JEE MAIN 2024 ONLINE 30TH JANUARY MORNING SHIFT

Consider a Disc of mass \(5 \mathrm{~kg}\), radius \(2 \mathrm{~m}\), rotating with angular velocity of \(10 \mathrm{~rad} / \mathrm{s}\) about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is ________ J.

An ideal gas undergoes a cyclic transformation starting from the point A and coming back to the same point by tracing the path \(\mathrm{A} \rightarrow \mathrm{B} \rightarrow \mathrm{C} \rightarrow \mathrm{A}\) as shown in the diagram above. The total work done in the process is __________ J.

$$\text { Number of integral terms in the expansion of }\left\{7^{\left(\frac{1}{2}\right)}+11^{\left(\frac{1}{6}\right)}\right\}^{824} \text { is equal to _________. }$$

In a closed organ pipe, the frequency of fundamental note is \(30 \mathrm{~Hz}\). A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to \(110 \mathrm{~Hz}\). If the organ pipe has a cross-sectional area of \(2 \mathrm{~cm}^2\), the amount of water poured in the organ tube is __________ g. (Take speed of sound in air is \(330 \mathrm{~m} / \mathrm{s}\))

If IUPAC name of an element is "Unununnium" then the element belongs to n^th group of Periodic table. The value of n is ________.

Let \(\alpha=1^2+4^2+8^2+13^2+19^2+26^2+\ldots\) upto 10 terms and \(\beta=\sum_\limits{n=1}^{10} n^4\). If \(4 \alpha-\beta=55 k+40\), then \(\mathrm{k}\) is equal to __________.