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Maths-

General

Easy

Question

A function $f$ is defined by $f open parentheses x close parentheses equals 2 plus open parentheses x minus 1 close parentheses to the power of 2 divided by 3 end exponent$ in [0, 2]. Which of the following is not correct?

$f$ is not derivable in (0, 2)
$f$ is continuous in [0, 2]
$f (0) = f (2)$
Rolle’s Theorem is true in [0, 2]

The correct answer is: Rolle’s Theorem is true in [0, 2]

Given, $f open parentheses x close parentheses equals 2 plus open parentheses x minus 1 close parentheses to the power of 2 divided by 3 end exponent$
By using Rolle’s theorem, the given function is not differentiable at $x equals 1 comma$ which cannot satisfy Rolle’s theorem.

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q₁, q₂ , q₃ and q₄ are point charges located at points as shown in the figure and S is a spherical Gaussian surface of radius R. Which of the following is true according to the Gauss’s law?

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