Class 11th

The number of distinct real roots of x4 – 4x + 1 = 0 is:

If y, K and $\eta$  are the value of Young's modulus, bulk modulus of rigidity of any material respectively. Choose

n mole of perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.

A->B         : Isothermal expansion at temperature T so that the volume is doubled from V₁ to V₂ and Pressure changes from P₁ to P₂.

B->C         : Isobaric compression at pressure P₂ to initial volume V₁.

C->A         : Isobaric change leading to change of pressure from P₂ to P₁.

Total work done in the complete cycle ABCA is:

Moment of inertia (M.I) of four bodies, having same mass and radius, and reported as:

I₁ = M.I. of thin circular ring about its diameter

I₂ = M.I. of circular disc about an axis perpendicular to disc and going through the centre,

I₃ = M.I. of solid cylinder about its axis and

I₄ = M.I. of solid sphere about its diameter.

Two stars of masses m and 2m at a distance d rotate about their common  centre of mass in free space. The

If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph?

Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is 'a'. The metal sheet is heated uniformly, bya small temperature   $\Delta T,$ so that its new temperature is T +   $\Delta T.$ Calculate the increase in the volume of the metal box.

For a chemical reaction A + B $?$ C + D

$\left({\Delta }_r{H}^{\Theta }=80kJmo{l}^{-1}\right)$ the entropy change ${\Delta }_r{S}^{\Theta }$ depends on the temperature T (in K) as ${\Delta }_r{S}^{\Theta }=2T\left(J{K}^{-1}mo{l}^{-1}\right).$

Minimum temperature at which it will become spontaneous is-------------K. (Integer)

The number of significant figures in 50000.020 * 10^-3 is………………