Page 1 CBSE TEST PAPER-01 CLASS - XII MATHEMATICS (Calculus: Application of Derivatives) Topic: - Application of Derivatives 1. The length x of a rectangle is decreasing at the rate of 3 cm/ mint and the width y is increasing at the rate of 2cm/min. when x = 10cm and y = 6cm, find the ratio of change of (a) the perimeter (b) the area of the rectangle. [4] 2. Find the interval in which the function of given by f(x) = 4x 3 â€“ 6x 2 â€“ 72x + 30 is (a) strictly increasing (b) strictly decreasing. [4] 3. Find point on the curve 2 2 1 4 25 x y + = at which the tangents are (i) parallel to x â€“ axis (ii) parallel to y â€“ axis [4] 4. Use differentiate to approximate ( ) 1 3 25 [4] 5. Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is 8 27 of the volume of the sphere. [6] 6. The volume of a cube is increasing at a rate of 9cm 3 /s. How fast is the surface area increasing when the length of on edge is 10cm? [4] 7. Find the interval in which the function is strictly increasing and decreasing. (x+1) 3 (x-3) 3 [4] 8. Find the equations of the tangent and normal to curve 2 3 2 3 2 x y + = at (1, 1) [4] 9. IF the radius of a sphere is measured as 9cm with an error of 0.03cm, then find the approximate error in calculating its volume. [4] 10. A wire of length 28m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces to that the combined areas of the square and the circle is minimum. [6]Read More

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