JEE MAIN 2024 ONLINE 4TH APRIL MORNING SHIFT

The enthalpy of formation of ethane \((\mathrm{C}_2 \mathrm{H}_6)\) from ethylene by addition of hydrogen where the bond-energies of \(\mathrm{C}-\mathrm{H}, \mathrm{C}-\mathrm{C}, \mathrm{C}=\mathrm{C}, \mathrm{H}-\mathrm{H}\) are \(414 \mathrm{~kJ}, 347 \mathrm{~kJ}, 615 \mathrm{~kJ}\) and \(435 \mathrm{~kJ}\) respectively is \(-\) __________ \(\mathrm{kJ}\)

A alternating current at any instant is given by \(i=[6+\sqrt{56} \sin (100 \pi t+\pi / 3)]\) A. The \(r m s\) value of the current is ______ A.

In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied Mathematics; at least 85 and at most 95 studied Physics; at least 75 and at most 90 studied Chemistry; 30 studied both Physics and Chemistry; 50 studied both Chemistry and Mathematics; 40 studied both Mathematics and Physics and 10 studied none of these subjects. Let \(m\) and \(n\) respectively be the least and the most number of students who studied all the three subjects. Then \(\mathrm{m}+\mathrm{n}\) is equal to ___________.

\(\mathrm{Xg}\) of ethylamine is subjected to reaction with \(\mathrm{NaNO}_2 / \mathrm{HCl}\) followed by water; evolved dinitrogen gas which occupied \(2.24 \mathrm{~L}\) volume at STP. X is _________ \(\times 10^{-1} \mathrm{~g}\).

Two forces \(\overline{\mathrm{F}}_1\) and \(\overline{\mathrm{F}}_2\) are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between \(\vec{F}_1\) and \(\vec{F}_2\) is \(\cos ^{-1}\left(\frac{1}{n}\right)\). The value of \(|n|\) is _______.

Let \(a=1+\frac{{ }^2 \mathrm{C}_2}{3 !}+\frac{{ }^3 \mathrm{C}_2}{4 !}+\frac{{ }^4 \mathrm{C}_2}{5 !}+...., \mathrm{b}=1+\frac{{ }^1 \mathrm{C}_0+{ }^1 \mathrm{C}_1}{1 !}+\frac{{ }^2 \mathrm{C}_0+{ }^2 \mathrm{C}_1+{ }^2 \mathrm{C}_2}{2 !}+\frac{{ }^3 \mathrm{C}_0+{ }^3 \mathrm{C}_1+{ }^3 \mathrm{C}_2+{ }^3 \mathrm{C}_3}{3 !}+....\) Then \(\frac{2 b}{a^2}\) is equal to _________.