BE Civil Engineering
BE Computer Engineering
BE Mechanical Engineering
BE Biotechnology
BE Marine Engineering
BE Printing and Packaging Technology
BE Production Engineering
BE IT (Information Technology)
BE Electrical Engineering
BE Electronics and Telecommunication Engineering
BE Instrumentation Engineering
BE Electronics Engineering
BE Chemical Engineering
BE Construction Engineering
BE Biomedical Engineering
BE Automobile Engineering
Academic Year: 2017-2018
Date: December 2017
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(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
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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
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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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