A system is provided with \(50 \mathrm{~J}\) of heat and the work done on the system is \(10 \mathrm{~J}\). What is the change in internal energy of the system in joules?

The wavelength of the electron in the ground state of hydrogen atom is y \(Å\). What is the wavelength of the electron in the fourth orbit of \(\mathrm{He}^{+}\)ion (in \(Å\) ) is

Observe the following Ellingham diagram, and identify the incorrect statement regarding it

\(\mathrm{K}_{\mathrm{c}}\) for the following reaction is 99.0
\(\mathrm{A}_2(\mathrm{~g}) \stackrel{\mathrm{T}(\mathrm{~K})}{\rightleftharpoons} \mathrm{B}_2(\mathrm{~g})\)
In a one litre flask, 2 moles of \(\mathrm{A}_2\) was heated to \(\mathrm{T}(\mathrm{K})\) and the above equilibrium is reached. The concentrations at equilibrium of \(\mathrm{A}_2\) and \(\mathrm{B}_2\) are \(\mathrm{C}_1\left(\mathrm{~A}_2\right)\) and \(\mathrm{C}_2\left(\mathrm{~B}_2\right)\) respectively. Now, one mole of \(\mathrm{A}_2\) was added to flask and heated to \(\mathrm{T}(\mathrm{K})\) to establish the equilibrium again. The concentrations of \(\mathrm{A}_2\) and \(\mathrm{B}_2\) are \(\mathrm{C}_3\left(\mathrm{~A}_2\right)\) and \(\mathrm{C}_4\left(\mathrm{~B}_2\right)\) respectively. What is the value of \(\mathrm{C}_3\left(\mathrm{~A}_2\right)\) in \(\mathrm{mol}^{-1}\) ?

In the reaction sequence,
\(\mathrm{C}_2 \mathrm{H}_5 \mathrm{Cl}+\mathrm{KCN} \stackrel{\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}}{\longrightarrow} X \underset{\Delta}{\stackrel{\mathrm{H}_3 \mathrm{O}^{\oplus}}{\longrightarrow}}$$Y\)
What is the molecular formula of \(Y\) ?

In the following sequence of reactions, what is the end product (D) ?
\(\mathrm{C}_2\mathrm{H}_2\mathrm{Br} \xrightarrow{\mathrm{KCN}} \mathrm{A} \xrightarrow{\mathrm{H}_3 \mathrm{O}^{+}} \mathrm{B} \xrightarrow{\mathrm{LiA} \ell \mathrm{H}_4} \mathrm{C} \xrightarrow[\mathrm{573 ~K}]{\mathrm{Cu}} \mathrm{D}\).

An electron is moving in Bohr's fourth orbit. Its de-Broglie wave length is \(\lambda\). What is the circumference of the fourth orbit?

Let \(A=\{-4,-2,-1,0,3,5\}\) and \(f: \mathrm{A} \rightarrow \mathbf{R}\) be defined by \(f(x)=\left\{\begin{array}{ccc}3 x-1 & \text { for } & x>3 \\ x^2+1 & \text { for } & -3 \leq x \leq 3 \\ 2 x-3 & \text { for } & x < -3\end{array}\right.\) Then the range of \(f\) is

A parallel plate capacitor of capacity \(100 \mu \mathrm{F}\) is charged by a battery of 50 volts. The battery remains connected and if the plates of the capacitor are separated so that the distance between them becomes double the original distance, the additional energy given by the battery to the capacitor in joules is

The correct order of atomic radii of N, F, Al, Si is

If the line \(x+2 y-5=0\) and \(3 x-y-1=0\) denote two diameters of a circle of radius 5 units, then the equation of the circle is

If the cofactors of the elements 3,7 and 6 of the matrix \(\left[\begin{array}{ccc}1 & 2 & 3 \\ 4 & -1 & 7 \\ 2 & 4 & 6\end{array}\right]\) are a, b and c respectively, then
\(\left[\begin{array}{lll}\mathrm{a} & \mathrm{b} & \mathrm{c}\end{array}\right]\left[\begin{array}{l}1 \\ 4 \\ 2\end{array}\right]+\left[\begin{array}{lll}\mathrm{a} & \mathrm{b} & \mathrm{c}\end{array}\right]\left[\begin{array}{l}3 \\ 7 \\ 6\end{array}\right]=\)

If \(a\) is the determinant of the adjoint of the matrix \(\left[\begin{array}{lll}1 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 3\end{array}\right]\) and \(b\) is the determinant of the inverse of the matrix \(\left[\begin{array}{ccc}1 & 2 & 3 \\ 4 & -3 & -1 \\ 2 & 1 & -4\end{array}\right]\) then \(\frac{\mathrm{b}+1}{18 \mathrm{~b}}=\)