JEE MAIN 2024 ONLINE 31ST JANUARY EVENING SHIFT

The magnetic flux \(\phi\) (in weber) linked with a closed circuit of resistance \(8 \Omega\) varies with time (in seconds) as \(\phi=5 t^2-36 t+1\). The induced current in the circuit at \(t=2 \mathrm{~s}\) is __________ A.

If 5 moles of an ideal gas expands from \(10 \mathrm{~L}\) to a volume of \(100 \mathrm{~L}\) at \(300 \mathrm{~K}\) under isothermal and reversible condition then work, \(\mathrm{w}\), is \(-x \mathrm{~J}\). The value of \(x\) is __________.

(Given R = 8.314 J K\(^{-1}\) mol\(^{-1}\))

Let \(f: \rightarrow \mathbb{R} \rightarrow(0, \infty)\) be strictly increasing function such that \(\lim _\limits{x \rightarrow \infty} \frac{f(7 x)}{f(x)}=1\). Then, the value of \(\lim _\limits{x \rightarrow \infty}\left[\frac{f(5 x)}{f(x)}-1\right]\) is equal to

By what percentage will the illumination of the lamp decrease if the current drops by 20%?

Let \(A=\{1,2,3, \ldots \ldots \ldots \ldots, 100\}\). Let \(R\) be a relation on \(\mathrm{A}\) defined by \((x, y) \in R\) if and only if \(2 x=3 y\). Let \(R_1\) be a symmetric relation on \(A\) such that \(R \subset R_1\) and the number of elements in \(R_1\) is \(\mathrm{n}\). Then, the minimum value of \(\mathrm{n}\) is _________.