BE Civil Engineering
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BE Automobile Engineering
Academic Year: 2016-2017
Date: June 2017
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Prove that ๐๐๐๐−๐(๐๐๐ ๐ฝ) = ๐๐๐๐−๐(๐๐๐ ๐ฝ)
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 5๐ฝ in terms of tan ๐ฝ & 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 ๐ "๐๐๐ " ๐ 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=๐๐
Chapter: [10] Indeterminate Forms, Numerical Solutions of Transcendental Equations and System of Linear Equations
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University of Mumbai previous year question papers Semester 1 (FE First Year) Applied Mathematics 1 with solutions 2016 - 2017
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