Efficiency of a heat engine whose sink is at temperature of \(300 \mathrm{~K}\) is \(40 \%\). To increase the efficiency to \(60 \%\), keeping the sink temperature constant, the source temperature must be increased by

Particles and their anti-particles have

Calculate the heat absorbed by the system in going through the process shown in figure

A heavy nucleus having mass number 200 gets disintegrated into two small fragments of mass numbers 80 and 120. If binding energy per nucleon for parent atom is \(6.5 \mathrm{MeV}\) and for daughter nuclii is \(7 \mathrm{MeV}\) and \(8 \mathrm{MeV}\) respectively, then the energy released in the decay will be

A vessel contains 3 moles of \(\mathrm{He}, 1\) mole of Ar, 5 moles of \(\mathrm{N}_2\) and 3 moles of \(\mathrm{H}_2\). If the vibrational modes are ignored, the total internal energy of the system of gases is

In case of diffraction 1 if ' \(a\) ' is a slit width and 1 is the wavelength of the incident light, then the required condition for diffraction to take place is

The voltage \(\mathrm{V}_0\) in the network shown is

Two towers \(A\) and \(B\), each of height \(20 \mathrm{~m}\) are situated a distance \(200 \mathrm{~m}\) apart. A body thrown horizontally from the top of the tower \(A\) with a velocity \(20 \mathrm{~ms}^{-1}\) towards the tower \(B\) hits the ground at point \(P\) and another body thrown horizontally from the top of tower \(B\) with a velocity \(30 \mathrm{~ms}^{-1}\) towards the tower \(A\) hits the ground at point \(Q\). If a car starting from rest from \(P\) reaches \(Q\) in 10 seconds, then the acceleration of the car is \(\left(\right.\) acceleration due to gravity \(\left.=10 \mathrm{~ms}^{-2}\right)\)

The IUPAC name of the following compound is

The angle between the straight lines \(3 x+4 y+9=0\) and \(x-7 y-22=0\) is

\(\int \frac{\log _e x}{\left(1+\log _e x\right)^2} d x=\)

If \(f(x)=\int \frac{d x}{\left(x^2+2\right)}\) and \(f(\sqrt{2})=0\), then \(f(0)=\)

If \(\mathrm{C}_{\mathrm{j}}\) stands for \({ }^{\mathrm{n}} \mathrm{C}_{\mathrm{j}}\), then
\(\frac{\mathrm{C}_0}{2}+\frac{\mathrm{C}_1}{2.2^2}+\frac{\mathrm{C}_2}{3.2^3}+\ldots+\frac{\mathrm{C}_{\mathrm{n}}}{(\mathrm{n}+1) 2^{\mathrm{n}+1}}=\)