JEE MAIN 2023 ONLINE 12TH APRIL MORNING SHIFT

A body cools from \(80^{\circ} \mathrm{C}\) to \(60^{\circ} \mathrm{C}\) in 5 minutes. The temperature of the surrounding is \(20^{\circ} \mathrm{C}\). The time it takes to cool from \(60^{\circ} \mathrm{C}\) to \(40^{\circ} \mathrm{C}\) is :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A : In the Ellingham diagram, a sharp change in slope of the line is observed for \(\mathrm{Mg} \rightarrow \mathrm{MgO}\) at \(\sim 1120^{\circ} \mathrm{C}\)

Reason R: There is a large change of entropy associated with the change of state

In the light of the above statements, choose the correct answer from the options given below

If \(\frac{1}{n+1}{ }^{n} \mathrm{C}_{n}+\frac{1}{n}{ }^{n} \mathrm{C}_{n-1}+\ldots+\frac{1}{2}{ }^{n} \mathrm{C}_{1}+{ }^{n} \mathrm{C}_{0}=\frac{1023}{10}\) then \(n\) is equal to :

An engine operating between the boiling and freezing points of water will have

A. efficiency more than 27%.

B. efficiency less than the efficiency of a Carnot engine operating between the same two temperatures.

C. efficiency equal to \(27 \%\)

D. efficiency less than \(27 \%\)

Choose the correct answer from the options given below:

Match List I with List II

Choose the correct answer from the options given below:

Let \(< a_{\mathrm{n}} >\) be a sequence such that \(a_{1}+a_{2}+\ldots+a_{n}=\frac{n^{2}+3 n}{(n+1)(n+2)}\). If \(28 \sum_\limits{k=1}^{10} \frac{1}{a_{k}}=p_{1} p_{2} p_{3} \ldots p_{m}\), where \(\mathrm{p}_{1}, \mathrm{p}_{2}, \ldots ., \mathrm{p}_{\mathrm{m}}\) are the first \(\mathrm{m}\) prime numbers, then \(\mathrm{m}\) is equal to