JEE MAIN 2024 ONLINE 29TH JANUARY EVENING SHIFT

Standard enthalpy of vapourisation for \(\mathrm{CCl}_4\) is \(30.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\). Heat required for vapourisation of \(284 \mathrm{~g}\) of \(\mathrm{CCl}_4\) at constant temperature is ________ \(\mathrm{kJ}\).

(Given molar mass in \(\mathrm{g} \mathrm{mol}^{-1} ; \mathrm{C}=12, \mathrm{Cl}=35.5\))

Let for any three distinct consecutive terms \(a, b, c\) of an A.P, the lines \(a x+b y+c=0\) be concurrent at the point \(P\) and \(Q(\alpha, \beta)\) be a point such that the system of equations

$$\begin{aligned} & x+y+z=6, \\ & 2 x+5 y+\alpha z=\beta \text { and } \end{aligned}$$

\(x+2 y+3 z=4\), has infinitely many solutions. Then \((P Q)^2\) is equal to _________.

A physical quantity \(Q\) is found to depend on quantities \(a, b, c\) by the relation \(Q=\frac{a^4 b^3}{c^2}\). The percentage error in \(a, b\) and \(c\) are \(3 \%, 4 \%\) and \(5 \%\) respectively. Then, the percentage error in \(Q\) is :

The ascending acidity order of the following H atoms is

Let the area of the region \(\left\{(x, y): 0 \leq x \leq 3,0 \leq y \leq \min \left\{x^2+2,2 x+2\right\}\right\}\) be A. Then \(12 \mathrm{~A}\) is equal to __________.

A particle is moving in a circle of radius \(50 \mathrm{~cm}\) in such a way that at any instant the normal and tangential components of it's acceleration are equal. If its speed at \(\mathrm{t}=0\) is \(4 \mathrm{~m} / \mathrm{s}\), the time taken to complete the first revolution will be \(\frac{1}{\alpha}\left[1-e^{-2 \pi}\right] \mathrm{s}\), where \(\alpha=\) _________.