the image of the point A (2, 3) under the same matrix.
Group B [17×4=68]
Q.9 If f(x) = 2x-1, g(x) = x2 + x. For what value of x, f -1g(x) = 1?
Q.10 Solve: x3 - 19x + 30 = 0
Q.11 The sum of first four terms of a G.P is 240 and the sum of next four terms is 15, find the first term and common ratio.
Q.12 Maximize: Z = 4x + y under the constraints
x + 2y 4, x + y 3, x 0, y 0.
Q.13 Solve by matrix method:
and
Q.14 The vertices of rhombus PQRS in which P (2, 3) and R (-6, 5). Find the equation of the diagonal QS.
Q.15 Find the equation of a pair of straight lines passing through the origin and perpendicular to the line represented by 5x2 - 8xy + 3y2 = 0.
Q.16 Find the equation of the circle whose centre is (2, 7) and which has the radius same as the circle x2 + y2 + 14x + 16y + 24 = 0
Q.17 Prove that:
Cos A. Cos2A. Cos 4A. Cos8A =
Q.18 If A+B+C = , prove that
Q.19 Solve: Tan2A - (1+ ) Tan A+ = 0
Q.20 Two towers are 120m apart and the height of one is double than the other. From the middle point of the line joining their foot, an observer finds the angles of elevation of their tops are found to be complementary, find the height of the tower.
Q.21 Prove that vector method that the median drawn from the vertex to the base of an isosceles triangle is perpendicular to the base.
Q.22 A triangle with vertices A (2,3), B( 5,1) and C( 3,4) is reflected successively in the lines y = 1 and x = 2, find by stating coordinates and graphically represent images under these transformation. State also the single transformation given by the combinations of this transformation.
Q.23 Triangle PQR whose vertices are P (2, 5) , Q (3,1) and R( 5,4) maps by 2 x 2 matrix on to the triangle P'Q'R' with the vertices P'(-5,2), Q'(-1,3) and R'(-4,5). Find the matrix.
Q.24 Find mean deviation from median from the given data.
Marks 20 25 30 35 40
No. of students 5 10 12 8 5
Q.25 Find standard deviation and coefficient of variation from the given data.
X: 12, 15, 29, 37, 41, 49
Best of Luck!
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