Page 1 CBSE TEST PAPER02 CLASS  XII MATHEMATICS (Calculus : Continuity and Differentiability) Topic: Differentiation 1. Find all points of discontinuity if [4]   3, if x 3 ( ) 2 , if 3 < x < 3 6x+2, if x 3 x f x x + = ? ? =  ? ? = ? 2. Differentiate 3 2 5 cos .sin ( ) I B y x x = [4] 3. Find dy dx if 3 2 2 3 81 x x y xy y + + + = [4] 4. Differentiate xy = e (xy) [4] 5. Find dy dx if (cos sin 0) and (sin 0 cos ) x a y a ? ? ? ? = + =  [4] 6. If y = 3 cos (log x) + 4 sin (log x). Show that x 2 y 2 + xy 1 + y = 0 [4] 7. Verify Rolle’s Theorem for the function f(x) = x 2 + 2x – 8, x?[4, 2] [4] 8. Find dy dx 1 sin tan 1 cos x y x  ? ? = ? ? + ? ? [4] 9. If x = a (cos t + t sin t) and y = a (sin t – t cos t), find 2 2 d y dx [4] 10. If f(x) g(x) h(x) l m n a b c y = Prove that f'(x) g'(x) h'(x) l m n a b c dy dx = [4]Read More
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