Which of the following best describes the diagram of molecular orbital?

Number of colourless lanthanoid ions among the following is _______. \(\mathrm{Eu}^{3+}, \mathrm{Lu}^{3+}, \mathrm{Nd}^{3+}, \mathrm{La}^{3+}, \mathrm{Sm}^{3+}\)

Total number of species from the following which can undergo disproportionation reaction _______. \(\mathrm{H}_2 \mathrm{O}_2, \mathrm{ClO}_3^{-}, \mathrm{P}_4, \mathrm{Cl}_2, \mathrm{Ag}, \mathrm{Cu}^{+1}, \mathrm{~F}_2, \mathrm{NO}_2, \mathrm{~K}^{+}\)

In Tollen's test for aldehyde, the overall number of electron(s) transferred to the Tollen's reagent formula \(\left[ Ag \left( NH _{3}\right)_{2}\right]^{+}\) per aldehyde group to form silver mirror is \(......\). (Round off to the Nearest integer)

During which of the following processes, does entropy decrease ? \((A)\) Freezing of water to ice at \(0^{\circ} C\) \((B)\) Freezing of water to ice at \(-10^{\circ} C\) \((C)\) \(N _{2}( g )+3 H _{2}( g ) \rightarrow 2 NH _{3}( g )\) \((D)\) Adsorption of \(CO ( g )\) and lead surface \((E)\) Dissolution of \(NaCl\) in water

At \(300\, K\), the vapour pressure of a solution containing \(1\) mole of \(n-\)hexane and \(3\) moles of \(n-\)heptane is \(550\, mm\) of \(Hg\). At the same temperature, if one more mole of n-heptane is added to this solution, the vapour pressure of the solution increases by \(10\, mm\) of \(Hg\). What is the vapour pressure in \(mm Hg\) of \(n-\)heptane in its pure state..........\(?\)

Two elements \(A\) and \(B\) which form \(0.15\,moles\) of \(A _{2} B\) and \(AB _{3}\) type compounds. If both \(A _{2} B\) and \(A B_{3}\) weigh equally, then the atomic weight of \(A\) is \(....\) times of atomic weight of \(B\).

A fly wheel is accelerated uniformly from rest and rotates through \(5 \,rad\) in the first second. The angle rotated by the fly wheel in the next second, will be.........\(rad\)

Let the function,
\(f(x)= \begin{cases}-3 a x^2-2, & x \lt 1 \\ a^2+b x, & x \geqslant 1\end{cases}\)
be differentiable for all \(x \in \mathbf{R}\), where \(\mathbf{a}\gt1, \mathbf{b} \in \mathbf{R}\). If the area of the region enclosed by \(y=f(x)\) and the line \(y=-20\) is \(\alpha+\beta \sqrt{3}, \alpha, \beta \in Z\), then the value of \(\alpha+\beta\) is ________

A geostationary satellite is orbiting around an arbitary planet \(^{\prime} P ^{\prime}\) at a height of \(11 R\) above the surface of \(^{\prime} P ^{\prime} ,\) \(R\) being the radius of \(^{\prime} P .^{\prime}\) The time period of another satellite in hours at a height of \(2R\) from the surface of \(^{\prime} P ^{\prime}\) is \(........\).\(^{\prime} P ^{\prime}\) has the time period of \(24\, hours.\)

Statement \(I:\) If three forces \(\vec{F}_{1}, \vec{F}_{2}\) and \(\vec{F}_{3}\) are represented by three sides of a triangle and \(\overrightarrow{{F}}_{1}+\overrightarrow{{F}}_{2}=-\overrightarrow{{F}}_{3}\), then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement \(II:\) A triangle made up of three forces \(\overrightarrow{{F}}_{1}, \overrightarrow{{F}}_{2}\) and \(\overrightarrow{{F}}_{3}\) as its sides taken in the same order, satisfy the condition for translatory equilibrium. In the light of the above statements, choose the most appropriate answer from the options given below:

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s . The EMF induced in the loop is ___________ mV.

Let \( \alpha_{1}, \alpha_{2}, \alpha_{3}, \alpha_{4} \) be an A.P. of four terms such that each term of the A.P. and its common difference \( l \) are integers. If \( \alpha_{1}+\alpha_{2}+\alpha_{3}+\alpha_{4}=48 \) and \( \alpha_{1},\alpha_{2},\alpha_{3},\alpha_{4}+l^{4}=361 \) then the largest term of the A.P. is equal to