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: 2016-2017

Date: June 2017

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Prove that 𝒕𝒂𝒏𝒉−𝟏(𝒔𝒊𝒏 𝜽) = 𝒄𝒐𝒔𝒉−𝟏(𝒔𝒆𝒄 𝜽)

Chapter: [5] Complex Numbers

Prove that the matrix `1/sqrt3` `[[ 1,1+i1],[1-i,-1]]` is unitary.

Chapter: [5] Complex Numbers

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

Chapter: [5] Complex Numbers

If Z=tan^1 (x/y), where` x=2t, y=1-t^2, "prove that" d_z/d_t=2/(1+t^2).`

Chapter: [5] Complex Numbers

Find the nth derivative of cos 5x.cos 3x.cos x.

Chapter: [5] Complex Numbers

Evaluate : `Lim_(x→0) (x)^(1/(1-x))`

Chapter: [5] Complex Numbers

Find all values of `(1+i)^(1/3)` & show that their continued

Product is (1+i).

Chapter: [5] Complex Numbers

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Find non singular matrices P & Q such that PAQ is in normal form where A `[[2,-2,3],[3,-1,2],[1,2,-1]]`

Chapter: [7] Matrices

Find the maximum and minimum values of `f(x,y)=x^3+3xy^2-15x^2-15y^2+72x`

Chapter: [8] Partial Differentiation

If u=`f((y-x)/(xy),(z-x)/(xz)),"show that" x^2 (del_u)/(del_x)+y^2 (del_u)/(del_y)+x^2 del_u/del_z=0`

Chapter: [5] Complex Numbers

Using encoding matrix `[[1,1],[0,1]]` ,encode & decode the message "MUMBAI"

Chapter: [7] Matrices

Prove that log `[tan(pi/4+(ix)/2)]=i.tan^-1(sinhx)`

Chapter: [6.02] Logarithm of Complex Numbers

Obtain tan 5𝜽 in terms of tan 𝜽 & show that `1-10tan^2 x/10+5tan^4 x/10=0`

Chapter: [6.02] Logarithm of Complex Numbers

If y=etan_1x. prove that `(1+x^2)yn+2[2(n+1)x-1]y_n+1+n(n+1)y_n=0`

Chapter: [6.02] Logarithm of Complex Numbers

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Express `(2x^3+3x^2-8x+7)` in terms of (x-2) using taylor'r series.

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

Prove that `tan_1 x=x-x^3/3+x^5/5+.............`

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

If `Z=x^2 tan-1y /x-y^2 tan -1 x/y del`

Prove that `(del^z z)/(del_ydel_x)=(x^2-y^2)/(x^2+y^2)`

Chapter: [6.02] Logarithm of Complex Numbers

Investigate for what values of 𝝁 "𝒂𝒏𝒅" 𝝀 the equations : `2x+3y+5z=9`

`7x+3y-2z=8`

`2x+3y+λz=μ`

Have (i) no solution (ii) unique solution (iii) Infinite value

Chapter: [7] Matrices

Obtain the root of `x^3-x-1=0` by Newton Raphson Method` (upto three decimal places).

Chapter: [7] Matrices

Find tanhx if 5sinhx-coshx = 5

Chapter: [6.02] Logarithm of Complex Numbers

If u= `sin^-1 ((x+y)/(sqrtx+sqrty)), " prove that ""`i.xu_x+yu_y=1/2 tanu`

ii. `x^2uxx+2xyu_xy+y^2u_(y y)=(-sinu.cos2u)/(4cos^3u)`

Chapter: [7] Matrices

Solve the following system of equation by Gauss Siedal Method,20x+y-2z=17

3x+20y-z =-18

2x-3y+20z=𝟐𝟓

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

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