Rising Nepal Secondary Boarding School

First Terminal Examination 2075

Class: 10 F.M. 50

Time: 1 hr. 30 mins. Subject: Optional Mathematics P.M. 16

Group 'A'

18

  1. If & then prove that AB is an identity matrix.
  2. If & , find the determinant of PQ.
  3. If a line 2x + 3y = 6 is perpendicular to the line ax + 4y = 3, find the value of a.
  4. Prove that:
  5. Prove that: tan800 = tan100 + 2tan700
  6. Prove that: 2sin2(900 – A) = 1 + cos2A
  7. Prove that: tanθ(1 + cos2θ) = sin2θ
  8. Which matrix pre-multiplies to the matrix to get (4 1).
  9. Prove that:

Group 'B'

32

  1. If & then show that A2 – 8B – 17I = O, where I and O are unit and zero matrices of order 2x2.
  2. Solve the given pair of equation by the matrix method:

3x – 5y = 3

4x + 3y = 4

  1. If a line passing through the points (4, -p) and (-2, 6) is parallel to the line having equation 2y + 3x = -3, find the value of p.
  2. Find the equation of straight line passing through the point (1, 0) and inclined at an angle 300 with the line .
  3. Prove that: (1 + sin2θ + cos2θ)2 = 4cos2θ(1 + sin2θ)
  4. Prove that:
  5. Prove that:
  6. If and , prove that:

-O-