RISING NEPAL SECONDARY BOARDING SCHOOL

Class: 9 FINAL EXAMINATION 2077 F.M: 50

Time: 2hrs. Sub: Opt. Maths P.M: 16

Group 'A'

22

  1. Construct a 2x3 matrix whose elements aij are given by:
    aij = 4i-2j
  2. If ,find the values of p, q, r, s.
  3. Find the equation of a straight line which is inclined to the X-axis at an angle 300 & cuts off an intercept 3 from Y-axis.
  4. If and , show that (A+B)T = AT+BT
  5. Express 32015'30'' into radian measure.
  6. Show that:
  7. Show that: 3(sinA + cosA) – (sinA + cosA)3 = 2(sin3A + cos3A)
  8. Prove that: 1 + tanA.tan2A = sec2A
  9. Prove that: sin(A+B) + sin(A-B) = 2sinAcosB
  10. Find the area of the quadrilateral whose vertices are (2, 1), (5, -2), (3, 4) and (3, -7).
  11. Find the co-ordinates of the point which divides the line joining the points (-4, -2) and (4, 8) in the ratio 3:2, internally.

Group 'B'

28

  1. Prove that the points (3, 1), (6, 3) and (-1, 7) are the vertices of a right-angled triangle.
  2. A(1, 2) and B(5, 3) are two points. Find the locus of a point 'P' so that PA:PB = 2:3.
  3. If , find a matrix X such that & .
  4. The point P(a, b) lies on the line x – 2y = 2 and the point Q(b, a) lies on the line 2x + y = 6. Find the equation of PQ.
  5. Prove that:
  6. Prove that:
  7. In which ratio does the line joining (3, 2) and (5, 0) divide the join of (2, 1) and (5, 2).

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