A stream of electrons from a heated filaments was passed two charged plates kept at a potential difference \(V\, esu.\) If \(e\) and \(m\) are charge and mass of an electron, respectively, then the value of \(h/\lambda ,\) (where \(\lambda\) is wavelength associated with electron wave) is given by :

The reaction \(2N_2O_5\,(g) \to  4NO_2\,(g) + O_2\,(g)\) follows first order kinetics. The pressure of a vessel containing only \(N_2O_5\) was found to increase from \(50\,mmHg\) to \(87 .5\,mmHg\) in \(30\,min.\) The pressure exerted by the gases after \(60\,min.\) will be .......... \(mmHg\) (assume temperature remains constant)

The number of \(sp^2\) hybrid orbitals in a molecule of benzene is

If a reaction follows the Arrhenius equation, the plot \(\ln k\) vs \(1/(RT)\) gives straight line with a gradient \((-y)\) \(unit\). The energy required to activate the reactant is

Given below are two statements :
Statement I : A homolepitc octahedral complex, formed using monodentate ligands, will not show stereoisomerism.
Statement II : cis- and trans- platin are heteroleptic complexes of Pd.
In the light of the above statements, choose the correct answer from the options given below.

Which of the following statement is true with respect to \(\mathrm{H}_2 \mathrm{O}, \mathrm{NH}_3\) and \(\mathrm{CH}_4\) ?
A. The central atoms of all the molecules are \(\mathrm{sp}^3\) hybridized.
B. The \(\mathrm{H}-\mathrm{O}-\mathrm{H}, \mathrm{H}-\mathrm{N}-\mathrm{H}\) and \(\mathrm{H}-\mathrm{C}-\mathrm{H}\) angles in the above molecules are \(104.5^{\circ}, 107.5^{\circ}\) and \(109.5^{\circ}\), respectively.
C. The increasing order of dipole moment is \(\mathrm{CH}_4 \lt \mathrm{NH}_3 \lt \mathrm{H}_2 \mathrm{O}\).
D. Both \(\mathrm{H}_2 \mathrm{O}\) and \(\mathrm{NH}_3\) are Lewis acids and \(\mathrm{CH}_4\) is a Lewis base.
E. A solution of \(\mathrm{NH}_3\) in \(\mathrm{H}_2 \mathrm{O}\) is basic. In this solution \(\mathrm{NH}_3\) and \(\mathrm{H}_2 \mathrm{O}\) act as Lowry-Bronsted acid and base respectively.
Choose the correct answer from the options given below:

The major product \([B]\) in the following sequence of reactions is \(\begin{array}{*{20}{c}}
  {C{H_3} - C = CH - C{H_2}C{H_3}} \\ 
  {|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} \\ 
  {CH{{(C{H_3})}_2}\,\,\,\,\,\,\,\,\,\,} 
\end{array}\xrightarrow[{(ii)\,{H_2}{O_2},O{H^ - }}]{{(i)\,{B_2}{H_6}}}[A]\)\(\xrightarrow[\Delta ]{{dil.\,{H_2}S{O_4}}}[B]\)

Normal of  the curve \({x^2} + 2xy - 3{y^2} = 0\) at point \((1,1)\) intersect curve again at  which quadrant

40 mL of a mixture of \(\mathrm{CH}_3 \mathrm{COOH}\) and HCl (aqueous solution) is titrated against 0.1 M NaOH solution conductometrically. Which of the following statement is correct?

The series of positive multiples of \(3\) is divided into sets : \(\{3\},\{6,9,12\},\{15,18,21,24,27\}, \ldots\) Then the sum of the elements in the \(11^{\text {th }}\) set is equal to \(................\)

Let \(f(x)=x-1\) and \(g(x)=e^x\) for \(x \in \mathbb{R}\). If \(\frac{d y}{d x}=\left(e^{-2 \sqrt{x}} g(f(f(x)))-\frac{y}{\sqrt{x}}\right), y(0)=0\), then \(y(1)\) is :-

Assertion : Nitrogen and oxygen are the main components in the atmosphere but these do not react to form oxides of nitrogen. Reason : The reaction between nitrogen and oxygen requires high temperature.

A point on the ellipse, \(4x^2 + 9y^2 = 36\), where the normal is parallel to the line, \(4x -2y-5 = 0\) , is