For the reaction at \(298 \mathrm{~K}, 2 \mathrm{~A}+\mathrm{B} \rightarrow \mathrm{C} . \Delta \mathrm{H}\) \(=400 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and \(\Delta \mathrm{S}=0.2 \mathrm{~kJ} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\). The reaction will become spontaneous above _______ \(\mathrm{K}\).

The element with which of the following outer electron configuration may exhibit the largest number of oxidation states in its compounds 

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

Which among the following species has unequal bond lengths?

Galvanization is applying a coating of :

For the following Assertion and Reason, the correct option is Assertion : The \(pH\) of water increases with increase in temperature. Reason : The dissociation of water into \(H^+\) and \(OH^-\) is an exothermic reaction.

Compound \(A\) from the following reaction sequence is:   

In a \(\triangle A B C\), suppose \(y=x\) is the equation of the bisector of the angle \(B\) and the equation of the side \(A C\) is \(2 x-y=2\). If \(2 A B=B C\) and the point \(A\) and \(B\) are respectively \((4,6)\) and \((\alpha, \beta)\), then \(\alpha+2 \beta\) is equal to

Consider the following two statements : Statement \(I\) : For any two non-zero complex numbers \(\mathrm{z}_1, \mathrm{z}_2\) \(\left(\left|z_1\right|+\left|z_2\right|\right)\left|\frac{z_1}{\left|z_1\right|}+\frac{z_2}{\left|z_2\right|}\right| \leq 2\left(\left|z_1\right|+\left|z_2\right|\right)\) and Statement \(II\) : If \(\mathrm{x}, \mathrm{y}, \mathrm{z}\) are three distinct complex numbers and a, b, c are three positive real numbers such that \(\frac{a}{|y-z|}=\frac{b}{|z-x|}=\frac{c}{|x-y|}\), then \(\frac{\mathrm{a}^2}{\mathrm{y}-\mathrm{z}}+\frac{\mathrm{b}^2}{\mathrm{z}-\mathrm{x}}+\frac{\mathrm{c}^2}{\mathrm{x}-\mathrm{y}}=1\) Between the above two statements,

Given below are two statements: Statement \((I)\) : When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account. Statement \((II)\) : Ampere's circuital law does not depend on Biot-Savart's law. In the light of the above statements, choose the correct answer from the options given below:

Let \(f : R \rightarrow R\) be a function such that \(f(x)=\frac{x^2+2 x+1}{x^2+1}\). Then

A plane electromagnetic wave is moving in free space with velocity \(c =3 \times 10^8 m / s\) and its electric field is given as \(\overrightarrow{ E }=54 \sin ( kz -\omega t ) \hat{ j } V / m\), where \(\hat{j}\) is the unit vector along \(y\)-axis. The magnetic field vector \(\overrightarrow{ B }\) of the wave is :

If compound A reacts with \(B\) following first order kinetics with rate constant \(2.011 \times 10^{-3} s ^{-1}\). The time taken by \(A\) (in seconds) to reduce from \(7\,g\) to \(2\,g\) will be \(.........\) (Nearest Integer) \([\log 5=0.698, \log 7=0.845, \log 2=0.301]\)