Class 12 CBSE Maths Continuity & Differentiability Board Questions

Continuity and differentiability in class 12 is about, if a function f(x) is said to be continuous at a point x = a, if Left hand limit of f(x) at(x = a) = Right hand limit of f(x) at (x = a) = Value of f(x) at (x = a) i.e. if at x = a, LHL = RHL = f(a)

class 12 CBSE Maths C&D BoardsQuestions

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Important Questions
Board Questions





Cont. and Diff. BoardsQuestions
2016
Q1 Find the values of p and q, for which


is continuous at x = π/2.

solutions
2017
Q1 Find the value of c in Rolle's theorem for the function f(x) = x3— 3x in [-√3,0]

solutions
Q2 Determine the value of 'k' for which the following function is continuous at x=3:


solutions
2020
Q1 The greatest integer function defined by f(x) = [x], 0 < x < 2 is not differentiable at x=_______

solutions
Differentiation
2016
Q1 If x = a sin 2t( 1 + cos 2t) and y = b cos 2t ( 1 - cos 2t), find the values of
dy / dx
at t =
π / 4
and t =
π / 3

OR

if y = xx prove that
d2y / dx2
-
1 / y
(
dy / dx
)2 -
y / x
= 0

solutions
2017
Q2 if xy + yx = ab then find
dy / dx

OR

If ey(x + 1) = 1, then show that
d2y / dx2
= (
dy / dx
)2

solutions
2018
Q3 If log(x2 + y2) = 2 tan-1(
y / x
), show that
dy / dx
=
x + y / x - y

OR

If xy - yx = ab, find
dy / dx


solutions
Q4 If f(x) = x+ 1, find
d / dx
(fof)(x)

solutions
Q5 If y = (sin-1x)2 , prove that ( 1- x2)
d2y / dx2
- x
dy / dx
- 2 = 0

solutions
2019
Q6 If sin y = x cos(a + y), then show that
dy / dx
=
cos2(a + y) / cos a

Also show that
dy / dx
= cos a, when x = 0

solutions
Q7 Differentiate tan-1 (
cosx - sinx / cosx + sinx
) with respect to x.

solutions
Q8 If x = a sec3 θ and y = a tan3 θ, find
d2y / dx2
at θ = π/3
OR

If y = etan-1x prove that ( 1+ x2)
d2y / dx2
+ (2x - 1)
dy / dx
= 0

solutions
2020
Q9 If x = at2, y = 2at then find
d2y / dx2


solutions
Q10 If y = ex2cosx + (cos x)x, then find
dy / dx


solutions

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