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Find the increment and differential of each of the following functions for the given values of the variables and their increments.



𝑥 ln 𝑦 + 𝑦 ln 𝑥; 𝑥 = 𝑦 = 1, ∆𝑥 = 0.01, ∆𝑦 = 0.02

Find by use of differentials the approximate total area of a right circular cone whose base radius



and height are 5.03 inches and 11.89 inches, respectively.

Find, approximately, the amount of metal in a closed tin can 3 inches in diameter and 5 inches


high, if the metal is 1/32 inches thick.

A volume of 0.36 m3 of air initially at a temperature of 20oC and a 03 pressure of 4bar is compressed reversibly and isothermally to a final

volume of 0.06m3. Calculate the mass, the final pressure, work done and

heat transfer. The specific heat and gas constant can be taken as 1kJ/kgK

and 287 J/kg


What is the use of Indentation in Python?

What is procedure oriented paradigm ?

A piulley supporting a load of 400 N is mounted at C on a horizontal beam .if the beam weighs 800N,find the support reactions at A and B . neglect the weights of the pulley.

A wholesaler packs bags of sugar with a nominal weight of 1000g using an automatic machine. A retailer is considering the purchase of a large batch, does not want too many bags to be noticeably underweight: he states that the sampling plan for the lot of 5000 bags requires a sample size of 80 and acceptance number of 1. Complete the Cumulative Poisson Distribution Table in Table 1 and sketch an Operational Characteristic (OC) Curve for eight points.


I. Explain the difference between Taniguchi “top-down approach” to the “bottom-up approach” of Drexler.









II. Explain the importance of coating superparamagnetic colloids In Vivo and In Vitro applications.







III. Discuss the potential applications of nanotechnology in the field of energy and environment.

Explain the difference between installation and insulation.



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