On a new scale of temperature, which is linear and called the \(\text{W}\) scale, the freezing and boiling points of water are \(39^\circ ~\text{W}\) and \(239^\circ ~\text{W}\) respectively. What will be the temperature on the new scale corresponding to a temperature of \(39^\circ ~\text{C}\) on the Celsius scale?
1. \(78^\circ ~\text{W}\)
2. \(117^\circ ~\text{W}\)
3. \(200^\circ ~\text{W}\)
4. \(139^\circ ~\text{W}\)

If \(Q\), \(E\), and \(W\) denote respectively the heat added, the change in internal energy, and the work done in a closed cycle process, then:

A closed-loop \(PQRS\) carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments \(PS,\) \(SR,\) and \(RQ\) are \(F_1, F_2~\text{and}~F_3\) respectively, and are in the plane of the paper and along the directions shown, then which of the following forces acts on the segment \(QP?\)
        

1. \(F_{3} - F_{1} - F_{2}\)

2. \(\sqrt{\left(F_{3} - F_{1}\right)^{2} + F_{2}^{2}}\)

3. \(\sqrt{\left(F_{3} - F_{1}\right)^{2} - F_{2}^{2}}\)

4. \(F_{3} - F_{1} + F_{2}\)

The decay constants of two radioactive materials X₁ and X₂ are \(5\lambda\) and \(\lambda\) respectively. Initially, they have the same number of nuclei.  The ratio of the number of nuclei of X₁ to that of X₂  will be \(1/e\) after a time:
1. \(\lambda\)

2. \(\frac{1}{2\lambda }\)

3. \(\frac{1}{4\lambda }\)

4. \(\frac{e}{\lambda }\)

Two thin lenses of focal lengths f₁ and f₂ are in contact and coaxial. The power of the combination is:

1. $\sqrt{\frac{{\mathrm{f}}_1}{{\mathrm{f}}_2}}$

2. $\sqrt{\frac{{\mathrm{f}}_2}{{\mathrm{f}}_1}}$

3. $\frac{{\mathrm{f}}_1+{\mathrm{f}}_2}{{\mathrm{f}}_1{\mathrm{f}}_2}$

4. None of the above

The distance travelled by a particle starting from rest and moving with an acceleration \(\frac{4}{3}\) ms^-2, in the third second is:
1. \(6\) m
2. \(4\) m
3. \(\frac{10}{3}\) m
4. \(\frac{19}{3}\) m

The circuit is equivalent to: 
     

1. AND gate
2. NAND gate
3. NOR gate
4. OR gate

A particle of mass \(m,\) charge \(Q,\) and kinetic energy \(T\) enters a transverse uniform magnetic field of induction \(\vec B.\) What will be the kinetic energy of the particle after seconds?