The atomic numbers of elements \(X, Y\) and \(Z\) are 19, 21 and 25 respectively. The number of electrons present in the \(M\)-shell of these elements follow the order

What is the correct order of atomic radius of \(\mathrm{Al}, \mathrm{Na}, \mathrm{B}\) and \(\mathrm{Be} ?\)

The freezing point of solution containing \(10 \mathrm{~mL}\) of non-volatile and non-electrolyte liquid " \(A\) " in \(500 \mathrm{~g}\) of water is \(-0.413^{\circ} \mathrm{C}\). If \(K_f\) of water is \(1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\) and the molecular weight of \(A=60 \mathrm{~g} \mathrm{~mol}^{-1}\), what is the density of the solution in \(\mathrm{g} \mathrm{mL}^{-1}\) ? (Assume \(\Delta_{\text {mix }} V=0\) )

The correct order of enthalpy of vaporisation of noble gases is

Sulphur dioxide reacts with chlorine in the presence of charcoal to give

Which one of the following oxides is reduced by water gas to obtain the metal during its extraction?

\[ \begin{aligned} & \text { Given } \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(l) ; \Delta \mathrm{H}=-285 \mathrm{~kJ} \ & \mathrm{~N}_2 \mathrm{O}_5(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(l) \rightarrow 2 \mathrm{HNO}_3(l) ; \Delta \mathrm{H}=-76.6 \mathrm{~kJ} \ & \mathrm{~N}_2(\mathrm{~g})+3 \mathrm{O}_2(\mathrm{~g})+\mathrm{H}_2(\mathrm{~g}) \rightarrow 2 \mathrm{HNO}_3(l) ; \Delta \mathrm{H}=-348.2 \mathrm{~kJ} \ & \text { Calculate the } \Delta \mathrm{H} \text { of } 2 \mathrm{~N}_2(\mathrm{~g})+5 \mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{~N}_2 \mathrm{O}_5(\mathrm{~g}) \end{aligned} \] Calculate the \(\Delta \mathrm{H}\) of \(2 \mathrm{~N}_2(\mathrm{~g})+5 \mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{~N}_2 \mathrm{O}_5(\mathrm{~g})\).

The period of \(\tan k y+\sin k y\), where \(k=1+4+9+\ldots 20\) terms, is

\((p, q)\) is the point of intersection of a latus rectum and an asymptote of the hyperbola \(9 x^2-16 y^2=144\). If \(p\gt0\) and \(q\gt0\) then \(q=\)

Consider a spherical planet which is rotating about its axis such that the speed of a point on its equator is \(v\) and the effective acceleration due to gravity on the equator is \(\frac{1}{3}\) of its value at the poles. What is the escape velocity for a particle at the pole of this planet.

A telephonic communication service is working at a carrier frequency of \(20 \mathrm{GHz}\). Only \(20 \%\) of it is utilized for transmission. If each channel requires a bandwidth of \(5 \mathrm{kHz}\), then the number of telephonic channels that can be transmitted simultaneously are

The equation of the circle passing through the points of intersection of the circles \(x^2+y^2+6 x+4 y-12=0\), \(x^2+y^2-4 x-6 y-12=0\) and having radius \(\sqrt{13}\) is

Let \(f(x)=\left\{\begin{array}{cc}1+6 x-3 x^2, & x \leq 1 \ x+\log _2\left(b^2+7\right), & x>1\end{array}\right.\). Then the set of all possible values of \(b\) such that \(f(1)\) is the maximum value of \(f(x)\) is