\(\mathrm{S}=\{\mathrm{z} \in \mathrm{C} /|\mathrm{z}-1+\mathrm{i}|=1\}\) represents

In \(\triangle \mathrm{ABC}\), if \(\frac{1}{\mathrm{r}_1}, \frac{1}{\mathrm{r}_2}\) and, \(\frac{1}{\mathrm{r}_3}\) are in arithmetic progression, then \(\mathrm{r}_2: \mathrm{r}=\)

A plane passing through \((-1,2,3)\) and whose normal makes equal angles with the coordinate axes is

The functions \(f(x)=x e^{-x}, \forall(x \in R)\) attains a maximum value at \(x\) is equal to

The interval in which the function $f\left(x\right)=2x^2-\log x,$ for $x>0$ decreases is

If \((1+x)^n=p_0+p_1 x+p_2 x^2+\ldots+p_n x^n\), then \(p_0+p_3+p_6+\ldots=\)

If the mean and standard deviation of a binomial distribution are $20$ and $4$, respectively, then the number of trials is ________

The distance of the point $\left(1,2\right)$ from the line $x+y+5=0$ measured along the line parallel to $3x-y=7$ is equal to

The first ionization enthalpies of $\mathrm{Mg}$ and $\mathrm{Al}$ can be expected to be

Calculate the $\mathrm{pOH}$ of $0.10\mathrm{MHCl}$ solution.

Let $a,b,c$ be such that $(b+c)\ne 0$ and

$\left|\begin{array}{ccc}a& a+1& a-1\\ -b& b+1& b-1\\ c& c-1& c+1\end{array}\right|$$+\left|\begin{array}{ccc}a+1& b+1& c-1\\ a-1& b-1& c+1\\ {\left(-1\right)}^{n+2}a& {\left(-1\right)}^{n-1}b& {\left(-1\right)}^{n}c\end{array}\right|=0$

Then the value of $n$ is

If two vectors \(\mathbf{A}\) and \(\mathbf{B}\) are mutually perpendicular, then the component of \(\mathbf{A}-\mathbf{B}\) along the direction of \(\mathbf{A}+\mathbf{B}\) is

Match the following List I with List II.
\(\begin{array}{|c|c|c|}
\hline & \text { List I } & \text { List II } \\
\hline \text { (A) } & \text { Transverse wave (i) } & \begin{array}{l}
\text {Vibrations parallel to the } \\
\text {direction of propagation }
\end{array} \\
\hline \text { (B) } & \begin{array}{l}
\text {Longitudinal wave }
\end{array} & \begin{array}{l}
\text {Vibrations perpendicular to } \\
\text {the direction of propagation }
\end{array} \\
\hline \text { (C) } & \text { Beats } & \begin{array}{l}
\text {Superposition of waves } \\
\text {travelling in the opposite directions }
\end{array} \\
\hline \text { (D) } & \text { Stationary waves (iv) } & \begin{array}{l}
\text {Superposition of waves } \\
\text {travelling in same direction }
\end{array} \\
\hline
\end{array}\)
The correct answer is