VITEEE 2025 | Application of Derivatives Question 1 | Mathematics

Let $f(x)$ be a polynomial of degree 6 divisible by $x^3$ and having a point of extremum at $x=2$. If $f^{\prime}(x)$ is divisible by $1+x^2$, then find the value of $\frac{3 f(2)}{f(1)}$

None of these

VITEEE 2025

MCQ (Single Correct Answer)

-1

The function, $f(x)=(3 x-7) x^{2 / 3}, x \in R$ is increasing for all $x$ lying in

$(-\infty, 0) \cup\left(\frac{3}{7}, \infty\right)$

$(-\infty, 0) \cup\left(\frac{14}{15}, \infty\right)$

$\left(-\infty, \frac{14}{15}\right)$

$\left(-\infty, \frac{14}{15}\right) \cup(0, \infty)$

VITEEE 2025

MCQ (Single Correct Answer)

-1

The minimum value of $(u-v)^2+\left(\sqrt{2-u^2}-\frac{9}{v}\right)^2$, where $0 < u < \sqrt{2}$ and $v > 0$

VITEEE 2024

MCQ (Single Correct Answer)

-1

The length of three sides of a trapezium are equal, each being 10 cms . Then, the maximum area $\left(\mathrm{cm}^2\right)$ of the trapezium is

$75 \sqrt{2}$

$50 \sqrt{2}$

$50 \sqrt{3}$

$75 \sqrt{3}$

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