Page 1 CBSE TEST PAPER-02 CLASS - XII MATHEMATICS (Calculus: Application of Derivatives) Topic: - application of derivatives 1. A ladder 5m long is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall, at the rate 2cm/s. how fast is its height on the wall decreasing when the foot of the ladder is 4m away from the wall. [4] 2. A particle moves along the curve 6y = x 3 + 2. Find the points on the curve at which the y-coordinate is changing 8 times as fast as the x â€“ coordinate. [4] 3. Find the interval in which increase/decrease. ( ) sin 3 , 0, 2 f x x x p ? ? = ? ? ? ? ? [4] 4. Find the intervals in which the function f given by ( ) sin cos , 0 2 f x x x x p = + = = is strictly increasing or decreasing. [4] 5. Find the equation, of the tangent line to the curve y = x 2 â€“ 2x + 7 which is (a) Parallels to the line 2x â€“ y + 9 = 0 (b) Perpendicular to the line 5y â€“ 15x = 13 [4] 6. Find the equation of the tangent to the hyperbola 2 2 2 2 1 x y a b - = at the point (x o, y o). [4] 7. Find the approximate value of ( ) 1 2 0.0037 [4] 8. Using differentiates find the approximate value of ( ) 3 2 3.968 [4] 9. Show that the right circular cone of least curved surface area and given volume has an altitude equal to 2 time the radius of the base. [6] 10. Show that semi â€“ vertical angle of right circular cone of given surface area and maximum volume is 1 1 sin 3 - ? ? ? ? ? ? [6]Read More

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