The value of the numerically greatest term in the expansion of $(2x+3y{)}^{11}$ when $x=\frac{1}{2}$ and $y=\frac{1}{3}$ is

\(\lim _{n \rightarrow \infty}\left[\frac{n+3}{n^2+1^2}+\frac{n+6}{n^2+2^2}+\frac{n+9}{n^2+3^2}+\ldots+\frac{2}{n}\right]=\)

Number of triangles whose vertices are the points \((x, y)\) in the XY-plane with integer coordinates satisfying \(0 \leq x \leq 4\) and \(0 \leq y \leq 4\) is

If \(A\) is a square matrix of order 3 , then \(\left|\operatorname{Adj}\left(\operatorname{Adj} A^2\right)\right|=\)

If \(z=\sec (y-a x)+\tan (y+a x)\), \(\frac{\partial^2 z}{\partial x^2}-a^2 \frac{\partial^2 z}{\partial y^2}\) is equal to

If \(\alpha, \beta\) are non-zero integers and \(\mathrm{z}=(\alpha+i \beta)(2+7 i)\) is a purely imaginary number, then minimum value of \(|z|^2\) is

If \(x=\sin 2 \theta \cos 3 \theta, y=\sin 3 \theta \cos 2 \theta\), then \(\frac{d y}{d x}=\)

The stability order of the given alkenes is

The standard reduction potentials of \(\mathrm{Zn}^{2+}\left|\mathrm{Zn}, \mathrm{Cu}^{2+}\right| \mathrm{Cu}\) and \(\mathrm{Ag}^{+} \mid \mathrm{Cu}\) and \(\mathrm{Ag}^{+} \mid \mathrm{Ag}\) are respectively \(-0.76,0.34\) and \(0.8 \mathrm{~V}\). The following cells were constructed : (1) \(\mathrm{Zn}\left|\mathrm{Zn}^{2+}\right|\left|\mathrm{Cu}^{2+}\right| \mathrm{Cu}\) (2) \(\mathrm{Zn}\left|\mathrm{Zn}^{2+}\right|\left|\mathrm{Ag}^{+}\right| \mathrm{Ag}\) (3) \(\mathrm{Cu}\left|\mathrm{Cu}^{2+} \| \mathrm{Ag}^{+}\right| \mathrm{Ag}\) What is the correct order of \(E_{\text {cell }}^{\circ}\) of these cells?

The reaction conditions used for converting 1, 2-dibromo ethane to ethylene are

A slab of stone of area \(3600 \mathrm{~cm}^2\) and thickness \(10 \mathrm{~cm}\) is exposed on the lower surface to steam at \(100^{\circ} \mathrm{C}\). A block of ice at \(0^{\circ} \mathrm{C}\) rests on upper surface of the slab. In one how \(4.8 \mathrm{~kg}\) of ice is melted. The thermal conductivity of the stone in \(\int \mathrm{s}^{-1} \mathrm{~m}^{-1} \mathrm{k}^{-1}\) is (Latent heat of ice \(=3.36 \times 10^5 \mathrm{~J} / \mathrm{kg}\) )

If ${\int }_0^{2a}{x}^2\sqrt{2ax-x^2}dx=k{a}^4$, then $k:\pi =$

Observe the following reaction \(2 A+B \longrightarrow C\) The rate of formation of \(\mathrm{C}\) is \(2.2 \times 10^{-3} \mathrm{~mol}\) \(\mathrm{L}^{-1} \min ^{-1}\). What is the value of \(-\frac{d[A]}{d t}\) (in mol \(\left.\mathrm{L}^{-1} \min ^{-1}\right) ?\)