Two electric resistors have equal values of resistance \(R\). Each can be operated with a power of 320 watts ( \(W\) ) at 220 volts. If the two resistors are connected in series to a 110 volts electric supply, then the power generated in each resistor is

The centre of mass of three particles of masses \(1 \mathrm{~kg}, 2 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) is at \((2,2,2)\). The position of the fourth mass of \(4 \mathrm{~kg}\) to be placed in the system as that the new centre of mass is at \((0,0,0)\) is.

A ball of mass \(2 \mathrm{~kg}\) is moving in \(x y\)-plane with a potential energy given as \(U=(12 x+16 y) \mathrm{J}, x\) and \(y\) being in metre. Assume the initial position of the ball at \(t=0\) is at origin \((0,0)\) and it is moving with a velocity of \((15 \hat{\mathbf{i}}+20 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}\). Then, identify the correct statement.

Which of the following statement is incorrect?

A fully charged capacitor has a capacitance \(C\). It is discharged through a small coil of resistance wire, embedded in a block of specific heat \(s\) and mass \(m\) under thermally isolated conditions. If the temperature of the block is raised by \(\Delta T\), the potential difference \(V\) across the capacitor initially is

Match the following table. \begin{array}{|c|c|c|c|} \hline & List-I & & List-II \ \hline A. & \begin{array}{l}\text { Michelson-Morley } \ \text { experiment }\end{array} & I. & \begin{array}{l}\text { The existence of } \ \text { anti-matter }\end{array} \ \hline B. & \begin{array}{l}\text { Stern-Gerlach } \ \text { experiment }\end{array} & II. & \begin{array}{l}\text { The existence of } \ \text { de-Broglie matter waves }\end{array} \ \hline C. & \begin{array}{l}\text { Davisson-Germer } \ \text { experiment }\end{array} & III. & Electrons have spins \ \hline D. & \begin{array}{l}\text { Anderson discovery } \ \text { of positron }\end{array} & \mathrm{IV}. & \begin{array}{l}\text { The non-existence of } \ \text { ether }\end{array} \ \hline \end{array} \(\begin{array}{llll}A & B & C & D\end{array}\)

If $5 \mathrm{mg}$ of ${}^{235}U$ is completely destroyed in an atom bomb, then approximate total energy released is (given that the energy released per fission is $200 \mathrm{MeV}$)

A cup of coffee cools from \(150^{\circ} \mathrm{F}\) to \(144^{\circ} \mathrm{F}\) in \(1 \mathrm{~min}\) in a room temperature at \(72^{\circ} \mathrm{F}\). How much time with the coffee take to cool from \(110^{\circ} \mathrm{F}\) to \(104^{\circ} \mathrm{F}\) in the same room?

A particle of mass \(1 \mathrm{~kg}\) is projected with an initial velocity \(10 \mathrm{~ms}^{-1}\) at an angle of projection \(45^{\circ}\) with the horizontal. The average torque acting on the projectile, between the time at which it is projected and the time at which it strikes the ground, about the point of projection in newton-metre is

A water barrel having water upto a depth \(d\) is placed on a table of height \(h\). A small hole is made on the wall of the barrel at its bottom. If the stream of water coming out of the hole falls on the ground at a horizontal distance \(R\) from the barrel, then the value of \(d\) is

The temperature of a body shown by a faulty Celsius thermometer is \(49^{\circ} \mathrm{C}\) and by a correct Fahrenheit thermometer is \(122^{\circ} \mathrm{F}\). The correction to be applied to the faulty thermometer is

Wires \(A\) and \(B\) have resistivities \(\rho_A\) and \(\rho_B\), \(\left(\rho_B=2 \rho_A\right)\) and have lengths \(l_A\) and \(l_B\). If the diameter of the wire \(B\) is twice that of \(A\) and the two wires have same resistance, then \(\frac{l_B}{l_A}\) is

A highway truck has two horns \(A\) and \(B\). When sounded together, the driver records 50 beats in 10 seconds. With horn \(B\) blowing and the truck moving towards a wall at a speed of \(10 \mathrm{~m} / \mathrm{s}\), the driver noticed a beat frequency of \(5 \mathrm{~Hz}\) with the echo. When frequency of \(A\) is decreased the beat frequency with two horns sounded together increases. Calculate the frequency of horn \(A\). (Speed of sound in air \(=330 \mathrm{~m} / \mathrm{s}\) )