Page 03 MARKS ATTEMPT ALL QUESTIONS Total marks — 60 1. Functions f and g are defined on suitable domains by ( ) 5 f x x = and ( ) cos 2 g x x = . (a) Evaluate ( ) ( ) 0 f g . (b) Find an expression for ( ) ( ) g f x . 2. The point P (−2, 1) lies on the circle 2 2 8 6 15 0 x y x y + − − − = . Find the equation of the tangent to the circle at P. 3. Given ( ) 12 4 1 y x = − , find dy dx . 4. Find the value of k for which the equation ( ) 2 4 5 0 x x k + + − = has equal roots. 5. Vectors u and v are 5 1 1 ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ − ⎝ ⎠ and 3 8 6 ⎛ ⎞ ⎜ ⎟ − ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ respectively. (a) Evaluate u .v. (b) u w 3 π Vector w makes an angle of 3 π with u and 3 = w . Calculate u .w. 1 2 4 2 3 1 3 [Turn over