Two cylindrical vessels of equal cross sectional area of $2{\mathrm{m}}^2$ contain water upto heights 10 m and 6 m , respectively. If the vessels are connected at their bottom then the work done by the force of gravity is (Density of water is $10^3\mathrm{kg}/{\mathrm{m}}^3$ and $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$ )

A solid steel ball of diameter 3.6 mm acquired terminal velocity $2.45\times 10^{-2}\mathrm{m}/\mathrm{s}$ while falling under gravity through an oil of density $925\mathrm{kg}{\mathrm{m}}^{-3}$. Take density of steel as $7825\mathrm{kg}{\mathrm{m}}^{-3}$ and g as $9.8\mathrm{m}/{\mathrm{s}}^2$. The viscosity of the oil in SI unit is

A body of mass ‘m’ connected to a massless and unstretchable string goes in vertical circle of radius ‘R’ under gravity g. The other end of the string is fixed at the center of circle. If velocity at top of circular path is $n\sqrt{gR}$ , where, n ≥ 1, then ratio of kinetic energy of the body at bottom to that at top of the circle is :

A bob of mass $m$ is suspended at a point $O$ by a light string of length $l$ and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity $v_0$ at the point ' A ', the string becomes slack when, the bob reaches at the point ' $D$ '. The ratio of the kinetic energy of the bob at the points B and C is _________.

A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point $A$ is $10\mathrm{m}/\mathrm{s}$. The ratio of its kinetic energies at point B and C is : (Take acceleration due to gravity as $10\mathrm{m}/{\mathrm{s}}^2$)

A car of mass ' $m$ ' moves on a banked road having radius ' $r$ ' and banking angle $\theta$. To avoid slipping from banked road, the maximum permissible speed of the car is $v_0$. The coefficient of friction $\mu$ between the wheels of the car and the banked road is

A sportsman runs around a circular track of radius $r$ such that he traverses the path $A B A B$. The distance travelled and displacement, respectively, are

A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is $8\mathrm{m}/\mathrm{s}$. The speed of the particle on the rim of the wheel at the same level as the centre of wheel, will be :

For the circuit shown above, equivalent GATE is :

The truth table for the circuit given below is:

Which of the following circuits represents a forward biased diode? Choose the correct answer from the options given below:

Refer to the circuit diagram given in the figure. which of the following observations are correct? A. Total resistance of circuit is $6\Omega$ B. Current in Ammeter is 1 A C. Potential across $A B$ is 4 Volts. D. Potential across CD is 4 Volts E. Total resistance of the circuit is $8\Omega$. Choose the correct answer from the options given below:

What is the current through the battery in the circuit shown below?

Consider the following statements : A. The junction area of solar cell is made very narrow compared to a photo diode. B. Solar cells are not connected with any external bias. C. LED is made of lightly doped p-n junction. D. Increase of forward current results in continuous increase of LED light intensity. E. LEDs have to be connected in forward bias for emission of light. Choose the correct answer from the options given below :

The output of the circuit is low (zero) for : (A) $X=0, Y=0$ (B) $X=0, Y=1$ (C) $X=1, Y=0$ (D) $X=1, Y=1$ Choose the correct answer from the options given below :

Which of the following circuits has the same output as that of the given circuit?

The output voltage in the following circuit is (Consider ideal diode case)

A zener diode with 5 V zener voltage is used to regulate an unregulated dc voltage input of 25 V . For a $400\Omega$ resistor connected in series, the zener current is found to be 4 times load current. The load current $\left(I_L\right)$ and load resistance $\left(R_L\right)$ are :

In the following circuit, the reading of the ammeter will be $($ Take Zener breakdown voltage $=4\mathrm{V})$