Class 11th

An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is S? and that of the other part is S?. Given that S? > S?. If the piston is removed then the total entropy of the system will be :

Given below are two statements:
Statement I: Bohr's theory accounts for the stability and line spectrum of Li²? ion.
Statement II: Bohr's theory was unable to explain the splitting of spectral lines in the presence of a magnetic field.
In the light of the above statements, choose the most appropriate answer from the options given below:

The value of Σ[r=0 to 6] (⁶Cᵣ ⋅ ⁶C₆₋ᵣ) is equal to:

If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately :
[Take g = 10 ms⁻², the radius of earth, R = 6400*10³ m, Take π = 3.14]

If the integral ∫[0 to 10] (sin(2πx)) / (e^(x-[x])) dx = αe⁻¹ + βe⁻¹/² + γ where α, β, γ are integers and [x] denotes the greatest integer less than or equal to x, then the value of α + β + γ is equal to:

The function of time representing a simple harmonic motion with time period of π/ω is:

The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is L. The magnitude of the areal velocity of the planet is:

Let L be a tangent line to parabola y² = 4x - 20 at (6,2). If L is also a tangent to the ellipse x²/2 + y²/b = 1, then the value of b is equal to:

For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to ( where γ is the ratio of specific heats):

A particle of mass m moves in a circular orbit under the central potential field, V(r) = -C/r, where C is a constant. The correct radius-velocity graph of the particle's motion is;