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A particle is executing Simple Harmonic Motion of amplitude 6 m and period 3⋅ 5

seconds. Find the maximum velocity of the particle.


Write the limitations of the Malthusian model of population growth.


Write the three-dimensional Gaussian model dispersion for the atmospheric pollution

problem. Modify the model under the following assumptions:

(i) Wind velocity is in only y -direction.

(ii) Mass transfer due to bulk motion in the y -direction overshadows the

contributions due to mass diffusion.

(iii) Motion is in steady state.

(iv) Wind speed is constant.

(v) Diffusivities are constant in all the directions.


Find the equilibrium price in a perfectly competitive market with the supply function S(p)= (-p2 + 4)/3 the demand function D( p) = (− p + 2 )Using the static criterion of Walras, determine whether the price is stable or not.


Find the equilibrium price in a perfectly competitive market with the supply function S(p)= (-p2 + 4)/3 the demand function D( p) = (− p + 2 )Using the static criterion of Walras, determine whether the price is stable or not.


Consider the blood flow in an artery following Poiseuille’s law. If the length of the

artery is 3 cm, radius is 7×10-3 cam and driving force is


5×103 dynes/cm2, then


using blood viscosity, µ = 0 ⋅ 027 poise, find the

(i) velocity u( y) and the maximum peak velocity of blood, and

(ii) shear stress at the wall of the artery.


A body is falling free in a vacuum. The fall is necessarily related to the gravitational 

acceleration g and the height h from which the body is dropped. Use dimensional 

analysis to show that the velocity V of the falling body satisfies the relation 

V / √gh = constant


If the average ticket price for movie A in its first week was 1.4 times the average ticket price in its third week, what was the average ticket price for movie A in its first week?


"Use a 6- bit BCD code to encode the word 'MATH'"


If xz⁴i-2ײyzj+2yz³k ,find ∆×A at point (1,-1,1)