Drug \(X\) becomes ineffective after \(50 \%\) decomposition. The original concentration of drug in a bottle was \(16 \mathrm{mg} / \mathrm{mL}\) which becomes \(4 \mathrm{mg} / \mathrm{mL}\) in 12 months. The expiry time of the drug in months is __________. Assume that the decomposition of the drug follows first order kinetics.

Consider titration of \(NaOH\) solution versus \(1.25\, M\) oxalic acid solution. At the end point following burette readings were obtained. \((i)\) \(4.5\, mL\) \(\quad (ii)\) \(4.5\, mL\) \(\quad (iii)\) \(4.4\, mL\) \((iv)\) \(4.4\, mL\) \(\quad (v)\) \(4.4\, mL\) If the volume of oxalic acid taken was \(10.0 \,mL\) then the molarity of the \(NaOH\) solution is .... \(M.\) (Rounded-off to the nearest integer)

Given below are four compounds:
(a) n-propyl chloride,
(b) iso-propyl chloride,
(c) sec-butyl chloride,
(d) neo-pentyl chloride.
Percentage of carbon in the one which exhibits optical isomerism is:

Gaseous cyclobutene isomerizes to butadiene in a first order process which has a \('k'\) value of \(3.3 \times 10^{-4} s ^{-1}\) at \(153^{\circ} C\). The time in minutes it takes for the isomerization to proceed \(40 \%\) to completion at this temperature is .......... (Rounded off to the nearest integer)

For any given series of spectral lines of atomic hydrogen, let \(\Delta \bar V\, = \,\Delta {\bar V_{\max }}\, - \,\Delta {\bar V_{\min }}\) be the difference in maximum and minimum frequencies in \(cm^{-1}.\) the ration \(\Delta {\bar V_{Lymann}}/\,\Delta {\bar V_{Balmer}}\) is

One half cell in a voltaic cell is constructed by dipping silver rod in \(AgNO_3\) solution of unknown concentration, other half cell is \(Zn\) rod dipped in \(1\) molar solution of \(ZnSO_4\). A voltage of \(1.60\text{ V}\) is measured at \(298\text{ K}\) for this cell. What is the concentration of \(Ag^+\) ions used in terms of \(\log x\) (\(x = [Ag^+]\)) ?
\(E^\circ_{Zn^{2+}/Zn} = -0.76\text{ V}\), \(E^\circ_{Ag^+/Ag} = +0.80\text{ V}\), \(\dfrac{2.303 RT}{F} = 0.059\text{ V}\)

At \(-20^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) pressure, a cylinder is filled with equal number of \(\mathrm{H}_2 . \mathrm{I}_2\) and \(\mathrm{HI}\) molecules for the reaction \(\mathrm{H}_2(\mathrm{~g})+\mathrm{I}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g})\), the \(\mathrm{K}_{\mathrm{p}}\) for the process is \(\mathrm{x} \times 10^{-1} \cdot \mathrm{x}=\) _______. [Given : \(\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\) ]

Let three vectors \(\overrightarrow{\mathrm{a}}=\alpha \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}\), \(\vec{b}=5 \hat{i}+3 \hat{j}+4 \hat{k}, \vec{c}=x \hat{i}+y \hat{j}+z \hat{k}\) from a triangle such that \(\overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}\) and the area of the triangle is \(5 \sqrt{6}\). if \(\alpha\) is a positive real number, then \(|\overrightarrow{\mathrm{c}}|^2\) is :

Let M denote the set of all real matrices of order \(3 \times 3\) and let \(\mathrm{S}=\{-3,-2,-1,1,2\}\). Let
\(\mathrm{S}_1=\left\{\mathrm{A}=\left[a_{\mathrm{ij}}\right] \in \mathrm{M}: \mathrm{A}=\mathrm{A}^{\mathrm{T}} \text { and } a_{\mathrm{ij}} \in \mathrm{~S}, \forall \mathrm{i}, \mathrm{j}\right\}, \)
\( \mathrm{S}_2=\left\{\mathrm{A}=\left[a_{\mathrm{ij}}\right] \in \mathrm{M}: \mathrm{A}=-\mathrm{A}^{\mathrm{T}} \text { and } a_{\mathrm{ij}} \in \mathrm{~S}, \forall \mathrm{i}, \mathrm{j}\right\}, \)
\( \mathrm{S}_3=\{\mathrm{A}=\left[a_{\mathrm{ij}}\right] \in \mathrm{M}: a_{11}+a_{22}+a_{33}=0\) and \(a_{\mathrm{ij}} \in \mathrm{~S}, \forall \mathrm{i}, \mathrm{j}\}\)
If \(n\left(\mathrm{~S}_1 \cup_2 \mathrm{US}_3\right)=125 \alpha\), then \(\alpha\) equals _______

If the mirror image of the point \(\mathrm{P}(3,4,9)\) in the line \(\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-2}{1}\) is \((\alpha, \beta, \gamma)\), then \(14(\alpha+\beta+\gamma)\) is :

A circle touching the \(x-\) axis at \((3, 0)\) and making an intercept of length \(8\) on the \(y-\) axis passes through the point 

Let a parabola \(P\) be such that its vertex and focus lie on the positive \(x\) - axis at a distance \(2\) and \(4\) units from the origin, respectively. If tangents are drawn from \(O\,(0,0)\) to the parabola \(P\) which meet \(\mathrm{P}\) at \(\mathrm{S}\) and \(\mathrm{R}\), then the area (in \(sq.\, units\)) of \(\triangle \mathrm{SOR}\) is equal to:

A solution is \(0.1\, \mathrm{M}\) in \(\mathrm{Cl}^{-}\)and \(0.001\, \mathrm{M}\) in \(\mathrm{CrO}_{4}{ }^{2-}\). Solid \(\mathrm{AgNO}_{3}\) is gradually added to it. Assuming that the addition does not change in volume and \(\mathrm{K}_{\mathrm{sp}}(\mathrm{AgCl})=1.7 \times 10^{-10} \,\mathrm{M}^{2}\) and \(\mathrm{K}_{\mathrm{sp}}\left(\mathrm{Ag}_{2} \mathrm{CrO}_{4}\right)=1.9 \,\times 10^{-12} \mathrm{M}^{3}\) Select correct statement from the following :