Category 21MAT21

VTU Model Question Papers 2022 Download in PDF

Download VTU Model Question Paper for 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, 8th, All semesters and Odd and Even Semesters in PDF VTU 1st Year Model Question Papers 2022…

Apply Stoke’s theorem and evaluate

4.C] Apply Stoke’s theorem to evaluate ∬ 𝑐𝑢𝑟𝑙 𝐹⃗ ∙ 𝑛̂𝑑𝑠 , where 𝐹⃗ = (𝑥2+𝑦2)𝑖̂− 2𝑥𝑦𝑗̂, taken around the rectangle bounded by the lines 𝑥 = ±𝑎, 𝑦 =…

Apply Green’s theorem and Solve the Problem

4.B] Apply Green’s theorem to evaluate ∫c[(3𝑥 − 8𝑦2)𝑑𝑥 + (4𝑦 − 6𝑥𝑦)𝑑𝑦] 𝐶, where C is the boundary of the region bounded by 𝑥 = 0, 𝑦 = 0,…

With usual notations derive a one-dimensional heat equation.

5.C] With usual notations derive a one-dimensional heat equation. Answer:-

Explain Couple and its characteristics.

3.A] Explain Couple and its characteristics. Answer:-

Derive one-dimensional wave equation

5.C] Derive a one-dimensional wave equation Answer:-

Using Green’s theorem, evaluate ∫_c(𝑥𝑦 + 𝑦^2)𝑑𝑥 + 𝑥^2𝑑𝑦, where C is bounded by 𝑦 =𝑥 and 𝑦 = 𝑥^2

4.B] Using Green’s theorem, evaluate ∫c (𝑥𝑦 + 𝑦2)𝑑𝑥 + 𝑥2𝑑𝑦, where C is bounded by𝑦 = 𝑥 and 𝑦 = 𝑥2 Answer:-

Solve 𝜕^2𝑧/𝜕𝑥^2=𝑥𝑦 subject to the conditions 𝜕𝑧/𝜕𝑥=log(1+𝑦), when 𝑥=1 and 𝑧=0, when 𝑥=0.07

5.B] Solve = 𝑥𝑦 subject to the conditions = log(1 + 𝑦), when 𝑥 = 1 and 𝑧 = 0, when 𝑥 = 0. Answer:-

Solve 𝑥(𝑦^2−𝑧^2)𝑝+𝑦(𝑧^2−𝑥^2)𝑞−𝑧(𝑥^2−𝑦^2) = 0

6.C] Solve 𝑥(𝑦2 − 𝑧2)𝑝 + 𝑦(𝑧2 − 𝑥2)𝑞 − 𝑧(𝑥2 − 𝑦2) = 0 Answer:-

Using double integration find the area between the parabolas 𝑦^2=4𝑎𝑥 and 𝑥^2=4𝑎𝑦

2.B] Using double integration find the area between the parabolas 𝑦2 = 4𝑎𝑥 and 𝑥2 = 4𝑎y. Answer:-