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12th Maths Sectionwise paper - 02 (Differentiation)

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MATHEMATICS Class II Pre-Uni Plus 2016-17 Topics Board Section-wise Test - 02 Differentiability, Differentiation and Application of derivatives Max. Marks 100 Duration Date 3 hrs 15 min 27-12-2016 Instructions 1. Do not overwrite. 2. Draw a line using pen at the end of each answer. 3. Steps adopted in solving problems should be clearly shown. 4. In case of violation of the above conditions, the answer scripts will not be considered for valuation. PART - A I. Answer the following questions [10 1 = 10] 1. Examine the continuity of the function f(x) = 2x2 1 at x = 3. 2. Find the derivative of y 1 x 3. If y = cos(2cos x). Then find 4. Find 4 3 3 x 3 2 . dy . dx dy if y = sin(xx). dx 5. If x = 4t, y 4 dy y . Then show that . t dx x 6. State Rolle s theorem. 7. Find the rate of change of the area of a circle with respect to radius r when r = 3 cm. 8. Find the slope of the tangent to the curve y = 3x4 4x at x = 4. 9. Show that the function f(x) = 3x + 17 is strictly increasing on R. 10. Find the extreme values of the function f(x) = x2. PART - B II. Answer any TEN of the following questions 2x 3; x 2 11. Find all the points of discontinuity of the function f (x) . 2x 3; x 2 12. Prove that the function f(x) = |x 1|, x R is not differentiable at x = 1. 13. If y x 14. If y 1 dy prove that x 2 xy 2 0 . x dx e x log x dy . Then find . sin 3x dx 2P1617MBSWT2 1 [10 2 = 20]

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