For a first order reaction, \(A\to  P\), \(t_{1/2}\) (half-life) is\(10\,days\). The time required for \(\frac{{{1^{th}}}}{4}\) conversion of \(A\) (in days) is: \((\ln\, 2\, = 0.693,\, \ln\, 3\, = 1.1)\).

\(250\, \mathrm{~mL}\) of \(0.5\, \mathrm{M}\, \mathrm{NaOH}\) was added to \(500\, \mathrm{~mL}\) of \(1\, \mathrm{M}\, \mathrm{HCl}\) The number of unreacted \(\mathrm{HCl}\) molecules in the solution after complete reaction is \(......\,\times 10^{21}\). (Nearest integer) \(\left(\mathrm{N}_{\mathrm{A}}=6.022 \times 10^{23}\right)\)

The correct statement amongst the following is :

The five successive ionization enthalpies of an element are \(800,2427,3658,25024\) and \(32824\) \(kJ mol ^{-1}\). The number of valence electrons in the element is 

Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below. \(\mathrm{A}+\mathrm{B} \underset{\text { Step } 3}{\text { Step } 1} \mathrm{C} \xrightarrow{\text { Step } 2} \mathrm{P}\) Some details of the above reaction are listed below.

Step	Rate constant\(\left(\sec ^{-1}\right)\)	Activation energy\(\left(\mathrm{kJ} \mathrm{mol}^{-1}\right)\)
\(1\)	\({k}_1\)	\(300\)
\(2\)	\({k}_2\)	\(200\)
\(3\)	\({k}_3\)	\(\mathrm{Ea}_3\)

If the overall rate constant of the above transformation (k) is given as \(\mathrm{k}=\frac{\mathrm{k}_1 \mathrm{k}_2}{\mathrm{k}_3}\) and the overall activation energy \(\left(E_2\right)\) is \(400 \mathrm{~kJ} \mathrm{~mol}^{-1}\), then the value of \(\mathrm{Ea}_3\) is _______ \(\mathrm{kJ} \mathrm{mol}^{-1}\). (nearest integer)

The number of species having non-pyramidal shape among the following is \((A)\) \({SO}_{3}\)   \((B)\) \({NO}_{3}^{-}\)    \((C)\) \({PCl}_{3}\)   \((D)\) \({CO}_{3}^{2-}\)

Consider the isomers of hydrocarbon with molecular formula \(C_5H_{10}\). These isomers do not decolourise \(KMnO_4\) solution. These isomers are subjected to chlorination with chlorine in presence of light to give monochloro compounds. The total number of monochloro compounds (structural isomers only) formed is _______.

Elements X and Y belong to Group 15. The difference between the electronegativity values of 'X' and phosphorus is higher than that of the difference between phosphorus and 'Y'. 'X' & 'Y' are respectively

In Young's double slit experiment, the distance between slits and the screen is \(1 .0\,\,m\) and monochromatic light of \(600\,\,nm\)  is being used. A person standing near the slits is looking at the fringe pattern. When the separation between the slits is varied, the interference pattern disappears for a particular distance \(d_0\) between the slits . If the angular resolution of the eye is \(\frac {1}{60}^o,\) the value of \(d_0\)  is close to......\(mm\)

Ice at \(-20\,^oC\) is added to \(50\,g\) of water at \(40\,^oC.\) When the temperature of the mixture reaches \(0\,^oC,\) it is found that \(20\,g\) of ice is still unmelted. The amount of ice added to the water was close to ........\(g\) (Specific heat of water \(= 4.2\,J/g/^oC)\) Heat of fusion of water at \(0^oC = 334\,J/g\) )

\(\frac{6}{3^{26}}+\frac{10 \cdot 1}{3^{25}}+\frac{10 \cdot 2}{3^{24}}+\frac{10 \cdot 2^2}{3^{23}}+\ldots+\frac{10 \cdot 2^{24}}{3}\) is equal to

The number of integral values of \(k\) for which the line, \(3 x+4 y=k\) intersects the circle, \(\mathrm{x}^{2}+\mathrm{y}^{2}-2 \mathrm{x}-4 \mathrm{y}+4=0\) at two distinct points is

The ' spin only ' magnetic moment value of \(\mathrm{MO}_4{ }^{2-}\) is _______ BM. (Where \(\mathrm{M}\) is a metal having least metallic radii. among \(\mathrm{Sc}, \mathrm{Ti}, \mathrm{V}, \mathrm{Cr}, \mathrm{Mn}\) and \(\mathrm{Zn}\) ). (Given atomic number: \(\mathrm{Sc}=21, \mathrm{Ti}=22, \mathrm{~V}=23\), \(\mathrm{Cr}=24, \mathrm{Mn}=25\) and \(\mathrm{Zn}=30)\)