Amongst the following, the total number of compounds whose aqueous solution turns red litmus paper blue is
\(\begin{array}{llll}
\mathrm{KCN} & \mathrm{K}_2 \mathrm{SO}_4 & \left(\mathrm{NH}_4\right)_2 \mathrm{C}_2 \mathrm{O}_4 & \mathrm{NaCl} \\
\mathrm{Zn}\left(\mathrm{NO}_3\right)_2 & \mathrm{FeCl}_3 & \mathrm{~K}_2 \mathrm{CO}_3 & \mathrm{NH}_4 \mathrm{NO}_3 \\
\mathrm{LiCN} & & &
\end{array}\)

Paragraph:
When a metal rod \(M\) is dipped into an aqueous colourless concentrated solution of compound \(\mathrm{N}\), the solution turns light blue. Addition of aqueous \(\mathrm{NaCl}\) to the blue solution gives a white precipitate \(\mathrm{O}\). Addition of aqueous \(\mathrm{NH}_3\) dissolves \(\mathrm{O}\) and gives an intense blue solution.
Question:
The compound \(N\) is

To form a complete monolayer of acetic acid on \(1 \mathrm{~g}\) of charcoal, \(100 \mathrm{~mL}\) of \(0.5 \mathrm{M}\) acetic acid was used. Some of the acetic acid remained unadsorbed. To neutralize the unadsorbed acetic acid, 40 \(\mathrm{mL}\) of \(1 \mathrm{M} \mathrm{NaOH}\) solution was required. If each molecule of acetic acid occupies \(\mathbf{P} \times 10^{-23} \mathrm{~m}^2\) surface area on charcoal, the value of \(\mathbf{P}\) is _______ [Use given data: Surface area of charcoal \(=1.5 \times 10^2 \mathrm{~m}^2 \mathrm{~g}^{-1} ;\) Avogadro's number \(\left(\mathrm{N}_{\mathrm{A}}\right)=6.0 \times 10^{23}\) \(\left.\mathrm{mol}^{-1}\right]\)

\(2.5 \mathrm{~mL}\) of \(\frac{2}{5} \mathrm{M}\) weak monoacidic base \(\left(K_b=1 \times 10^{-12}\right.\) at \(\left.25^{\circ} \mathrm{C}\right)\) is titrated with \(\frac{2}{15}\) \(\mathrm{M} \mathrm{HCl}\) in water at \(25^{\circ} \mathrm{C}\). The concentration of \(\mathrm{H}^{+}\)at equivalence point is \(\left(K_w=1 \times 10^{-14}\right.\) at \(\left.25^{\circ} \mathrm{C}\right)\)

The work function ( \(\Phi\) ) of some metals is listed below. The number of metals which will show photoelectric effect when light of \(300 \mathrm{~nm}\) wavelength falls on the metal is

The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is (are) correct?

In the reaction,
\(
2 \mathrm{X}+\mathrm{B}_2 \mathrm{H}_6 \longrightarrow\left[\mathrm{BH}_2(\mathrm{X})_2\right]^{+}\left[\mathrm{BH}_4\right]^{-}
\)
The amine (s) \(X\), is (are)

Let $\stackrel{r}{7\overbrace{5\dots 5}7}$ denote the $\left(r+2\right)$ digit number where the first and the last digits are $7$ and the remaining $r$ digits are $5$. Consider the sum $S=77+757+7557+\dots +\stackrel{98}{7\overbrace{5\dots 5}7}$. If $S= \frac{7{\displaystyle \stackrel{99}{\overbrace{5\dots 5 }}}7+m}{n}$, where $m$ and $n$ are natural numbers less than $3000$, then the value of $m+n$ is

Paragraph:

Schemes \(1\) and \(2\) describe sequential transformation of alkynes \(\mathbf{M}\) and \(\mathbf{N}\). Consider only the major products formed in each step for both the schemes.



Question:
The correct statement with respect to product \(\mathbf{Y}\) is

A galvanometer gives full scale deflection with $0·006 A$ current. By connecting it to a $4990 \Omega$ resistance, it can be converted into a voltmeter of range $0-30 V$. If connected to a $\frac{2\mathrm{n}}{249}\mathrm{\Omega }$ resistance, it becomes an ammeter of range $0- 1·5 A$. The value of $n$ is

A ball is thrown from ground at an angle $\mathrm{\theta }$ with horizontal and with an initial speed ${\mathrm{u}}_0.$ For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when it hits the ground for the first time is ${\mathrm{V}}_1.$ After hitting the ground, ball rebounds at the same angle $\mathrm{\theta }$ but with a reduced speed of $\frac{{\mathrm{u}}_0}{\mathrm{\alpha }}.$ Its motion continues for a long time as shown in figure. If the magnitude of average velocity of the ball for entire duration of motion is $0.8{\mathrm{V}}_1,$ the value of $\mathrm{\alpha }$ is______

Paragraph :
When liquid medicine of density \(\rho\) is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop.
We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension \(T\) when the radius of the drop is \(R\). When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.
Question :
If \(r=5 \times 10^{-4} \mathrm{~m}, \rho=10^3 \mathrm{~kg} \mathrm{~m}^{-3}\), \(g=10 \mathrm{~ms}^{-2}, T=0.11 \mathrm{Nm}^{-1}\), the radius of the drop when it detaches from the dropper is approximately

An acidified solution of $0.05 \mathrm{M} {\mathrm{Zn}}^{2+}$ is saturated with $0.1 \mathrm{M} {\mathrm{H}}_2\mathrm{S}$. What is the minimum molar concentration $\left(\mathrm{M}\right)$ of ${\mathrm{H}}^{+}$ required to prevent the precipitation of $\mathrm{ZnS}$? Use ${\mathrm{K}}_{\mathrm{sp}}\left(\mathrm{ZnS}\right)=1.25\times {10}^{-22}$ and overall dissociation constant of ${\mathrm{H}}_2\mathrm{S}, {\mathrm{K}}_{\mathrm{NET}}={\mathrm{K}}_1{\mathrm{K}}_2=1\times {10}^{-21}$