Statement - I: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>:</mo><mi>R</mi><mo>→</mo><mi>R</mi></math> be a function such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>|</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>|</mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>≤</mo><msup><mi>x</mi><mn>2</mn></msup><mo>,</mo><mo> </mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∀</mo><mi>x</mi><mo>∈</mo><mi>R</mi></math> then <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> is differentiable at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn></math>. Statement - II: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>:</mo><mi>R</mi><mo>→</mo><mi>R</mi></math> be a function such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>|</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>|</mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>≤</mo><msup><mi>x</mi><mi>p</mi></msup><mo>,</mo><mo> </mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∀</mo><mi>x</mi><mo>∈</mo><mi>R</mi></math> then <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> is differentiable at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn></math> for any whole number <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>'</mo><mi>p</mi><mo>'</mo></math>

Statement - I: f : R R be a function such that | f ( x ) | x 2 , x R then f ( x ) is differentiable at x = 0 .

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Q.
Statement - I: $f : R \to R$ be a function such that $| f (x) |$ $\leq x^{2},$ $\forall x \in R$ then $f (x)$ is differentiable at $x = 0$ .

Statement - II: $f : R \to R$ be a function such that $| f (x) |$ $\leq x^{p},$ $\forall x \in R$ then $f (x)$ is differentiable at $x = 0$ for any whole number $' p'$

Solution

1 Both statement – I and statement II are true

2 Both statement- I and statement II are false

3 Statement I is true and statement II is false

4 Statement I is false and statement II is true

Ans.
(3)

Conceptual

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Solution

Q. Statement - I: f:R→R be a function such that |f(x)|≤x2, ∀x∈R then f(x) is differentiable at x=0. Statement - II: f:R→R be a function such that |f(x)|≤xp, ∀x∈R then f(x) is differentiable at x=0 for any whole number 'p'

1 Both statement – I and statement II are true

2 Both statement- I and statement II are false

3 Statement I is true and statement II is false

4 Statement I is false and statement II is true

Ans. (3) Conceptual

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Conceptual