A convex lens of focal length \(20\, cm\) produces images of the same magnification \(2\) when an object is kept at two distances \(x_1\) and \(x_2\) \((x_1 > x_2)\) from the lens. The ratio of \(x_1\) and \(x_2\) is

Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is \(V\). The potential difference between the points A and B (shown in the figure) is :

A uniformly thick wheel with moment of inertia \(I\) and radius \(R\) is free to rotate about its centre of mass (see fig). A massless string is wrapped over its rim and two blocks of masses \(\mathrm{m}_{1}\) and \(\mathrm{m}_{2}\left(\mathrm{m}_{1}>\mathrm{m}_{2}\right)\) are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when \(\mathrm{m}_{1}\) descents by a distance \(h\) is

Some distant star is to be observed by some telescope of diameter of objective lens \(a\), at an angular resolution of \(3.0\times 10^{-7}\) radian. If the wavelength of light from the star reaching the telescope is \(500\) nm, the minimum diameter of the objective lens of the telescope is ________ cm. (nearest integer)

The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is \(I_{1}\). The same rod is bent into a ring and its moment of inertia about a diameter is \(I _{2}\). If \(\frac{ I _{1}}{ I _{2}}\) is \(\frac{ x \pi^{2}}{3}\), then the value of \(x\) will be ...............

Two forces having magnitude \(A\) and \(\frac{ A }{2}\) are perpendicular to each other. The magnitude of their resultant is

Train \(A\) and train \(B\) are running on parallel tracks in the opposite directions with speeds of \(36\, km / hour\) and \(72 \,km / hour,\) respectively. A person is walking in train \(A\) in the direction opposite to its motion with a speed of \(1.8\, km / hr\). Speed (in \(ms ^{-1}\) ) of this person as observed from train \(B\) will be close to (take the distance between the tracks as negligible)

A vector in \(x-y\) plane makes an angle of \(30^{\circ}\) with \(y\)-axis The magnitude of \(y\)-component of vector is \(2 \sqrt{3}\). The magnitude of \(x\)-component of the vector will be

For extrinsic semiconductors; when doping level is increased;

A car accelerates from rest at a constant rate \(\alpha\) for some time after which it decelerates at a constant rate \(\beta\) to come to rest. If the total time elapsed is \(t\) seconds, the total distance travelled is

Suppose that the angular velocity of rotation of earth is increased. Then, as a consequence.

The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest Young's modulus?