BE Printing and Packaging Technology

BE Civil Engineering

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BE Electrical Engineering

BE Biomedical Engineering

BE Chemical Engineering

BE Electronics Engineering

BE Marine Engineering

BE Computer Engineering

BE IT (Information Technology)

BE Biotechnology

BE Instrumentation Engineering

BE Production Engineering

BE Automobile Engineering

BE Mechanical Engineering

BE Electronics and Telecommunication Engineering

Academic Year: 2017-2018

Date: December 2017

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Separate into real and imaginary parts of cos`"^-1((3i)/4)`

Chapter: [6.02] Logarithm of Complex Numbers

Show that the matrix A is unitary where A = `[[alpha+igamma,-beta+idel],[beta+idel,alpha-igamma]]` is unitary if `alpha^2+beta^2+gamma^2+del^2=1`

Chapter: [7] Matrices

If `z=tan(y-ax)+(y-ax)^(3/2)` then show that `(del^2z)/(delx^2)= a^2 (del^2z)/(dely^2)`

Chapter: [8] Partial Differentiation

`"If" x=uv & y=u/v "prove that" jj^1=1`

Chapter: [5] Complex Numbers

Find the n^th derivative of `x^3/((x+1)(x-2))`

Chapter: [6.01] Successive Differentiation

Using the matrix A = `[[-1,2],[-1,1]]`decode the message of matrix C= `[[4,11,12,-2],[-4,4,9,-2]]`

Chapter: [7] Matrices

`"If" sin^4θcos^3θ = acosθ + bcos3θ + ccos5θ + dcos7θ "then find" a,b,c,d.`

Chapter: [9] Applications of Partial Differentiation , Expansion of Functions

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Using Newton Raphson method solve 3x – cosx – 1 = 0. Correct upto 3 decimal places.

Chapter: [9] Applications of Partial Differentiation , Expansion of Functions

Find the stationary points of the function x3+3xy2-3x2-3y2+4 & also find maximum and minimum values of the function.

Chapter: [9] Applications of Partial Differentiation , Expansion of Functions

Show that xcosecx = `1+x^2/6+(7x^4)/360+......`

Chapter: [9] Applications of Partial Differentiation , Expansion of Functions

Reduce matrix to PAQ normal form and find 2 non-Singular matrices P & Q.

`[[1,2,-1,2],[2,5,.2,3],[1,2,1,2]]`

Chapter: [7] Matrices

If y= cos (msin_1 x).Prove that `(1-x^2)y_n+2-(2n+1)xy_(n+1)+(m^2-n^2)y_n=0`

Chapter: [9] Applications of Partial Differentiation , Expansion of Functions

State and Prove Euler’s Theorem for three variables.

Chapter: [8] Partial Differentiation

Show that all roots of `(x+1)^6+(x-1)^6=0` are given by -icot`((2k+1)n)/12`where k=0,1,2,3,4,5.

Chapter: [5] Complex Numbers

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Show that the following equations: -2x + y + z = a, x - 2y + z = b, x + y - 2z = c have no solutions unless a +b + c = 0 in which case they have infinitely many solutions. Find these solutions when a=1, b=1, c=-2.

Chapter: [7] Matrices

If Z=f(x.y). x=r cos θ, y=r sinθ. prove that `((delz)/(delx))^2+((delz)/(dely))^2=((delz)/(delr))^2+1/r^2((delz)/(delθ))^2`

Chapter: [8] Partial Differentiation

If coshx = secθ prove that (i) x = log(secθ+tanθ). (ii) `θ=pi/2tan^-1(e^-x)`

Chapter: [9] Applications of Partial Differentiation , Expansion of Functions

Solve by Gauss Jacobi Iteration Method: 5x – y + z = 10, 2x + 4y = 12, x + y + 5z = -1.

Chapter: [10] Indeterminate Forms, Numerical Solutions of Transcendental Equations and System of Linear Equations

Prove that `cos^-1tanh(log x)+ = π – 2(x-x^3/3+x^5/5.........)`

Chapter: [9] Applications of Partial Differentiation , Expansion of Functions

If` y= e^2x sin x/2 cos x/2 sin3x. "find" y_n`

Chapter: [9] Applications of Partial Differentiation , Expansion of Functions

Evaluate `Lim _(x→0) (cot x)^sinx.`

Chapter: [9] Applications of Partial Differentiation , Expansion of Functions

Prove that log `[sin(x+iy)/sin(x-iy)]=2tan^-1 (cot x tanhy)`

Chapter: [9] Applications of Partial Differentiation , Expansion of Functions

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