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MathsMediumMCQ2021 · 24 Feb Shift 1

Q71.If 𝑓: 𝑅→𝑅 is a function defined by 𝑓𝑥= 𝑥- 1cos2𝑥- 1 𝜋, where · denotes the greatest integer function, then 𝑓 2 is: (1) discontinuous only at 𝑥= 1 (2) discontinuous at all integral values of 𝑥 except at 𝑥= 1 (3) continuous only at 𝑥= 1 (4) continuous for every real 𝑥

What This Question Tests

The problem requires checking the continuity of a function involving the greatest integer function and a trigonometric term, which often leads to discontinuities at integer points.

Concepts Tested

Greatest integer functionContinuity at a pointTrigonometric functions

Formulas Used

Definition of continuity: lim(x->a) f(x) = f(a)

Properties of greatest integer function

📚 NCERT Sections This Tests

11.8 — Light Of Frequency 7.21 × 1014 Hz Is Incident On A Metal Surface.

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11.8 Light of frequency 7.21 × 1014 Hz is incident on a metal surface. Electrons with a maximum speed of 6.0 × 105 m/s are ejected from the surface. What is the threshold frequency for photoemission of electrons?

1.3 — Define The Following Terms:

Chemistry Class 11 · Chapter 1

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1.3 Define the following terms: (i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.

11.7 — The Work Function For A Certain Metal Is 4.2 Ev. Will This Metal Give

Physics Class 12 · Chapter 11

68% match

11.7 The work function for a certain metal is 4.2 eV. Will this metal give hotoelectric emission for incident radiation of wavelength 330 nm?

📋 Question Details

Chapter: Limits & Continuity
Topic: Continuity of functions
Year: 2021
Shift: 24 Feb Shift 1
Q Number: Q71
Type: MCQ
NCERT Ref: Class 12 Mathematics Ch 5: Continuity and Differentiability

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