JEE MAIN 2024 ONLINE 9TH APRIL MORNING SHIFT

The heat of solution of anhydrous \(\mathrm{CuSO}_4\) and \(\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}\) are \(-70 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and \(+12 \mathrm{~kJ} \mathrm{~mol}^{-1}\) respectively.

The heat of hydration of \(\mathrm{CuSO}_4\) to \(\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}\) is \(-x \mathrm{~kJ}\). The value of \(x\) is ________. (nearest integer).

At the centre of a half ring of radius \(\mathrm{R}=10 \mathrm{~cm}\) and linear charge density \(4 \mathrm{~nC} \mathrm{~m}^{-1}\), the potential is \(x \pi \mathrm{V}\). The value of \(x\) is _________.

Let \(A=\{2,3,6,7\}\) and \(B=\{4,5,6,8\}\). Let \(R\) be a relation defined on \(A \times B\) by \((a_1, b_1) R(a_2, b_2)\) if and only if \(a_1+a_2=b_1+b_2\). Then the number of elements in \(R\) is __________.

When equal volume of \(1 \mathrm{~M} \mathrm{~HCl}\) and \(1 \mathrm{~M} \mathrm{~H}_2 \mathrm{SO}_4\) are separately neutralised by excess volume of \(1 \mathrm{M}\) \(\mathrm{NaOH}\) solution. \(x\) and \(y \mathrm{~kJ}\) of heat is liberated respectively. The value of \(y / x\) is __________.

The current flowing through the \(1 \Omega\) resistor is \(\frac{n}{10}\) A. The value of \(n\) is _______.

Let the centre of a circle, passing through the points \((0,0),(1,0)\) and touching the circle \(x^2+y^2=9\), be \((h, k)\). Then for all possible values of the coordinates of the centre \((h, k), 4\left(h^2+k^2\right)\) is equal to __________.