In the circuit shown, a four wire potentiometer is made of a \(400\, cm\) long wire, which extends between \(A\) and \(B\). The resistance per unit length of the potentiometer wire is \(r = 0.01\, \Omega /cm\). If an ideal voltmeter is connected as shown with jockey \(J\) at \(50\, cm\) from end \(A\), the expected reading of the voltmeter will be: ............... \(V\)

If speed \((V)\), acceleration \((A)\) and force \((F)\) are considered as fundamental units, the dimension of Young’s modulus will be

Space between the plates of a parallel plate capacitor of plate area \(4 \mathrm{~cm}^2\) and separation of (d) 1.77 mm, is filled with uniform dielectric materials with dielectric constants (3 and 5) as shown in figure. Another capacitor of capacitance 7.5 pF is connected in parallel with it. The effective capacitance of this combination is ________ pF. \(\left(\right.\) Given \(\left.\varepsilon_0=8.85 \times 10^{-12} \mathrm{~F} / \mathrm{m}\right)\)

A balloon has mass of \(10\,g\) in air. The air escapes from the balloon at a uniform rate with velocity \(4.5\,cm / s\). If the balloon shrinks in \(5\,s\) completely. Then, the average force acting on that balloon will be (in dyne).

A thermodynamic system is taken from an original state \(D\) to an intermediate state \(E\) by the linear process shown in the figure. Its volume is then reduced to the original volume from \(E\) to \(F\) by an isobaric process. The total work done by the gas from \(D\) to \(E\) to \(F\) will be \(......J\)

Figure here shows \(P\) and \(Q\) as two equally intense coherent sources emitting radiations of wavelength \(20 \,m\). The separation \(PQ\) is \(5.0 \,m\) and phase of \(P\) is ahead of the phase of \(Q\) by \(90^{0}\). \(A, B \) and \( C\) are three distant points of observation equidistant from the mid-point of \(PQ\). The intensity of radiations at \(A, B, C\)  will bear the ratio

A particle of mass \(9.1 \times 10^{-31}\, {kg}\) travels in a medium with a speed of \(10^{6}\, {m} / {s}\) and a photon of a radiation of linear momentum \(10^{-27} \,{kg}\, {m} / {s}\) travels in vacuum. The wavelength of photon is \(....\) times the wavelength of the particle.

The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is \(\left(\frac{x}{100}\right) \% .\) If the relative errors in measuring the mass and the diameter are \(6.0 \%\) and \(1.5 \%\) respectively, the value of \(x\) is

The ratio of the density of oxygen nucleus \(\left({ }_8^{16} O \right)\) and helium nucleus \(\left({ }_2^4 He \right)\) is

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason \(R\). Assertion A : Efficiency of a reversible heat engine will be highest at \(-273^{\circ} C\) temperature of cold reservoir. Reason \(R\) : The efficiency of Carnot's engine depends not only on temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as \(\eta=\left(1-\frac{ T _2}{ T _1}\right)\). In the light of the above statements, choose the correct answer from the options given below