The order of the average bond length of the given bonds is

Assertion : \(\left[\mathrm{B}\left(\mathrm{OH}_2\right)_6\right]^{3+}\) and \(\left[\mathrm{B}(\mathrm{OH})_4\right]^{-}\)form octahedral and tetrahedral structures. Reason : Being electron deficient, boron readily reacts with Lewis bases like \(\mathrm{H}_2 \mathrm{O}, \mathrm{OH}^{-}\) The correct option among the following is

The product obtained at anode when \(50 \%\) \(\mathrm{H}_2 \mathrm{SO}_4\) aqueous solution is electrolysed using platinum electrodes is :

Match the following.

A B C D

Phosphine is prepared by the reaction of \(\mathrm{P}_4\) with which of the following?

Match the following.

The correct answer 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?

Let \(P(x)\) be a polynomial of degree 3 having extreme value at \(x=1\). If \(\lim _{x \rightarrow 0}\left(\frac{P(x)+4}{x^2}+2\right)=6\), then \(\left(\frac{d P}{d x}\right)_{x=\frac{1}{2}}=\)

A bullet of mass $1 \mathrm{kg}$ fired with a speed $2 \mathrm{m} {\mathrm{s}}^{-1}$ from $x=0$ passes through a block of wood whose centre is kept at a distance of $10 \mathrm{m}$ from the origin as shown in figure. The retarding force $\left(F_r\right)$ on the bullet within the wooden block is $-\frac{0.5}{x}$. The minimum length of the block (upto one decimal digit) required to completely stop the bullet is (Assume $e^4=55$)

In the circuit shown below, the ammeter reading is zero. Then the value of the resistance \(R\) is

In the following compounds, the ones that give positive iodoform test are

\(\begin{aligned} & A(\alpha, \beta)=\left[\begin{array}{ccc}\cos \alpha & \sin \alpha & 0 \\ -\sin \alpha & \cos \alpha & 0 \\ 0 & 0 & e^\beta\end{array}\right] \\ & \Rightarrow[A(\alpha, \beta)]^{-1}=\end{aligned}\)

The differential equation obtained by eliminating the arbitrary constants \(a\) and \(b\) from \(x y=a e^x+b e^{-x}\) is