Consider an engine that absorbs 130 cal of heat from a hot reservoir and delivers 30 cal heat to a cold reservoir in each cycle. The engine also consumes 2 J energy in each cycle to overcome friction. If the engine works at 90 cycles per minute, what will be the maximum power delivered to the load? [Assume the thermal equivalent of heat is \(4.2 \mathrm{~J} / \mathrm{cal}]\)

The conducting loop in the form of a circle is placed in a uniform magnetic field with its plane perpendicular to the direction of the field. An emf will be induced in the loop, if

To which of the following quantities, the radius of the circular path of a charged particle moving at right angles to a uniform magnetic field is directly proportional?

Two charges \(+q\) and \(-q\) are placed at a distance \(a\) in a uniform electric fleld. The dipole moment of the combination is \(2 q a(\cos \theta i+\sin \theta)\). where, \(\theta\) is the angle between the direction of the field and the line joining the two charges. Which of the following statement(s) is/ase correct?

An alpha particle \(\left({ }^{4} \mathrm{He}\right)\) has a mass of 4.00300 amu. A proton has a mass of 1.00783 amu and a neutron has a mass of 1.00867 amu respectively. The binding energy of alpha estimated from these data is the closest to

A glass slab consists of thin uniform layers of progressively decreasing refractive indices RI (see figure) such that the RI of any layer is \(\mu-m \Delta \mu\). Here, \(\mu\) and \(\Delta \mu\) denote the \(\mathrm{RI}\) of 0 th layer and the difference in RI between any two consecutive layers, respectively. The integer \(m=0,1,2,3, \ldots\) denotes the numbers of the successive layers. A ray of light from the oth layer enters the 1st layer at an angle of incidence of \(30^{\circ}\). After undergoing the mth refraction, the ray emerges parallel to the interface. If \(\mu=1.5\) and \(\Delta \mu=0.015,\) the value of \(m\) is

A charged particle of charge \(q\) and mass \(m\) is placed at a distance \(2 R\) from the centre of a vertical cylindrical region of radius \(R\) where magnetic field varies as \(\vec{B}=\left(4 t^2-2 t+6\right) \hat{k}\) where \(t\) is time. Then which of the following statement(s) is/are true?

Let \(f(x)=x^2+x \sin x-\cos x\). Then

Suppose a machine produces metal parts that contain some defective parts witl probability \(0.05 .\) How many parts should be produced in order that the probability 0 atleast one part being defective is \(1 / 20\) more? (Given that, \(\log _{10} 95=1.977\) an \(\log _{10} 2=0.3\) )

A train approaching a railway platform with a speed of \(20 \mathrm{ms}^{-1}\) starts blowing the whistle. Speed of sound in air is \(340 \mathrm{ms}^{-1}\). If the frequency of the emitted sound from the whistle is \(640 \mathrm{Hz}\), the frequency of sound to a person standing on the platform will appear to be

\(\left(2^{3 \mathrm{n}}-1\right)\) will be divisible by \((\forall \mathrm{n} \in \mathrm{N})\)

The area of the region, bounded by the curves \(y=\sin ^{-1} x+x(1-x)\) and
\(y=\sin ^{-1} x-x(1-x)\) in the first quadrant, is

Metal ion responsible for the Minimata disease is