JEE MAIN 2024 ONLINE 5TH APRIL EVENING SHIFT

Consider the following single step reaction in gas phase at constant temperature.

$$2 \mathrm{~A}_{(\mathrm{g})}+\mathrm{B}_{(\mathrm{g})} \rightarrow \mathrm{C}_{(\mathrm{g})}$$

The initial rate of the reaction is recorded as \(\mathrm{r}_1\) when the reaction starts with \(1.5 \mathrm{~atm}\) pressure of \(\mathrm{A}\) and \(0.7 \mathrm{~atm}\) pressure of B. After some time, the rate \(r_2\) is recorded when the pressure of C becomes \(0.5 \mathrm{~atm}\). The ratio \(\mathrm{r}_1: \mathrm{r}_2\) is _________ \(\times 10^{-1}\). (Nearest integer)

The maximum height reached by a projectile is \(64 \mathrm{~m}\). If the initial velocity is halved, the new maximum height of the projectile is ______ \(\mathrm{m}\).

If \(1+\frac{\sqrt{3}-\sqrt{2}}{2 \sqrt{3}}+\frac{5-2 \sqrt{6}}{18}+\frac{9 \sqrt{3}-11 \sqrt{2}}{36 \sqrt{3}}+\frac{49-20 \sqrt{6}}{180}+\ldots\) upto \(\infty=2+\left(\sqrt{\frac{b}{a}}+1\right) \log _e\left(\frac{a}{b}\right)\), where a and b are integers with \(\operatorname{gcd}(a, b)=1\), then \(\mathrm{11 a+18 b}\) is equal to __________.

The fusion of chromite ore with sodium carbonate in the presence of air leads to the formation of products \(\mathrm{A}\) and \(\mathrm{B}\) along with the evolution of \(\mathrm{CO}_2\). The sum of spin-only magnetic moment values of A and B is _________ B.M. (Nearest integer)

[Given atomic number : \(\mathrm{C}: 6, \mathrm{Na}: 11, \mathrm{O}: 8, \mathrm{Fe}: 26, \mathrm{Cr}: 24\)]

A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is \(\frac{x}{5}\). The value of \(x\) is _________.

The number of real solutions of the equation \(x|x+5|+2|x+7|-2=0\) is __________.