Given below are two statements : Statement \(-I :\) The pentavalent oxide of group\(- 15\) element. \(E _{2} O _{5}\). is less acidic than trivalent oxide. \(E _{2} O _{3}\). of the same element. Statement \(-II :\) The acidic character of trivalent oxide of group \(15\) elements. \(E _{2} O _{3}\). decreases down the group. In light of the above statements. choose most appropriate answer from the options given below

Arrange the following bonds according to their average bond energies in descending order  \(\mathrm{C}-\mathrm{Cl}, \mathrm{C}-\mathrm{Br}, \mathrm{C}-\mathrm{F}, \mathrm{C}-\mathrm{I}\)

Which of the following sets of quantum numbers is not allowed?

Which statements are NOT TRUE about \( XeO_{2}F_{2} \)?
A. It has a see-saw shape.
B. Xe has 5 electron pairs in its valence shell in \( XeO_{2}F_{2} \).
C. The O-Xe-O bond angle is close to \( 180^{\circ} \).
D. The F-Xe-F bond angle is close to \( 180^{\circ} \).
E. Xe has 16 valence electrons in \( XeO_{2}F_{2} \).
Choose the correct answer from the options given below.

A proton and a \(Li ^{3+}\) nucleus are accelerated by the same potential. If \(\lambda_{L i}\) and \(\lambda_{P}\) denote the de Broglie wavelengths of \(Li ^{3+}\) and proton respectively, then the value of \(\frac{\lambda_{ Li }}{\lambda_{ P }}\) is \(x \times 10^{-1}\).The value of \(x\) is ............ (Rounded off to the nearest integer) (Mass of \(Li ^{3+}=8.3\) mass of proton)

The reaction that occurs in a breath analyser, a device used to determine the alcohol level in a person's blood stream is \(2 \mathrm{~K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}+8 \mathrm{H}_{2} \mathrm{SO}_{4}+3 \mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O} \rightarrow 2 \mathrm{Cr}_{2}\left(\mathrm{SO}_{4}\right)_{3}+\) \(3 \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}+2 \mathrm{~K}_{2} \mathrm{SO}_{4}+11 \mathrm{H}_{2} \mathrm{O}\) If the rate of appearance of \(\mathrm{Cr}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) is \(2.67 \,\mathrm{~mol}\) \(\min ^{-1}\) at a particular time, the rate of disappearance of \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}\) at the same time is ...... \(\mathrm{mol}\, \mathrm{min}^{-1}\) (Nearest integer)

For the reaction \(2 \mathrm{NO}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g})\), when \(\Delta \mathrm{S}=-176.0\, \mathrm{JK}^{-1}\) and \(\Delta \mathrm{H}=-57.8\, \mathrm{~kJ}\, \mathrm{~mol}^{-1}\), the magnitude of \(\Delta \mathrm{G}\) at \(298\, \mathrm{~K}\) for the reaction is \(......\,\mathrm{kJ} \mathrm{mol}^{-1} .\) (Nearest integer)

If \(\overrightarrow{ a }=\hat{ i }+2 \hat{ k }, \overrightarrow{ b }=\hat{ i }+\hat{ j }+\hat{ k }, \overrightarrow{ c }=7 \hat{ i }-3 \hat{ k }+4 \hat{ k }\) \(\overrightarrow{ r } \times \overrightarrow{ b }+\overrightarrow{ b } \times \overrightarrow{ c }=\overrightarrow{0}\) and \(\overrightarrow{ r } \cdot \overrightarrow{ a }=0\) then \(\overrightarrow{ r } \cdot \overrightarrow{ c }\) is equal to :

Fuel cell, using hydrogen and oxygen as fuels, \(A\). has been used in spaceship \(B\). has as efficiency of \(40 \%\) to produce electricity \(C\). uses aluminium as catalysts \(D\). is eco-friendly \(E\). is actually a type of Galvanic cell only

The position of a particle related to time is given by \(x =\left(5 t ^2-4 t +5\right) m\). The magnitude of velocity of the particle at \(t=2\,s\) will be \(...........ms^{-1}\)

The increasing order of the \(pK_b\) of the following compound is

Let \(a\) and \(b\) respectively be the semitransverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation \(9e^2 - 18e + 5 = 0.\) If \(S(5, 0)\) is a focus and \(5x = 9\) is the corresponding directrix of this hyperbola, then \(a^2 - b^2\)  is equal to