When a coin is tossed, p(X = r heads)=

If X B(20, 1 / 2) The variance is

 then the values of  a and b are

When a force is applied on a wire of uniform cross-sectional area   and length 4 m, the increase in length is 1 mm. what will be energy stored in it ?

On stretching a wire what is the elastic energy stored per unit volume?

The dot in figure represents the initial state of a gas An adiabat divides the p-V diagram into regions 1 and 2 as shown As the gas moves down along the adiabatic, the temperature

The dot in figure represents the initial state of a gas An adiabat divides the p-V diagram into regions 1 and 2 as shown For which of the following processes, the corresponding heat supplied to the system Q is positive

Two cylinder A and B having piston connected by massless rod (as shown in figure) The cross-sectional area of two cylinders are same & equal to ‘S’ The cylinder A contains m gm of an ideal gas at Pressure P & temperature The cylinder B contain identical gas at same temperature but has different mass The piston is held at the state in the position so that volume of gas in cylinder A & cylinder B are same & is equal to V₀ The walls & piston of cylinder A are thermally insulated, where as cylinder B is maintained at temperature The whole system is in vacuum Now the piston is slowly released and it moves towards left & mechanical equilibrium is reached at the state when the volume of gas in cylinder A becomes Then (here g for gas = 1.5) What will be the compressive force in connecting rod at equilibrium

Two cylinder A and B having piston connected by massless rod (as shown in figure) The cross-sectional area of two cylinders are same & equal to ‘S’ The cylinder A contains m gm of an ideal gas at Pressure P & temperature The cylinder B contain identical gas at same temperature but has different mass The piston is held at the state in the position so that volume of gas in cylinder A & cylinder B are same & is equal to V₀ The walls & piston of cylinder A are thermally insulated, where as cylinder B is maintained at temperature The whole system is in vacuum Now the piston is slowly released and it moves towards left & mechanical equilibrium is reached at the state when the volume of gas in cylinder A becomes Then (here g for gas = 1.5) If work done by the gas in cylinder B is W_B & work done by the gas in cylinder A is W_A then

Two cylinder A and B having piston connected by massless rod (as shown in figure) The cross-sectional area of two cylinders are same & equal to ‘S’ The cylinder A contains m gm of an ideal gas at Pressure P & temperature The cylinder B contain identical gas at same temperature but has different mass The piston is held at the state in the position so that volume of gas in cylinder A & cylinder B are same & is equal to V₀ The walls & piston of cylinder A are thermally insulated, where as cylinder B is maintained at temperature The whole system is in vacuum Now the piston is slowly released and it moves towards left & mechanical equilibrium is reached at the state when the volume of gas in cylinder A becomes Then (here g for gas = 1.5) The change in internal energy of gas in cylinder A

Two cylinder A and B having piston connected by massless rod (as shown in figure) The cross-sectional area of two cylinders are same & equal to ‘S’ The cylinder A contains m gm of an ideal gas at Pressure P & temperature The cylinder B contain identical gas at same temperature but has different mass The piston is held at the state in the position so that volume of gas in cylinder A & cylinder B are same & is equal to V₀ The walls & piston of cylinder A are thermally insulated, where as cylinder B is maintained at temperature The whole system is in vacuum Now the piston is slowly released and it moves towards left & mechanical equilibrium is reached at the state when the volume of gas in cylinder A becomes Then (here g for gas = 1.5) The mass of gas in cylinder B

If a spring extends by x cm loading then what is the energy stored by the spring ? (If is tension in the spring & K is spring constant)

We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 

Assertion : A random variable X takes the values 0,1,2. It’s mean is 0.6. If P(X=0) =0.5 then P(X=1) = 0.4
Reason: If X : S R is a discrete random variable with range 1 2 3 x , x , x ,.... then mean

Infinite limits in calculus occur when the function is unbounded and tends toward infinity or negative infinity as x approaches a given value.

A wire of length 50 cm and cross - sectional area of 1 mm² is extended by 1 mm what will be the required work?