A big drop is formed by coalescing \(1000\) small identical drops of water. If \(E_1\) be the total surface energy of \(1000\) small drops of water and \(E_2\) be the surface energy of single big drop of water, the \(E_1\) : \(\mathrm{E}_2\) is \(\mathrm{x}: 1\) where \(x\) = _____.

When current in a coil changes from \(5\,A\) to \(2\,A\) in \(0 .1\,s,\) average voltage of \(50\,V\) is produced. The self- inductance of the coil is.......\(H\)

Refer to the circuit diagram given below. The heat generated across the \(6\,\Omega\) resistance in \(100\) second is \(\dfrac{\alpha}{100}\) J. The value of \(\alpha\) is _______. (Nearest integer)

A rectangular loop of length \(2.5 \mathrm{~m}\) and width \(2 \mathrm{~m}\) is placed at \(60^{\circ}\) to a magnetic field of \(4 \mathrm{~T}\). The loop is removed from the field in \(10 \ \mathrm{sec}\). The average emf induced in the loop during this time is

Two resistance of \(100\ \Omega\) and \(200\  \Omega\) are connected in series with a battery of \(4 \mathrm{~V}\) and negligible internal resistance. \(A\) voltmeter is used to measure voltage across \(100 \Omega\) resistance, which gives reading as \(1 \mathrm{~V}\). The resistance of voltmeter must be _______ \(\Omega\).

The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be \(....m\) Given, the length of the rod is \(10 \sqrt{3} m\).

A uniform rod \(AB\) is suspended from a point \(X\), at a variable distance from \(x\) from \(A\), as shown. To make the rod horizontal, a mass \(m\) is suspended from its end \(A\). A set of \((m, x)\) values is recorded. The appropriate variable that give a straight line, when plotted, are

A parallel - plate capacitor with plate area \(A\) has separation \(d\) between the plates. Two dielectric slabs of dielectric constant \({K}_{1}\) and \({K}_{2}\) of same area \(\frac A2\) and thickness \(\frac d2\) are inserted in the space between the plates. The capacitance of the capacitor will be given by :

Name the logic gate equivalent to the diagram attached

The following diagram shows a Zener diode as a voltage regulator. The Zener diode is rated at \(V _{ Z }=5 V\) and the desired current in load is 5 mA . The unregulated voltage source can supply upto 25 V . Considering the Zener diode can withstand four times of the load current, the value of resistor \(R _{ S }\) (shown in circuit) should be ___________ \(\Omega\).

In an experiment to determine the Young's modulus, steel wires of five different lengths \((1,2,3,4\) and \(5\,m )\) but of same cross section \(\left(2\,mm ^{2}\right)\) were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is \(x \times 10^{11}\,Nm ^{-2}\), then the value of \(x\) is

Match List I with List \(II\) Choose the correct answer from the options given below: