Embibe Experts Solutions for Chapter: Solved Mathematics Paper-1, Exercise 1: Exercise

Find the vector equation of the plane whose Cartesian form of equation is $3x-4y+2z=5$.

Let $\mathrm{P}\left(\mathrm{C}\right)=0.4;\mathrm{P}\left(\mathrm{D}\right)=0.5;\mathrm{P}(\mathrm{C}\mid \mathrm{D})=0.6$. Are $C$ and $D$ independent events? Give a reason for your answer.

Examine the continuity of the function: $f\left(x\right)=\left\{\begin{array}{ll}\frac{\left|x\right|}{x},& x\ne 0\\ 1,& x=0\end{array}\right.$ at the point $x=0$.

Show that the maximum value of $f\left(x\right)=x+\frac{1}{x}$ is less than its minimum value.
 

$\left|\begin{array}{ccc}0& b& -c\\ -b& 0& a\\ c& -a& 0\end{array}\right|$ equals to

If $\left|\begin{array}{ccc}a& b& a-b\\ b& c& b-c\\ 2& 1& 0\end{array}\right|=0$, then $a,b$ and $c$ are in

Find the value of $k$ for which the function: $f\left(x\right)=\left\{\begin{array}{ll}kx+1,& x\le \pi \\ \cos x,& x>\pi \end{array}\right.$ is continuous at the point $x=\mathrm{\pi }$.

A test detects a disease correctly $80\%$ of time. But it fails to detect it correctly for $2\%$ of the time. A person is chosen at random from a large population of which $0.6\%$ have the disease. He underwent the test and was reported to have the disease. What is the probability that the person actually has the disease$?$