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

The external and internal radius of a hollow tube in the form of a right circular cylinder are $5 \mathrm{cm}$ and $4 \mathrm{cm}$. If the area of whole surface of the tube is $1188 \mathrm{sq}.\mathrm{cm}$, what is the length of the tube?

The probability that at least one of the events $A$ and $B$ occurs is $\mathrm{0.6.}$ If $A$ and $B$ occur simultaneously with probability $0.2,$ then  $P\left(\overline{A}\right)+P\left(\overline{B}\right)$ is: (where  $\overline{A}$  and  $\overline{B}$ are complements of $A$ and $B$ respectively)$$

Find the equation of the perpendicular to the line $x=5$, passing through the point $\left(5,8\right)$.

Given $P\left(A\right)=0.4$ and $P(A\cup B)=0.7$. Find $P\left(B\right)$ if  $A$ and $B$ are mutually exclusive.

If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2+\sqrt{2}x+3=0,$ form a quadratic polynomial with zeroes $\frac{1}{\alpha },\frac{1}{\beta }.$

Find all the equations of the straight lines in the family of the lines $y=mx-3,$ for which $m$ and the $x-$coordinate of the point of intersection of the lines with $x-y=6$ are integers.

Find the mean and standard deviation for the following data:

The graph shows a particular function $f$.

Find the set of values of $x$ for which $f\left(x\right)<0$.