You are asked to design a shaving mirror assuming that a person keeps it \(10\,cm\) from his face and views the magnified image of the face at the closest comfortable distance of \(25\,cm.\) The radius of curvature of the mirror would then be.....\(cm\)

Find the truth table for the function \(Y\) and \(A\) and \(B\) represented in the following figure.

A radioactive nucleus decays by two different processes. The half life for the first process is \(10\, s\) and that for the second is \(100 s\). the effective half life of the nucleus is close to\(.....sec\)

The potential energy of a particle of mass \(4\,kg\) in motion along the \(x\)-axis is given by \(U =4(1-\cos 4 x )\,J\). The time period of the particle for small oscillation \((\sin \theta \simeq \theta)\) is \(\left(\frac{\pi}{ K }\right)\,s\). The value of \(K\) is .......

Three identical particle \(A , B\) and \(C\) of mass \(100\, kg\) each are placed in a straight line with \(AB = BC =13 \,m\). The gravitational force on a fourth particle \(P\) of the same mass is \(F\), when placed at a distance \(13 \,m\) from the particle \(B\) on the perpendicular bisector of the line \(AC\). The value of \(F\) will be approximately\(....G\)

In a series \(L R\) circuit \(X_{L}=R\) and power factor of the circuit is \(P _{1}\). When capacitor with capacitance \(C\) such that \(X _{ L }= X _{ C }\) is put in series, the power factor becomes \(P_{2}\). The ratio \(\frac{ P _{1}}{ P _{2}}\) is

The mass density of a planet of radius \(R\) varies with the distance \(r\) from its centre as \(\rho( r )=\rho_{0}\left(1-\frac{ r ^{2}}{ R ^{2}}\right) .\) Then the gravitational field is maximum at

A bus moving along a straight highway with speed of \(72 \mathrm{~km} / \mathrm{h}\) is brought to halt within \(4 \mathrm{~s}\) after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is __________\(\mathrm{m}\).

Three infinitely long wires with linear charge density \(\lambda\) are placed along the \(x-a x i s, y\)-axis and \(z-\) axis respectively. Which of the following denotes an equipotential surface?

A parallel beam of light of wavelength \(900\,nm\) and intensity \(100\,Wm ^{-2}\) is incident on a surface perpendicular to the beam. Tire number of photons crossing \(1\,cm ^{2}\) area perpendicular to the beam in one second is :

Four resistances \(40 \ \Omega, 60\  \Omega, 90\  \Omega\) and \(110\  \Omega\) make the arms of a quadrilateral \(A,B,C,D\). Across \(AC\) is a battery of emf \(40\, V\) and internal resistance negligible. The potential difference across \(BD\) is \(V\) is...... 

Given below are two statements: One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) For measuring the potential difference across a resistance of \(600\,\Omega\), the voltmeter with resistance \(1000\,\Omega\) will be preferred over voltmeter with resistance \(4000\,\Omega\). Reason \(R:\) Voltmeter with higher resistance will draw smaller current than voltmeter with lower resistance. In the light of the above statements, choose the most appropriate answer from the options given below.