Page 1 CBSE TEST PAPER-05 CLASS - XII MATHEMATICS (Calculus: Continuity and Differentiability) Topic: - Differentiation 1. For what value of K is the following function continuous at x = 2? [4] 2x+1 ; x < 2 ( ) K ; x = 2 3 1 ; x > 2 f x x ? ? = ? ? - ? 2. Differentiate the following w.r.t. to x 1 1 1 tan 1 1 x x x x - ? ? + - - ? ? + + - ? ? [4] 3. If 2 1 5 12 1 sin 13 x x y - ? ? + - = ? ? ? ? ? ? find dy dx [4] 4. Discuss the continuity of the following function at x = 0 [4] 4 3 2 1 2 , x 0 ( ) tan 0 , x = 0 x x x f x x - ? + + ? ? = ? ? ? 5. Verify L.M.V theorem for the following function f(x) = x 2 + 2x + 3, for [4, 6] [4] 6. If sec 1 ( ) , sec 1 x f x x - = + find ( ) ' f x also find ' 2 f p ? ? ? ? ? ? [4] 7. If ( ) p q p q x y x y + = + prove that dy y dx x = [4] 8. If sin , cos x a pt y b pt = = find the value of 2 2 d y dx at t = 0 [4] 9. If ( ) 2 2 1 log 1 y x x x + = + - prove that ( ) 2 1 1 0 dy x xy dx + + + = [4] 10. If sin sin sin ........... y x x x = + + + + 8 prove that cos 2 1 dy x dx y = - [4] OR If sin sin( ) y x a y = + prove that 2 sin ( ) sin dy a y dx a + =Read More

Offer running on EduRev: __Apply code STAYHOME200__ to get INR 200 off on our premium plan EduRev Infinity!