No Author Solutions for Exercise 7: EXAM GALLERY

If $\underset{x\to c}{\lim }\left(\frac{f\left(x\right)}{g\left(x\right)}\right)$ exists, then

Let $L_1$ be a line with direction ratios $\left(-2,-1, 2\right)$ and $L_2$ be the line joining the points $\left(1,2,3\right)$ and $\left(3,2,1\right)$. If $\theta$ is the angle between the lines $L_1$ and $L_2,$ then$\left|\sin \theta \right|$ equals to

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two non-parallel vectors having equal magnitude, then the vector $\left(\overrightarrow{a}-\overrightarrow{b}\right)\times \left(\overrightarrow{a}\times \overrightarrow{b}\right)$ is parallel to

The numbers $a, b$ and $c$ are distinct and non-negative. If the three vectors $\left(a\hat{i}+a\hat{j}+c\hat{k}\right), \left(c\hat{i}+c\hat{j}+b\hat{k}\right)$ and $\left(\hat{i}+\hat{k}\right)$ are coplanar, then $c$ is

There are $30$ boys and $20$ girls in a class. The mean and variance of their marks are $65$ and $100$ in Maths, respectively. If $5$ grace marks are added to the score of each student, then the revised mean and variance will be, respectively.

If the ratio of the$7^{\text{th}}$ term from the beginning to the$7^{\text{th}}$ term from the end in the expansion of ${\left(2^{\frac{1}{3}}+3^{-\frac{1}{3}}\right)}^n$ is$\frac{1}{6},$  then the value of $n$ is

If three distinct positive numbers $a, b$ and $c$ are in $\mathrm{AP}$ such that $abc=4$, then the value of $b$ is always

If there are $30$ onto mappings from a set containing $n$ elements to the set $\{0,1\},$ then $n$ equals to