An object is dropped from a height \(h\) from the ground. Every time it hits the ground it looses \(50\%\) of its kinetic energy. The total distance covered as \(t \to \infty \) is

Two thin convex lenses of focal length 30 cm and 10 cm are placed coaxially, 10 cm apart. The power of this combination is :

A particle is projected with velocity \(u\) so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as \(\frac{n u^2}{25 g}\), where value of \(n\) is : (Given ' \(g\) ' is the acceleration due to gravity).

A square shaped hole of side \(l=\frac{a}{2}\) is carved out at a distance \(d =\frac{ a }{2}\) from the centre \('O'\) of a uniform circular disk of radius \(a\). If the distance of the centre of mass of the remaining portion from \(O\) is \(-\frac{a}{X},\) value of \(X\) (to the nearest integer) is.......

\(Y = A \sin \left(\omega t +\phi_{0}\right)\) is the time-displacement equation of a SHM. At \(t=0\) the displacement of the particle is \(Y =\frac{ A }{2}\) and it is moving along negative \(x\) -direction. Then the initial phase angle \(\phi_{0}\) will be ...... .

The actual value of resistance \(R\), shown in the figure is \(30\,\Omega \). This is measured in an experiment as shown using the standard formula \(R = \frac{V}{I}\) where \(V\) and \(I\) are the readings of the voltmeter and ammeter, respectively. If the measured value of \(R\) is \(5\%\) less, then the internal resistance of the voltmeter is ................. \(\Omega\)

When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted election is \(v _{1}\). When the frequency of incident radiation is increased to five times the threshold value, the maximum velocity of emitted electron becomes \(v _{2}\). If \(v _{2}= x\) \(v _{1}\), the value of \(x\) will be...........

When two resistance \(R_1\) and \(R_2\) connected in series and introduced into the left gap of a meter bridge and a resistance of \(10 \Omega\) is introduced into the right gap, a null point is found at \(60 cm\) from left side. When \(R_1\) and \(R_2\) are connected in parallel and introduced into the left gap, a resistance of \(3 \Omega\) is introduced into the right-gap to get null point at 40 cm from left end. The product of \(R_1 R_2\) is \(.............\Omega\)

Refer the figure given below. \(\mu_1\) and \(\mu_2\) are refractive indices of air and lens material. The height of image will be _______ cm.

A light wave is incident normally on a glass slab of refractive index \(1.5\). If \(4\%\) of light gets reflected and the amplitude of the electric field of the incident light is \(30\, V/m\), then the amplitude of the electric field for the wave propagating in the glass medium will be.......\( V/m\)

A parallel plate capacitor was made with two rectangular plates, each with a length of \(l=3 \mathrm{~cm}\) and breath of \(\mathrm{b}=1 \mathrm{~cm}\). The distance between the plates is \(3 \mu \mathrm{~m}\). Out of the following, which are the ways to increase the capacitance by a factor of 10 ?
A. \(l=30 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m}\)
B. \(l=3 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=30 \mu \mathrm{~m}\)
C. \(l=6 \mathrm{~cm}, \mathrm{~b}=5 \mathrm{~cm}, \mathrm{~d}=3 \mu \mathrm{~m}\)
D. \(l=1 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=10 \mu \mathrm{~m}\)
E. \(l=5 \mathrm{~cm}, \mathrm{~b}=2 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m}\)
Choose the correct answer from the options given below:

Wheatstone bridge principle is used to measure the specific resistance \(\left(S_1\right)\) of given wire, having length \(L\), radius \(r\). If \(X\) is the resistance of wire, then specific resistance is: \(S_1=X\left(\frac{\pi r^2}{L}\right)\). If the length of the wire gets doubled then the value of specific resistance will be :

The number of strictly increasing functions f from the set {1, 2, 3, 4, 5, 6} to the set {1, 2, 3,...,9} such that \( f(i)\ne i \) for \( 1\le i\le6, \) is equal to: