JEE MAIN 2023 ONLINE 8TH APRIL EVENING SHIFT

Work done by a Carnot engine operating between temperatures \(127^{\circ} \mathrm{C}\) and \(27^{\circ} \mathrm{C}\) is \(2 \mathrm{~kJ}\). The amount of heat transferred to the engine by the reservoir is :

Arrange the following gases in increasing order of van der Waals constant 'a'

A. Ar

B. \(\mathrm{CH}_{4}\)

C. \(\mathrm{H}_{2} \mathrm{O}\)

D. \(\mathrm{C}_{6} \mathrm{H}_{6}\)

Choose the correct option from the following.

Let the vectors \(\vec{u}_{1}=\hat{i}+\hat{j}+a \hat{k}, \vec{u}_{2}=\hat{i}+b \hat{j}+\hat{k}\) and \(\vec{u}_{3}=c \hat{i}+\hat{j}+\hat{k}\) be coplanar. If the vectors \(\vec{v}_{1}=(a+b) \hat{i}+c \hat{j}+c \hat{k}, \vec{v}_{2}=a \hat{i}+(b+c) \hat{j}+a \hat{k}\) and \(\vec{v}_{3}=b \hat{i}+b \hat{j}+(c+a) \hat{k}\) are also coplanar, then \(6(\mathrm{a}+\mathrm{b}+\mathrm{c})\) is equal to :

For a given transistor amplifier circuit in \(\mathrm{CE}\) configuration \(\mathrm{V}_{\mathrm{CC}}=1 \mathrm{~V}, \mathrm{R}_{\mathrm{C}}=1 ~\mathrm{k} \Omega, \mathrm{R}_{\mathrm{b}}=100 ~\mathrm{k} \Omega\) and \(\beta=100\). Value of base current \(\mathrm{I}_{\mathrm{b}}\) is

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

Assertion A : Sodium is about 30 times as abundant as potassium in the oceans.

Reason R : Potassium is bigger in size than sodium.

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

Let \(\mathrm{a}_{\mathrm{n}}\) be the \(\mathrm{n}^{\text {th }}\) term of the series \(5+8+14+23+35+50+\ldots\) and \(\mathrm{S}_{\mathrm{n}}=\sum_\limits{k=1}^{n} a_{k}\). Then \(\mathrm{S}_{30}-a_{40}\) is equal to :