An observer looks at a distant tree of height \(10\ m\) with a telescope of magnifying power of \(20\). To the observer the tree appears :

As shown in the figure, a spring is kept in a stretched position with some extension by holding the masses 1 kg and 0.2 kg with a separation more than spring natural length and are released. Assuming the horizontal surface to be frictionless, the angular frequency (in SI unit) of the system is :

A projectile is thrown upward at an angle \( 60^{\circ} \) with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is \( 45^{\circ} \) with the horizontal. The initial speed of the projectile is __________ in m/s.

A \(2\, \mu F\) capacitor \(C _{1}\) is first charged to a potential difference of \(10\, V\) using a battery.Then the battery is removed and the capacitor is connected to an uncharged capacitor \(C _{2}\) of \(8\, \mu F\). The charge in \(C _{2}\) on equilibrium condition is \(\ldots\,\mu C\). (Round off to the Nearest Integer)

\(ABC\) is a plane lamina of the shape of an equilateral triagnle. \(D,\) \(E\) are mid points of \(AB\), \(AC\) and \(G\) is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through \(G\) and perpendicular to the plane \(ABC\) is \(I _{0} .\) If part \(ADE\) is removed, the moment of inertia of the remaining part about the same axis is \(\frac{ NI _{0}}{16}\) where \(N\) is an integer. Value of \(N\) is

The distance between an object and a screen is \(100\, cm .\) A lens can produce real image of the object on the screen for two different positions between the screen and the object. The distance between these two positions is \(40\, cm .\) If the power of the lens is close to \(\left(\frac{ N }{100}\right) D\) where \(N\) is an integer, the value of \(N\) is.......

A thin convex lens \(L\) (refractive index \(= 1.5\)) is placed on a plane mirror \(M\). When a pin is placed at \(A\), such that \(OA = 18\, cm\), its real inverted image is formed at \(A\) itself, as shown in figure. When a liquid of refractive index \({\mu _1}\) is put between the lens and the mirror, the pin has to be moved to \(A’\). such that \(OA’ = 27\,cm\), to get its inverted real image at \(A'\) itself. The value of \({\mu _1}\) will be

In a Frank-hertz experiment, an electron of energy \(5.6\,eV\) passes through mercury vapour and emerges with an energy \(0.7\,eV.\) The minimum wavelength of photons emitted by mercury atoms is close to ............. \(nm\)

Two charges of \(-4 \ \mu \mathrm{C}\) and \(+4\  \mu \mathrm{C}\) are placed at the points \(A(1,0,4) \mathrm{m}\) and \(B(2,-1,5) \mathrm{m}\) located in an electric field \(\vec{E}=0.20 \hat{\mathrm{i}} \mathrm{V} / \mathrm{cm}\). The magnitude of the torque acting on the dipole is \(8 \sqrt{\alpha} \times 10^{-3} \mathrm{Nm}\), Where \(\alpha=\)___________

The velocity of upper layer of water in a river is \(36 kmh ^{-1}\). Shearing stress between horizontal layers of water is \(10^{-3} Nm ^{-2}\). Depth of the river is \(m\). (Co-efficiency of viscosity of water is \(10^{-2} \,Pa . s\) )

Four \(NOR\) gates are connected as shown in figure. The truth table for the given figure is :

A series LCR circuit with \(R = 20\ \Omega\), \(L = 1.6\text{ H}\) and \(C = 40\ \mu\text{F}\) is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is _______ \(\Omega\).