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: June 2018
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(1) Question no. 1 is compulsory.
(2) Attempt any 3 questions from remaining five questions.
Evaluate `int_0^oo5^(-4x^2)dx`
Chapter: [5] Differential Equations of First Order and First Degree
Solve `dy/dx=x.y` with help of Euler’s method ,given that y(0)=1 and find y when x=0.3
(Take h=0.1)
Chapter: [7] Numerical Solution of Ordinary Differential Equations of First Order and First Degree, Beta and Gamma Function
Evaluate `(d^4y)/(dx^4)+2(d^2y)/(dx^2)+y=0`
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Evaluate `int_0^1sqrt(sqrtx-x)dx`
Chapter: [8] Differentiation Under Integral Sign, Numerical Integration and Rectification
Solve : `(1+log x.y)dx +(1+x/y)`dy=0
Chapter: [5] Differential Equations of First Order and First Degree
Evaluate I = `int_0^1 int_0^(sqrt(1+x^2)) (dx.dy)/(1+x^2+y^2)`
Chapter: [9] Double Integration
Solve `xy(1+xy^2)(dy)/(dx)=1`
Chapter: [5] Differential Equations of First Order and First Degree
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Find the area inside the circle r=a sin๐ฝ and outside the cardioide r=a(1+cos๐ฝ )
Chapter: [10] Triple Integration and Applications of Multiple Integrals
Apply Rungee-Kutta Method of fourth order to find an approximate value of y when x=0.2 given that `(dy)/(dx)=x+y` when y=1 at x=0 with step size h=0.2.
Chapter: [7] Numerical Solution of Ordinary Differential Equations of First Order and First Degree, Beta and Gamma Function
Show that the length of curve `9ay^2=x(x-3a)^2 "is" 4sqrt3a`
Chapter: [8] Differentiation Under Integral Sign, Numerical Integration and Rectification
Change the order of integration of `int_0^1int_(-sqrt(2y-y^2))^(1+sqrt(1-y^2)) f(x,y)dxdy`
Chapter: [9] Double Integration
Find the volume of the paraboloid `x^2+y^2=4z` cut off by the plane ๐=๐
Chapter: [10] Triple Integration and Applications of Multiple Integrals
Show that `int_0^1(x^a-1)/logx dx=log(a+1)`
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
If ๐ satisfies the equation `(dy)/(dx)=x^2y-1` with `x_0=0, y_0=1` using Taylor’s Series Method find ๐ ๐๐ ๐= ๐.๐ (take h=0.1).
Chapter: [7] Numerical Solution of Ordinary Differential Equations of First Order and First Degree, Beta and Gamma Function
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Find the value of the integral `int_0^1 x^2/(1+x^3`๐ ๐ using Simpson’s (๐/๐)๐๐ rule.
Chapter: [8] Differentiation Under Integral Sign, Numerical Integration and Rectification
Find the value of the integral `int_0^1 x^2/(1+x^3`๐ ๐ using Trapezoidal rule
Chapter: [8] Differentiation Under Integral Sign, Numerical Integration and Rectification
Find the value of the integral `int_0^1 x^2/(1+x^3`๐ ๐ using Simpson’s (1/3)๐๐ rule.
Chapter: [8] Differentiation Under Integral Sign, Numerical Integration and Rectification
Solve `(y-xy^2)dx-(x+x^2y)dy=0`
Chapter: [5] Differential Equations of First Order and First Degree
Evaluate `int int int sqrt(1-x^2/a^2-y^2/b^2-x^2/c^2 )`dx dy dz over the ellipsoid `x^2/a^2+y^2/b^2+z^2/c^2=1.`
Chapter: [10] Triple Integration and Applications of Multiple Integrals
Evaluate `(2x+1)^2(d^2y)/(dx^2)-2(2x+1)(dy)/(dx)-12y=6x`
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
A resistance of 100 ohms and inductance of 0.5 henries are connected in series With a battery of 20 volts. Find the current at any instant if the relation between L,R,E is L `(di)/(dt)+Ri=E.`
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Solve by variation of parameter method `(d^2y)/(dx^2)+3(dy)/(dx)+2y=e^(e^x)`.
Chapter: [6] Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order
Evaluate `int int xy(x-1)dx dy` over the region bounded by ๐๐ = ๐,๐= ๐,๐ =๐ and ๐ = ๐
Chapter: [10] Triple Integration and Applications of Multiple Integrals
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