A rod Ab of length 1 is moving with ends remaining in contact with frictionless wall and floor. If at the instant, shown the velocity of end B is 2 m/s towards the negative direction of x. The speed of end A will be:
       

1.  $\sqrt{3}{\mathrm{ms}}^{-1}$

2.  $\frac{2}{\sqrt{3}}{\mathrm{ms}}^{-1}$

3.  $\sqrt{2}{\mathrm{ms}}^{-1}$

4.  $\frac{\sqrt{5}}{2}{\mathrm{ms}}^{-1}$

A slab consists of portions of different materials of the same thickness and having the conductivities K₁ and K₂. The equivalent thermal conductivity of the slab is:

1.  ${\mathrm{K}}_1+{\mathrm{K}}_2$

2.  $\sqrt{{\mathrm{K}}_1+{\mathrm{K}}_2}$

3.  $\frac{2{\mathrm{K}}_1{\mathrm{K}}_2}{{\mathrm{K}}_1+{\mathrm{K}}_2}$

4.  $\sqrt{\frac{{\mathrm{K}}_1{\mathrm{K}}_2}{{\mathrm{K}}_1+{\mathrm{K}}_2}}$

Two rigid boxes containing different ideal gases are placed on the table. Box \(A\) contains one mole of nitrogen at temperature \(T_0\), while box \(B\) contains \(1\) mole of helium at temperature \(\frac{7T_0}{3}\). The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes) then the final temperature of gases, \(T_f\) in terms of \(T_0\) is:
1. \( \frac{2 \mathrm{~T}_0}{5} \)
2. \( \frac{3 \mathrm{~T}_0}{7} \)
3. \( \frac{5 \mathrm{~T}_0}{3} \)
4. \( \frac{9 \mathrm{~T}_0}{7}\)
 

A thin bar magnet of length \(2L\) is bent at the mid-point so that the angle between them is \(60^\circ\). The new length of the magnet is:
1. \( \frac{\mathrm{L}}{2 \sqrt{3}} \)
2. \( \frac{\sqrt{3} \mathrm{~L}}{2} \)
3. \(\mathrm{~L} \)
4. \(\frac{2 \mathrm{~L}}{3}\)

1.  0.7 V

2.  1.2 V

3.  0.8 V

4.  0.9 V

Given that the reduced temperature, the reduced pressure, the reduced volume, Thus, it can be said that the reduced equation of state may be given as:

1.   

2.  

3.  

4.  

The suitable reaction steps to carry out the following transformation is:

1.  $\underset{\left(\mathrm{ii}\right) {\mathrm{H}}_2{\mathrm{O}}_2 . \mathrm{NaOH}}{\overset{\left(\mathrm{i}\right) {\mathrm{BH}}_3. \mathrm{THF}}{\to }} \stackrel{ {\mathrm{HlO}}_4 }{\to }$

2.  $\underset{{\left({\mathrm{CH}}_3\right)}_3 \mathrm{C}. \mathrm{COOH}. {\mathrm{OH}}^{-}}{\overset{\mathrm{Os} {\mathrm{O}}_4}{\to }} \underset{{\mathrm{H}}_2\mathrm{O}}{\overset{{\mathrm{K}}_3{\mathrm{Cr}}_2{\mathrm{O}}_7 . {\mathrm{H}}_2{\mathrm{SO}}_4}{\to }}$

3.  $\underset{\left(\mathrm{ii}\right) {\mathrm{H}}_2{\mathrm{O}}_2 . \mathrm{NaOH}}{\overset{\left(\mathrm{i}\right) {\mathrm{BH}}_3. \mathrm{THF}}{\to }} \underset{{\mathrm{CH}}_2{\mathrm{Cl}}_2}{\overset{ \mathrm{PCC} }{\to }}$

4.  $\stackrel{{\mathrm{H}}_2\mathrm{O} {\mathrm{H}}_2{\mathrm{SO}}_4 \left(\mathrm{dil}.\right)}{\to } \underset{{\mathrm{CH}}_2{\mathrm{Cl}}_2}{\overset{\mathrm{PCC}}{\to }}$