Class XII Maths Limits and Differentiation 4

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Question 1

Let the function f, g and h be defined as follows


h(x) = |x|³ for –1 ≤ x ≤ 1.
Which of these functions are differentiable at x = 0?

• Af and g only
• Bf and h only
• Cg and h only
• Dnone

Question 2

The number of points at which the function f(x) = max. {a – x, a + x, b}, – ∞ < x < ∞, 0 < a < b cannot be differentiable is

• A1
• B2
• C3
• Dnone

Question 3

If f(x) is differentiable everywhere, then

• A|f(x)| is differentiable everywhere
• B|f(x)|² is differentiable everywhere
• C
  f(x)|f(x)| is not differentiable at some point
• Df(x)+|f(x)| is differentiable everywhere

Question 4

A function f defined as f(x) = x[x] for –1 ≤ x ≤ 3 where [x] defines the greatest integer ≤ x is

• Acontinuous at all points in the domain of f but non-derivable at a finite number of points
• Bdiscontinuous at all points & hence non-derivable at all points in the domain of f
• Cdiscontinuous at a finite number of points but not derivable at all points in the domain of f
• Ddiscontinuous & also non-derivable at a finite number of points of f

Question 5

If f(x) = is differentiable at x = 0 then
(where k is an integer)

• Ak > 0
• Bk > 1
• Ck ≥ 1
• Dk ≥ 0

Question 6

The derivative of f(tan x) w.r.t. g(sec x) at x = , where f'(1) and g' () = 4, is-

• A
• B
• C1
• DNone of these

Question 7

Let f(x) is a function differentiable at x = c, then equals

• A
• B
• C
• Dnone of these

Question 8

Suppose φ(.) is a differentiable function. If φ(x + y) = φ(x) φ(y) for all real x and y and φ (5) = 2, φ ′(0) = 3, then φ ′(5) is

• A6
• B3
• C0
• Dnone of these

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