Embibe Experts Solutions for Chapter: Solved Mathematics Paper-2, Exercise 1: Exercise

$\mathrm{O}$ is the origin and $\mathrm{A}$ is the point $(a,b,c)$. Find the equation of the plane through $\mathrm{A}$ at right angles to $\mathrm{OA}$.

Examine the continuity of the function: $f\left(x\right)=\left\{\begin{array}{cc}\frac{|x-3|}{2(x-3)}& ,x\ne 3\\ 0& ,x=3\end{array}\right.$ at the point $x=3$.

Show that the maximum value of $\frac{\log x}{x}$ is $\frac{1}{e}$.

If $\left|\begin{array}{cc}2x& 5\\ 8& x\end{array}\right|=\left|\begin{array}{cc}6& -2\\ 7& 3\end{array}\right|$ write the value of $x$.

$\left|\begin{array}{ccc}1& 1& 1\\ 1& 1+x& 1\\ 1& 1& 1+y\end{array}\right|$ equals to

Find the area bounded by the curves $y^2=4ax$ and $x^2=4ay, a>0$.

Use elementary row operation to determine whether the following matrix is invertible and hence find the inverse whenever possible.

$\left(\begin{array}{ccc}1& 2& 1\\ 2& 1& -1\\ 1& 5& 4\end{array}\right)$

An examinee has to answer a question on a multiple choice type test. The answer to this question is either known to him or else he simply guesses at it. The probability that he knows the answer is $\frac{4}{5}$. He is correct in $25\%$ cases when he guesses at the answer. Find the probability that he knows the answer given that he answered it correctly.