BE Electrical Engineering

BE Marine Engineering

BE Automobile Engineering

BE Electronics Engineering

BE Mechanical Engineering

BE Production Engineering

BE Chemical Engineering

BE Printing and Packaging Technology

BE Instrumentation Engineering

BE IT (Information Technology)

BE Electronics and Telecommunication Engineering

BE Computer Engineering

BE Biomedical Engineering

BE Construction Engineering

BE Civil Engineering

BE Biotechnology

Academic Year: 2017-2018

Date: December 2017

(1) Question no. 1 is compulsory.

(2) Attempt any 3 questions from remaining five questions.

Evaluate `int_0^oo e^(-x^2)/sqrtxdx`

Chapter: [7] Numerical Solution of Ordinary Differential Equations of First Order and First Degree, Beta and Gamma Function

Solve `(D^3+1)^2y=0`

Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order

Solve the ODE `(y+1/3y^3+1/2x^2)dx+(x+xy^2)dy=0`

Chapter: [5] Differential Equations of First Order and First Degree

Use Taylor’s series method to find a solution of `(dy)/(dx) =1+y^2, y(0)=0` At x = 0.1 taking h=0.1 correct upto 3 decimal places.

Chapter: [7] Numerical Solution of Ordinary Differential Equations of First Order and First Degree, Beta and Gamma Function

Given `int_0^x 1/(x^2+a^2) dx=1/atan^(-1)(x/a)`using DUIS find the value of `int_0^x 1/(x^2+a^2) `

Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order

Find the perimeter of the curve r=a(1-cos 𝜽)

Chapter: [8] Differentiation Under Integral Sign, Numerical Integration and Rectification

Solve `(D^3+D^2+D+1)y=sin^2x`

Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order

Change the order of integration `int_0^aint_sqrt(a^2-x^2)^(x+3a)f(x,y)dxdy`

Chapter: [9] Double Integration

Evaluate `int int(2xy^5)/sqrt(x^2y^2-y^4+1)dxdy`, where R is triangle whose vertices are (0,0),(1,1),(0,1).

Chapter: [10] Triple Integration and Applications of Multiple Integrals

Find the volume enclosed by the cylinder `y^2=x` and `y=x^2` Cut off by the planes z = 0, x+y+z=2.

Chapter: [10] Triple Integration and Applications of Multiple Integrals

Using Modified Eulers method ,find an approximate value of y At x = 0.2 in two step taking h=0.1 and using three iteration Given that `(dy)/(dx)=x+3y` , y = 1 when x = 0.

Chapter: [7] Numerical Solution of Ordinary Differential Equations of First Order and First Degree, Beta and Gamma Function

Solve `(1+x)^2(d^2y)/(dx^2)+(1+x)(dy)/(dx)+y=4cos(log(1+x))`

Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order

Show that `int_0^asqrt(x^3/(a^3-x^3))dx=a(sqrtxgamma(5/6))/(gamma(1/3))`

Chapter: [8] Differentiation Under Integral Sign, Numerical Integration and Rectification

Solve `(D^2+2)y=e^xcosx+x^2e^(3x)`

Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order

Use polar co ordinates to evaluate `int int (x^2+y^2)^2/(x^2y^2)` 𝒅𝒙 𝒅𝒚 over yhe area Common to circle `x^2+y^2=ax "and" x^2+y^2=by, a>b>0`

Chapter: [10] Triple Integration and Applications of Multiple Integrals

Solve `ydx+x(1-3x^2y^2)dy=0`

Chapter: [5] Differential Equations of First Order and First Degree

Find the mass of a lamina in the form of an ellipse `x^2/a^2+y^2/b^2=1`, If the density at any point varies as the product of the distance from the

The axes of the ellipse.

Chapter: [10] Triple Integration and Applications of Multiple Integrals

Compute the value of `int_0^(pi/2) sqrt(sinx+cosx) dx` usingTrapezoidal rule by dividing into six Subintervals.

Chapter: [8] Differentiation Under Integral Sign, Numerical Integration and Rectification

Compute the value of `int_0^(pi/2) sqrt(sinx+cosx) dx` using Simpson’s (1/3)^{rd} rule by dividing into six Subintervals.

Chapter: [8] Differentiation Under Integral Sign, Numerical Integration and Rectification

Compute the value of `int_0^(pi/2) sqrt(sinx+cosx) dx` using Simpson’s (3/8)^{th} rule by dividing into six Subintervals.

Chapter: [8] Differentiation Under Integral Sign, Numerical Integration and Rectification

Change the order of Integration and evaluate `int_0^2int_sqrt(2y)^2 x^2/(sqrtx^4-4y^2)dxdy`

Chapter: [9] Double Integration

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

Chapter: [10] Triple Integration and Applications of Multiple Integrals

Solve by method of variation of parameters :`(D^2-6D+9)y=e^(3x)/x^2`

Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order

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