MEC-203 English Medium Solved Assignments 2025-26

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MEC-203 English Medium Solved Assignments 2025-26 Available

Part I
Answer the following questions. Each question carries 20 marks
2 × 20 = 40
1. a) Explain Taylor’s theorem to polynomial expansion.
b) Using Taylor’s approach, find Taylor’s series expansion for the function:
f(x,y,z)=x,y,z around the point (1,1,1)
2. Given the input matrix and the final demand vector:
𝐴 = [0.10 0.15 0.12 0.20 0 0.30 0.25 0.40 0.20 ] 𝑑 = [
100
200
300
]
a) Explain the economic meaning of the elements 0.30,0 and 200
b) Explain the economic meaning of (if any) of the third column sum
c) Explain the economic meaning of (if any) of the third row sum
d) Write out the specific input-output matrix equation for this model
e) Find the solution output levels of the three industries using Cramer’s rule.
Part II
Answer the following questions. Each question carries 12 marks.
6 X 12=60
3. a) What are isoperimetric problems?
b) Find the extremal for the functional
𝐽(. ) = ∫ 2𝑥𝑡
′2 𝑡𝑓
𝑡0
+24x(t).t) dt,
𝐵𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛 𝑥(𝑡0
) = 0, −𝑥(𝑡𝑓) = 2
t0=0, tf=2
4. a) Discuss the features of chi square, t and f test?
b) x1,x2…xn is a random sample from a Normal population N(µ,1). Show that
𝑥̅=
1
𝑛
∑ 𝑥𝑖
𝑛 2
𝑖=1
is an unbiased estimator of µ
2+1
5. Consider the following simple problem:
𝑚𝑖𝑛.{𝑔0
(𝑢)} = ∫ {(𝑥(𝑡))
2+ (𝑢(𝑡))2}10𝑑𝑡
Subject to 𝑑𝑥
𝑑𝑡= 𝑢(𝑡), 𝑥(0) = 1
6. Examine the following functions for maxima and minima:
a) 𝑧 = −𝑥
2 + 𝑥𝑦 − 𝑦
2 + 𝑥 + 5𝑦
b) 𝑦 = 𝑥
3 − 2𝑥
2 + 𝑥 − 6
7. Write short notes on following:
e) Euler-Lagrange equation
f) Central Limit theorem
g) Hamiltonian function
h) Cramer –Rao inequality