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MathsHardNumerical2022 · 25 Jun Shift 2

Q86.Let 𝑓𝑥= 2𝑥2 + 1 and 𝑔𝑥= 2𝑥- 3, 𝑥< 0 , where 𝑡 is the greatest integer ≤𝑡. Then, in the open interval 2𝑥+ 3, 𝑥≥0 -1, 1, the number of points where fog is discontinuous is equal to ______.

What This Question Tests

This question requires analyzing the continuity of a composite function involving a piecewise function and the Greatest Integer Function within a given interval, identifying all points where it becomes discontinuous.

Concepts Tested

Greatest Integer Function (GIF)Continuity of functionsComposite functions (fog)Points of discontinuity

Formulas Used

f(g(x))

📚 NCERT Sections This Tests

2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At

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9.15 — Apply Mirror Equation And The Condition:

Physics Class 12 · Chapter 9

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9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.

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.

📋 Question Details

Chapter: Limits & Continuity
Topic: Continuity of composite functions
Year: 2022
Shift: 25 Jun Shift 2
Q Number: Q86
Type: Numerical
NCERT Ref: Class 12 Mathematics Ch 5: Continuity and Differentiability

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