The same size images are formed by a convex lens when the object is placed at \(20\, cm\) or at \(10\, cm\) from the lens. The focal length of convex lens is ............ \(cm\).

What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

The gravitational field in a region is given by \(\vec E\) \(=(5\,N / kg)\, \hat i + (12\,N / kg)\,\hat j\) If the potential at the origin is taken to be zero, then the ratio of the potential at the points \((12\,m, 0)\) and \((0, 5\,m)\) is

In the circuit shown, the potential difference between \(A\) and \(B\) is ............. \(V\)

Two inclined planes are placed as shown in figure. A block is projected from the Point \(A\) of inclined plane \(A B\) along its surface with a velocity just sufficient to carry it to the top Point \(B\) at a height \(10 m\). After reaching the Point \(B\) the block slides down on inclined plane \(BC\). Time it takes to reach to the point \(C\) from point \(A\) is \(t (\sqrt{2}+1) s\). The value of \(t\) is........(use \(g =10 m / s ^{2}\) )

When the \(rms\) voltages \(V_L, V_C\) and \(V_R\) are measured respectively across the inductor \(L\), the capacitor \(C\) and the resistor \(R\) in a series \(LCR\) circuit connected to an \(AC\) source, it is found that the ratio \(V_L : V_C : V_R = 1 : 2 : 3\). If the \(rms\) voltage of the \(AC\) sources is \(100\, V\), the \(V_R\) is close to........\(V\)

Three point charges of magnitude \(5 \mu C , 0.16 \mu C\) and \(0.3 \mu C\) are located at the vertices \(A , B , C\) of a right angled triangle whose sides are \(AB =3\,cm\), \(BC =3 \sqrt{2}\,cm\) and \(CA =3\,cm\) and point \(A\) is the right angle corner. Charge at point \(A\) experiences \(N\) of electrostatic force due to the other two charges.

The diameter of the objective lens of microscope makes an angle \(\beta \) at the focus of the microscope. Further, the medium between the object and the lens is an oil of refractive index \(n\). Then the resolving power of the microscope

Two ideal polyatomic gases at temperatures \(T _{1}\) and \(T _{2}\) are mixed so that there is no loss of energy. If \(F _{1}\) and \(F _{2}, m _{1}\) and \(m _{2}, n _{1}\) and \(n _{2}\) be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is

An alternating voltage source \(V =260 \sin (628\,t )\) is connected across a pure inductor of \(5\,mH\). Inductive reactance in the circuit is \(......... \Omega\)

When a car is approaching the observer, the frequency of horn is \(100 Hz\). After passing the observer, it is \(50\,Hz\). If the observer moves with the car, the frequency will be \(\frac{ x }{3} Hz\) where \(x =.....\)

A beam of light travelling along \(X\)-axis is described by the electric field \(E _{ y }=900 \sin \omega( t - x / c )\). The ratio of electric force to magnetic force on a charge \(q\) moving along \(Y\)-axis with a speed of \(3 \times 10^{7}\,ms ^{-1}\) will be. [Given speed of light \(=3 \times 10^{8}\,ms ^{-1}\) ]

Three parallel plate capacitors each with area A and separation d are filled with two dielectric ( \(k _1\) and \(k _2\) ) in the following fashion. Which of the following is true? \(\left( k _1> k _2\right)\)