# Applied Mathematics 2 CBCGS 2016-2017 BE Mechanical Engineering Semester 2 (FE First Year) Question Paper Solution

Applied Mathematics 2 [CBCGS]
Date: June 2017

[20] 1
[3] 1.a

Evaluate int_0^∞ 3^(-4x^2) dx

Concept: Legendre’S Differential Equation
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
[3] 1.b

Solve (2y^2-4x+5)dx=(y-2y^2-4xy)dy

Concept: Particular Integrals of Differential Equation
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
[3] 1.c

Solve the ODE (D-1)^2 (D^2+1)^2y=0

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
[3] 1.d

Evaluate int_0^1 int_0^(x2) y/(ex) dy  dx

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
[3] 1.e

Evaluate int_0^1( x^a-1)/log x dx

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
[3] 1.f

Find the length of cycloid from one cusp to the next , where x=a(θ + sinθ) , y=a(1-cosθ)

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
[20] 2
[6] 2.a

Solve (D^2-3D+2) y= 2 e^x sin(x/2)

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
[6] 2.b

Using D.U.I.S prove that int_0^∞ e^-(x^+a^2/x^2) dx=sqrtpi/2 e^(-2a), a> 0

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
[8] 2.c

Change the order of integration and evaluate int_0^1 int_x^sqrt(2-x^2 x  dx  dy)/sqrt(x^2+y^2)

Concept: Differentiation Under Integral Sign with Constant Limits of Integration
Chapter: [8] Differentiation Under Integral Sign, Numerical Integration and Rectification
[20] 3
[6] 3.a

Evaluate int_0^1int_0^( 1-x)1int_0^( 1-x-y)     1/(x+y+z+1)^3 dx dy dz

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
[6] 3.b

Find the mass of the lemniscate 𝒓𝟐=𝒂𝟐𝒄𝒐𝒔 𝟐𝜽 if the density at any point is Proportional to the square of the distance from the pole .

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
[8] 3.c

Solve  x^2 (d^3y)/dx^3+3x (d^2y)/dx^2+dy/dx+y/x=4log x

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
[20] 4
[6] 4.a

Prove that for an astroid     x^(2/3) +y2/3= a^(2/3) the line 𝜽=𝝅/𝟔 Divide the arc in the first quadrant in a ratio 1:3.

Concept: Exact Differential Equations
Chapter: [5] Differential Equations of First Order and First Degree
[6] 4.b

Solve (D^2-7D-6)y=(1+x^2)e^(2x)

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
[8] 4.c

Apply Rungee Kutta method of fourth order to find an approximate Value of y when x=0.4 given that dy/dx=(y-x)/(y+x),y=1 𝒚=𝟏 𝒘𝒉𝒆𝒏 𝒙=𝟎 Taking h=0.2.

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
[20] 5
[6] 5.a

Use Taylor series method to find a solution of dy/dx=xy+1,y(0)=0 X=0.2 taking h=0.1 correct upto 4 decimal places.

Concept: Taylor’S Series Method
Chapter: [7] Numerical Solution of Ordinary Differential Equations of First Order and First Degree, Beta and Gamma Function
[6] 5.b

Solve by variation of parameters ((d^2y)/dx^2+1)y=1/(1+sin x)

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
[8] 5.c

Compute the value of int _0.2^1.4 (sin  x - In x+e^x)  Trapezoidal Rule (ii) Simpson’s (1/3)rd rule (iii) Simpson’s (3/8)th rule by dividing Into six subintervals.

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
[20] 6
[6] 6.a

Using beta functions evaluate int_0^(pi/6)  cos^6 3θ.sinθ dθ

Concept: Particular Integrals of Differential Equation
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
[6] 6.b

Evaluate int_0^(a/sqrt2) int_y^(sqrt(a2-y^2)) log (x^2+y^2) "dxdy by changing to polar Coordinates".

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
[8] 6.c

Evaluate int int int  x^2 yzdzdydzover the volume bounded by planes x=0, y=0, z=0 and x/a+y/b+z/c=1

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order

#### Request Question Paper

If you dont find a question paper, kindly write to us

View All Requests

#### Submit Question Paper

Help us maintain new question papers on Shaalaa.com, so we can continue to help students

only jpg, png and pdf files

## University of Mumbai previous year question papers Semester 2 (FE First Year) Applied Mathematics 2 with solutions 2016 - 2017

University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2 question paper solution is key to score more marks in final exams. Students who have used our past year paper solution have significantly improved in speed and boosted their confidence to solve any question in the examination. Our University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2 question paper 2017 serve as a catalyst to prepare for your Applied Mathematics 2 board examination.
Previous year Question paper for University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2-2017 is solved by experts. Solved question papers gives you the chance to check yourself after your mock test.
By referring the question paper Solutions for Applied Mathematics 2, you can scale your preparation level and work on your weak areas. It will also help the candidates in developing the time-management skills. Practice makes perfect, and there is no better way to practice than to attempt previous year question paper solutions of University of Mumbai Semester 2 (FE First Year).

How University of Mumbai Semester 2 (FE First Year) Question Paper solutions Help Students ?
• Question paper solutions for Applied Mathematics 2 will helps students to prepare for exam.
• Question paper with answer will boost students confidence in exam time and also give you an idea About the important questions and topics to be prepared for the board exam.
• For finding solution of question papers no need to refer so multiple sources like textbook or guides.