A convex lens of focal length \(20\,cm\) is placed in front of convex mirror with principal axis coinciding each other. The distance between the lens and mirror is \(10\,cm\). A point object is placed on principal axis at a distance of \(60\,cm\) from the convex lens. The image formed by combination coincides the object itself. The focal length of the convex mirror is \(...cm\).

For a charged spherical ball, electrostatic potential inside the ball varies with \(r\) as \(V =2 ar ^2+ b\). Here, \(a\) and \(b\) are constant and \(r\) is the distance from the center. The volume charge density inside the ball is \(-\lambda a \varepsilon\). The value of \(\lambda\) is \(...........\). \(\varepsilon=\) permittivity of medium.

For which of the following particles will it be most difficult to experimentally verify the deBroglie relationship?

Math List \(I\) with List \(II\) Choose the correct answer from the option given below:

A parallel palate capacitor with square plates is filled with four dielectrics of dielectric constants \(K_1, K_2, K_3, K_4\) arranged as shown in the figure. The effective dielectric constant \(K\) will be

Five persons \(P_1, P_2, P_3, P_4\) and \(P_5\) recorded object distance (u) and image distance (v) using same convex lens having power +5 D as \((25,96),(30,62)\), \((35,37),(45,35)\) and \((50,32)\) respectively. Identify correct statement

A ball of mass \(10\, kg\) moving with a velocity \(10 \sqrt{3} m / s\) along the \(x-\)axis, hits another ball of mass \(20\, kg\) which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along \(y-\)axis with a speed of \(10\) \(m / s\). The second piece starts moving at an angle of \(30^{\circ}\) with respect to the \(x-\)axis. The velocity of the ball moving at \(30^{\circ}\) with \(x-\) axis is \(x\, m / s\). The configuration of pieces after collision is shown in the figure below. The value of \(x\) to the nearest integer is

A rectangular parallelopiped is measured as \(1\,cm \times 1\,cm \times 100\,cm\). If its specific resistance is \(3 \times 10^{-7}\,\Omega\,m\), then the resistance between its two opposite rectangular faces will be \(..........x^{-7} \Omega\).

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?

An eight digit number divisible by \(9\) is to be formed using digits from \(0\) to \(9\) without repeating the digits. The number of ways in which this can be done is:

The domain of the function \(f(x)=\frac{\cos ^{-1}\left(\frac{x^{2}-5 x+6}{x^{2}-9}\right)}{\log _{e}\left(x^{2}-3 x+2\right)} \text { is }\)

The resistance of a conductor at \(15^{\circ} {C}\) is \(16\, \Omega\) and at \(100\, {C}\) is \(20\, \Omega\). What will be the temperature coefficient of resistance of the conductor?

As shown in the figure, a combination of a thin plano concave lens and a thin plano convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is \(30\,cm\) and refraction index of the material for both the lenses is \(1.75\). Both the lenses are placed at distance of \(40\,cm\) from each other. Due to the combination, the image of the object is formed at distance \(x =..........cm\), from concave lens.