A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an object is positioned in front of the mirror, what will be the nature and magnification of the image of the object ? (Figure drawn as schematic and not to scale)

A heater is designed to operate with a power of \(1000 \mathrm{~W}\) in a \(100 \mathrm{~V}\) line. It is connected in combination with a resistance of \(10 \Omega\) and a resistance \(R\), to a \(100 \mathrm{~V}\) mains as shown in figure. For the heater to operate at \(62.5 \mathrm{~W}\), the value of \(\mathrm{R}\) should be _______ \(\Omega\).

A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as _______.

A thin tube sealed at both ends is \(100\, cm\) long. It lies horizontally, the middle \(20\, cm\) containing mercury and two equal ends containing air at standard atmospheric pressure . If the tube is now turned to a vertical position, by what amount will the mercury be displaced ? (Given : cross-section of the tube can be assumed to be uniform) ........ \(cm\)

Monochromatic light of wavelength \(500 \mathrm{~nm}\) is used in Young's double slit experiment. An interference pattern is obtained on a screen When one of the slits is covered with a very thin glass plate (refractive index \(=1.5\) ), the central maximum is shifted to a position previously occupied by the \(4^{\text {th }}\) bright fringe. The thickness of the glass-plate is _______\(\mu \mathrm{m}\).

In a screw gauge when the circular scale is given five complete rotations it moves linearly by \(2.5\) mm. If the circular scale has \(100\) divisions, the least count of screw gauge is _____ mm.

A \(10\,V\) battery with internal resistance \(1\,\Omega \) and a \(15\,V\) battery with internal resistance \(0.6\,\Omega \) are connected in parallel to a voltmeter (see figure). The reading in the voltmeter will be close to ................ \(V\)

The figure shows a square loop \(L\) of side \(5\, cm\) which is connected to a network of resistances. The whole set up is moving towards right with a constant speed of \(1\, cms^{-1}\). At some instant, a part of \(L\) is in a uniform magnetic field of \(1\, T\), perpendicular to the plane of the loop. If the resistance of \(L\) is \(1.7\,\Omega \), the current in the loop at that instant will be close to.....\(\mu A\)

In a Young’s double slit experiment, the slits are placed \(0.320\,mm\) apart. Light of wavelength \(\lambda = 500\,nm\) is incident on the slits. The total number of bright fringes that are observed in the angular range \( - {30^o} \le \theta  \le {30^o}\) is

A body \(A,\) of mass \(m=0.1\; kg\) has an initial velocity of \(3 \hat{\mathrm{i}}\; \mathrm{ms}^{-1} .\) It collides elastically with another body, \(\mathrm{B}\) of the same mass which has an initial velocity of \(5 \hat{\mathrm{j}} \;\mathrm{ms}^{-1}\). After collision. A moves with a velocity \(\overline{\mathrm{v}}=4(\hat{\mathrm{i}}+\hat{\mathrm{j}})\). The energy of \(\mathrm{B}\) after collision is written as \(\frac{\mathrm{x}}{10} \;\mathrm{J}\) The value of \(x\) is

A moving coil of galvanometer when shunted with \(2\,\Omega\) resistance gives a full scale deflection for a current of \(500\) mA. When a resistance of \(470\,\Omega\) is connected in series it gives a full scale deflection for \(10\) V potential applied on it. The value of resistance of galvanometer coil is __________ \(\Omega\).

The current of \(5 \mathrm{~A}\) flows in a square loop of sides \(1\) \(\mathrm{m}\) is placed in air. The magnetic field at the centre of the loop is \(\mathrm{X} \sqrt{2} \times 10^{-7} \mathrm{~T}\). The value of \(\mathrm{X}\) is _______.

Two bodies of masses \(1\, kg\) and \(4\, kg\) are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency \(25\, rad/s\), and amplitude \(1.6\, cm\) while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is ..... \(N\) ( take \(g = 10\, ms^{-2}\))