Circle(s) touching $x$-axis at a distance 3 from the origin and having an intercept of length $2 \sqrt{7}$ on $y$-axis...

For a dilute solution containing 2.5 g of a non- volatile non- electrolyte solute in 100 g of water, the...

The major product H in the given reaction sequence is

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that...

The shape of $\mathrm{XeO}_2 \mathrm{~F}_2$ molecule is

Let $z$ be a complex number such that the imaginary part of $z$ is non zero and $a=z^2+z+1$ is real....

Using the data provided, calculate the multiple bond energy $\left(\mathrm{kJ} \mathrm{mol}^{-1}\right)$ of a $\mathrm{C} \equiv \mathrm{C}$ bond $\mathrm{C}_2 \mathrm{H}_2$. That...

The compound that undergoes decarboxlylation most readily under mild condition is

Perpendicular are drawn from points on the line $\frac{x+2}{2}=\frac{y+1}{-1}=\frac{z}{3}$ to the plane $x+y+z=3$. The feet of perpendiculars lie on the...

For $a \in R$ (the set of all real numbers), $a \neq-1, \lim _{n \rightarrow \infty} \frac{\left(1^a+2^a+\ldots+n^a\right)}{(n+1)^{a-1}[(n a+1)+(n a+2)+\ldots+(n a+n)]}=\frac{1}{60}$....

For $a>b>c>0$, the distance between $(1,1)$ and the point of intersection of the lines $a x+b y+c=0$ and $...

In the cyanide extraction process of silver from argentite ore, the oxidizing and reducing agents used are

The reaction of white phosphorous with aqueous NaOH gives phosphine along with another phosphorus containing compound. The reaction type; the...

Let complex numbers $\alpha$ and $\frac{1}{\bar{\alpha}}$ lies on circles $\left(x-x_0\right)^2+\left(y-y_0\right)^2=r^2$ and $\left(x-x_0\right)^2+\left(y-y_0\right)^2=4 r^2$, respectively. If $\mathrm{z}_0=\mathrm{x}_0+\mathrm{iy}$ satisfies the equation $2\left|\mathrm{z}_0\right|^2=\mathrm{r}^2+2$,...

Let $\overrightarrow{P R}=3 \hat{i}+\hat{j}-2 \hat{k}$ and $\overrightarrow{S Q}=\hat{i}-3 \hat{j}-4 \hat{k}$ determine diagonals of a parallelogram $P Q R S$ and...

A tetrapeptide has -COOH group on alanine. This produces glycine (Gly), valine (Val), phenyl alanine (Phe) and alanine (Ala), on...

The value of $\cot \left(\sum_{n=1}^{23} \cot ^{-1}\left(1+\sum_{k=1}^n 2 k\right)\right)$ is

EDTA ${ }^4$ is ethylenediaminetetraacetate ion. The total number of $\mathrm{N}-\mathrm{CO}-\mathrm{O}$ bond angles in $[\mathrm{CO}(\text { EDTA })]^{1-}$ complex ion...