Embibe Experts Solutions for Exercise 6: Assignment

The minimum value of $64 \sec \theta +27 \mathrm{cosec} \theta$ where $\theta \in \left(0,\frac{\pi }{2}\right)$ is

Consider the function $f\left(x\right)=x \cos x-\sin x$, then identify the statement which is correct.

The slope of the normal at the point with abscissa $x=-2$ of the graph of $f\left(x\right)=\left|x^2-\left|x\right|\right|$ is $\lambda$, then ${\left(\frac{1}{\lambda }\right)}^2$ is equal to

If the tangent at any point $\left(1, 2\right)$ on the curve $y=a{x}^2+bx+\frac{7}{2}$ be parallel to the normal at $\left(-2, 2\right)$ on the curve $y=x^2+6x+10$, then $\left(7a-12b\right)$ is equal to

If $\left(\lambda , \mu \right)$ be a point on curve $x^2=2y$, which is closest to point $\left(0, 5\right)$ then $\left({\lambda }^2+{\mu }^2\right)$ is

The greatest and least values of function $f\left(x\right)={\tan }^{-1}x-\frac{1}{2}\mathcal{l}\mathrm{n}x$ on $\left[\frac{1}{\sqrt{3}}, \sqrt{3}\right]$ are $M$ and $m$ respectively, then ${\left(\frac{\pi }{M+m}\right)}^3$ is equal to

If the curve $y=\frac{ax+b}{\left(x-4\right)\left(x-1\right)}$ has extreme value at $\left(2, -1\right)$, then the value of $15\left(5a+7b\right)$ is equal to

If the function $f\left(x\right)=\sin \left(\mathcal{l}\mathrm{n}x\right)-\cos \left(\mathcal{l}\mathrm{n}x\right)$ increases in the interval $\left(e^{x_1},e^{x_2}\right)$, then the value of $15\cos \left(x_1-x_2\right)$ is equal to