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...

$\mathrm{NiCl}_2\left\{\mathrm{P}_{\left(\mathrm{C}_2 \mathrm{H}_5\right)_2}\left(\mathrm{C}_6 \mathrm{H}_5\right)\right\}_2$ exhibits temperature dependent magnetic behaviour (paramagnetic/ diamagnetic). the coordination geometries of $\mathrm{Ni}^{2+}$ in the paramagnetic and diamagnetic...

The atomic masses of He and Ne are 4 and 20 a.m.u., respectively. The value of the de Broglie wavelength...

An aqueous solution ox $\mathbf{X}$ is added slowly to an aqueous solution of $\mathbf{Y}$ as shown in list I ....

The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a...

Match the chemical conversions in List I with the appropriate reagents in List II and select the correct answer using...

Two spherical planets $P$ and $Q$ have the same unfirom density $\rho$, masses $M_P$ and $M_Q$, an surface areas $A$...

The total number of carboxylic acid groups in the product P is

The total number of lone-pairs of electrons in melamine is