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5. (a) A particle is executing Simple Harmonic Motion of amplitude 6 m and period 3⋅ 5
seconds. Find the maximum velocity of the particle.
3(b) Write the limitations of the Malthusian model of population growth.
3. (a) The sales of a small factory since 2008 are as follows: (6)
Year Sales
(in ` lakhs)
2008 8
2009 10
2010 9
2011 11
2012 11
2013 12
Using 2008 as the zero year, find the least-square trend-line equation.
2(b) Write the three-dimensional Gaussian model dispersion for the atmospheric pollution
problem. Modify the model under the following assumptions: (5)
(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.
2. (a) Find the equilibrium price in a perfectly competitive market with the supply function
( ) ( 3/)4
2
S p = − p + and the demand function D( p) = − p + .2 Using the static
criterion of Walras, determine whether the price is stable or not.
1(b) Consider the blood flow in an artery following Poiseuille’s law. If the length of the
artery is 3 cm, radius is 3
7 10−
× cam and driving force is 3
5×10 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.
1. (a) 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.
Which of the following statements is INCORRECT about the purposes of assessment in emergent mathematics? 1) Assessment is used to guide teachers in their instructional planning. 2) Assessment is used to identify children who must be retained the following year. 3) Assessment is used for grading purposes. 4) Assessment helps teachers to evaluate their own teaching or programme.
Which one is NOT a method of assessment in emergent mathematics? 1) Observation 2) Oral discussion 3) Portfolio 4) Milestone
. Brandon’s response “Let’s join two shoe boxes together. It’s about the same size as the cereal box, just a little bigger” and “Let’s put the toothpaste box here in front,” explains his understanding of: 1) Estimation and prediction 2) Prediction and ordering 3) Estimation and positionality 4) Estimation and ordering
