Class XII Maths Limits and Differentiation 2

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Question 1

If [x] denotes the integral part of x and f(x) = [x] then-

• Af(x) is continuous in R
• Bf(x) is continuous in all integral points
• Cf(x) is discontinuous at all integers
• DNone of these

Question 2

A function f(x) is defined as below , x ≠ 0 and f(0) = a f(x) is continuous at x = 0 if a equals.

• A0
• B4
• C5
• D6

Question 3

   
where [x] denotes the greatest integer less than or equal to x, then in order that f(x) be continuous at x = 0, the value of k is -

• Aequal to 0
• Bequal to 1
• Cequal to – 1
• Dindeterminate

Question 4

The function defined by f(x) =
(where [⋅] denotes greatest integer function satisfies)

• Adiscontinuous for x = n^1/3 where n is any integer
• Bf(3/2) = 1
• Cf'(x) = 0 for –1 < x < 1
• Dnone of these

Question 5

If , then jump of discontinuity is

• A
• B
• C
• D

Question 6

If the function is continuous at x = 2 then A =

• A0
• B1
• C2
• DNone of these

Question 7

f(x) = [tan^–1x] where [ ·] denotes the greatest integer function, is discontinuous at -

• A– , 0 and
• B– , 0 and
• C–tan 1, tan 1, 0
• DNone of these

Question 8

Let f(x) = Sgn (x) and g(x) = x (x² –5x + 6). The function f(g (x)) is discontinuous at

• Ainfinitely many points
• Bexactly one points
• Cexactly three points
• Dno point

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