A wide tank of cross-section area A, containing a liquid to a height H, has an orifice at its base of area A/3. The initial velocity of top surface of liquid is

Two magnets A and B are identical and these are arranged as shown in the figure. Their length is negligible in comparison to the separation between them. A magnetic needle is placed between the magnets at point P which gets deflected through an angle θ under the influence of magnets. The ratio of distance d₁ and d₂ will be

In a Zener regulated power supply a Zener diode with V_Z = 6.0 V is used for regulation. The load current is to be 4.0 mA and the unregulated input is 10.0 V. What should be the value of series resistor R_S? Choose zener current to be 20 mA.

The main scale of vernier callipers reads in mm and its vernier scale is divided into 8 divisions which coincide with 5 divisions of the main scale. When the two jaws touch each other, the zero of the vernier coincides with the zero of main scale. When a rod is tightly placed along its length between the jaws, it is observed that the zero of vernier scale lies just left to 36^th division of main scale and fourth division of vernier scale coincides with one main scale division. The measured value is (in cm)

A swimmer crosses a river with minimum possible time 10 second. And when he reaches the other end starts swimming in the direction towards the point from where he started swimming. Keeping the direction fixed the swimmer crosses the river in 15 sec. The ratio of speed of swimmer with respect to water and the speed of river flow is (Assume constant speed of river & swimmer) :-

The equation of the stationary wave is :

Which of the following statements is wrong?

The moment of inertia about x-axis of uniform thin plate of density ρ kg/m² as shown in the figure is Npa⁷ / 21, then find the value of N.

A graph between velocity and displacement of a particle performing SHM is shown. Find the acceleration when the particle is at half of maximum displacement from mean position.

In an Air conditioner compartment of a train, a material of thermal conductivity K and thickness 10 cm is required to fullfill the purpose. To do so there is a need of two glass each of thickness 1 cm with air gap of 8 cm between them. If thermal conductivity of glass and air are 1 W/mk and 0.01 W/mk then the value of thermal conductivity K is

Three moles of an ideal monoatomic gas perform a cyclic process as shown in figure. The gas temperature in different states are T₁ = 400 K, T₂ = 800 K, T₃ = 2400 K and T₄ = 1200 K. Find the work done during the cycle.