WB JEE 2011 | Limits, Continuity and Differentiability Question 25 | Mathematics

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WB JEE 2011

MCQ (Single Correct Answer)

-0.25

The function f(x) = ax + b is strictly increasing for all real x if

a > 0

a < 0

a = 0

a $$\le$$ 0

WB JEE 2025

MCQ (Single Correct Answer)

-0.25

If $f(x)=\left\{\begin{array}{ll}x^2+3 x+a, & x \leq 1 \\ b x+2, & x>1\end{array}, x \in \mathbb{R}\right.$, is everywhere differentiable, then :

$a=3, b=5$

$a=0, b=5$

$a=0, b=3$

$a=b=3$

WB JEE 2025

MCQ (Single Correct Answer)

-0.25

Let $f(x)=|1-2 x|$, then

$f(x)$ is continuous but not differentiable at $x=\frac{1}{2}$.

$f(x)$ is differentiable but not continuous at $x=\frac{1}{2}$.

$f(x)$ is both continuous and differentiable at $x=\frac{1}{2}$.

$f(x)$ is neither differentiable nor continuous at $x=\frac{1}{2}$.

WB JEE 2025

MCQ (Single Correct Answer)

-0.25

A function $f: \mathbb{R} \rightarrow \mathbb{R}$, satisfies $f\left(\frac{x+y}{3}\right)=\frac{f(x)+f(y)+f(0)}{3}$ for all $x, y \in \mathbb{R}$. If the function ' $f$ ' is differentiable at $x=0$, then $f$ is

linear

quadratic

cubic

biquadratic

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