Three bodies a ring, a solid cylinder and a solid sphere roll down an inclined plane without slipping. They start from rest. Which of the bodies reaches bottom of plane with minimum velocity?

Two ammeters $A_1$ and $A_2$ are connected as shown in the given figure. By neglecting the internal resistance of the ammeters, the reading in the meter $A_1$ is

The range of frequency bands used for standard AM broadcast is

Consider a physical quantity, $Z$ expressed as $Z=\frac{A{B}^{\frac{1}{2}}}{C^2}.$ If the relative error in the magnitudes of $A\mathit{,} B$ and $C$ is $1\%$ then the relative error in $Z$ will be, 

Three unequal resistances are connected in parallel. Two of these resistances are in the ratio 1:2. The equivalent resistance of these three resistors connected in parallel is \(1 \Omega\). What is the highest resistance value among these three resistances if no resistance is fractional?

A convex lens of radii of curvature 6 cm and 12 cm is immersed in a liquid of refractive index 1.3. If the refractive index of the material of the lens is 1.5, then the focal length of the lens when immersed in the liquid is

Two particles \(A\) and \(B\) initially at rest, move towards each other, under mutual force of attraction. At an instance when the speed of \(A\) is \(v\) and speed of \(B\) is \(2 v\), the speed of centre of mass \((\mathrm{CM})\) is

Two bodies of \(6 \mathrm{~kg}\) and \(4 \mathrm{~kg}\) masses have their velocity \(5 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+10 \hat{\mathbf{k}}\) and \(10 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) respectively. Then the velocity of their centre of mass is

Statement (I) : The slope of kinetic energy-displacement curve of a body in motion will be directly proportional to its acceleration. Statement (II) : From a height of \(15 \mathrm{~m}\) a ball is projected vertically upwards with a velocity of \(30 \mathrm{~m} / \mathrm{s}\). If the ball rises to the same height after hitting the ground, the loss of its energy on hitting the ground is \(30 \%\). Statement (III) : The velocity acquired by a body of mass ' \(m\) ' after travelling a fixed distance from rest under the action of a constant force is directly proportional to mass ' \(\mathrm{m}\) '. Which of the following is correct?

Two concentric coils of 10 turns each are placed in the same plane. Their radii are \(20 \mathrm{~cm}\) and \(40 \mathrm{~cm}\) and carry 0.2 and \(0.3 \mathrm{~A}\). current respectively in opposite directions. The magnetic induction (in T) at the centre is

A source at rest emits sound waves of frequency 102 Hz . Two observers are moving away from the source of sound in opposite directions each with a speed of \(10 \%\) of the speed of sound. The ratio of the frequencies of sound heard by the observers is

An ideal gas at \(127^{\circ} \mathrm{C}\) is compressed suddenly to \(\frac{8}{27}\) of its initial volume. If \(\gamma=\frac{5}{3}\) for an ideal gas, then rise in its temperature is

A transmitting antenna has a height \(20 \mathrm{~m}\). What will be the height of receiving antenna, if the maximum distance between them for satisfactory communication in line-of-sight (LOS) mode is \(40 \mathrm{~km}\) ? (The earth radius is \(6400 \mathrm{~km}\).)