Chemical nature of the nitrogen oxide compound obtained from a reaction of concentrated nitric acid and \(\mathrm{P}_{4} \mathrm{O}_{10}\) (in \(4: 1\) ratio \()\) is:

The reaction of \(\mathrm{H}_{3} \mathrm{N}_{3} \mathrm{B}_{3} \mathrm{Cl}_{3}\) \((A)\) with \(\mathrm{LiBH}_{4}\) in tetrahydrofurane gives inorganic benzene \((B)\). Further, the reaction of \((A)\) with \((C)\) leads to \(\mathrm{H}_{3} \mathrm{N}_{3} \mathrm{B}_{3}(\mathrm{Me})_{3}\). than Compounds \((\mathrm{B})\) and \((\mathrm{C})\) respectively, are

A solution is prepared by dissolving 0.3 g of a non - volatile non - electrolyte solute 'A' of molar mass 60 g \( mol^{-1} \) and 0.9 g of a non - volatile non - electrolyte solute 'B' of molar mass 180 g \( mol^{-1} \) in 100 mL \( H_{2}O \) at \( 27^{\circ}C \). Osmotic pressure of the solution will be
[Given: \( R=0.082~L \) atm \( K^{-1} \) \( mol^{-1} \)]

Which of the following combination of statements is true regarding the interpretation of the atomic orbitals? \((1)\) An electron in an orbital of high angular momentum stays away from the nucleus than an electron in the orbital of lower angular momentum. \((2)\) For a given value of the principal quantum number, the size of the orbit is inversely proportional to the azimuthal quantum number \((3)\) According to wave mechanics, the ground state angular momentum is equal to \(\frac {h}{2\pi }\) \((4)\) The plot of \(\Psi \,\,Vs\,\,r\) for various azimuthal quantum numbers, shows peak shifting towards higher \(r\) value

A solution containing \(62\,g\) ethylene glycol in \(250\,g\) water is cooled to \(-10\,^oC. \) If \(K_f\) for water is \(1.86\,K\,kg\,mol^{-1},\) the amount of water(in \(g\) ) separated as ice is

The pair from the following pairs having both compounds with net non-zero dipole moment is

In which of the following reactions \(H_2O_2\) acts as a reducing agent ?

Let \(m_{1}, m_{2}\) be the slopes of two adjacent sides of a square of side a such that \(a^{2}+11 a+3\left(m_{2}^{2}+m_{2}^{2}\right)=220\). If one vertex of the square is \((10(\cos \alpha-\sin \alpha), 10(\sin \alpha+\cos \alpha))\), where \(\alpha \in\left(0, \frac{\pi}{2}\right)\) and the equation of one diagonal is \((\cos \alpha-\sin \alpha) x +(\sin \alpha+\cos \alpha) y =10\), then  \(72 \left(\sin ^{4} \alpha+\cos ^{4} \alpha\right)+a^{2}-3 a+13\) is equal to.

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.

Reason (R) : In isothermal process, \(\mathrm{PV}=\) constant, while in adiabatic process \(\mathrm{PV}^\gamma=\) constant. Here \(\gamma\) is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas.

In the light of the above statements, choose the correct answer from the options given below :

A body weight \(W\), is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be

The mean and variance of \(n\) observations are \(8\) and \(16\), respectively. If the sum of the first \((n-1)\) observations is \(48\) and the sum of squares of the first \((n-1)\) observations is \(496\), then the value of \(n\) is:

If \(M_0\) is the mass of isotope \({ }_5^{12} B, M_p\) and \(M_n\) are the masses of proton and neutron, then nuclear binding energy of isotope is _______.

Let \(f:[0, \infty) \rightarrow \mathbb{R}\) be differentiable function such that \(f(\mathrm{x})=1-2 \mathrm{x}+\int_0^x e^{x-t} f(t) \mathrm{dt}\) for all \(\mathrm{x} \in[0, \infty)\).
Then the area of the region bounded by \(\mathrm{y}=f(\mathrm{x})\) and the coordinate axes is