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: 2018-2019
Date: दिसंबर 2018
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1) Question No. 1 is compulsory
2) Attempt any 3 questions from remainging five questions.
Show that sec h-1(sin θ) =log cot (`theta/2` ).
Chapter: [6.02] Logarithm of Complex Numbers
Show that a matrix A = `1/2[(sqrt2,-isqrt2,0),(isqrt2,-sqrt2,0),(0,0,2)]` is unitary.
Chapter: [7] Matrices
Evaluate `lim_(x->0) sinx log x.`
Chapter: [6.01] Successive Differentiation
Find the nth derivative of y=eax cos2 x sin x.
Chapter: [6.02] Logarithm of Complex Numbers
If 𝒙 = r cos θ and y= r sin θ prove that JJ-1=1.
Chapter: [7] Matrices
Using coding matrix A=`[(2,1),(3,1)]` encode the message THE CROW FLIES AT MIDNIGHT.
Chapter: [7] Matrices
Find all values of `(1 + i)^(1/3` and show that their continued product is (1+ 𝒊 ).
Chapter: [5] Complex Numbers
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Find the non-singular matrices P & Q such that PAQ is in normal form where`[(1,2,3,4),(2,1,4,3),(3,0,5,-10)]`
Chapter: [7] Matrices
Find maximum and minimum values of x3 +3xy2 -15x2-15y2+72x.
Chapter: [9] Applications of Partial Differentiation , Expansion of Functions
If U = `e^(xyz) f((xy)/z)` prove that `x(delu)/(delx)+z(delu)/(delx)2xyzu` and `y(delu)/(delx)+z(delu)/(delz)=2xyzu` and hence show that `x(del^2u)/(delzdelx)=y(del^2u)/(delzdely)`
Chapter: [6.01] Successive Differentiation
By using Regular falsi method solve 2x – 3sin x – 5 = 0.
Chapter: [10] Indeterminate Forms, Numerical Solutions of Transcendental Equations and System of Linear Equations
If y=sin[log(x2+2x+1)] then prove that (x+1)2yn+2 +(2n +1)(x+ 1)yn+1 + (n2+4)yn=0.
Chapter: [6.01] Successive Differentiation
State and prove Euler’s Theorem for three variables.
Chapter: [8] Partial Differentiation
By using De Moivre's Theorem obtain tan 5θ in terms of tan θ and show that `1-10 tan^2(pi/10)+5tan^4(pi/10)=0`.
Chapter: [5] Complex Numbers
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Investigate for what values of λ and μ the equations
2x + 3y + 5z = 9
7x + 3y - 2z = 8
2x + 3y + λz = μ have
A. No solutions
B. Unique solutions
C. An infinite number of solutions.
Chapter: [7] Matrices
Find nth derivative of `1/(x^2+a^2.`
Chapter: [6.01] Successive Differentiation
If z = f (x, y) where x = eu +e-v, y = e-u - ev then prove that `(delz)/(delu)-(delz)/(delv)=x(delz)/(delx)-y(delz)/(dely).`
Chapter: [8] Partial Differentiation
Solve using Gauss Jacobi Iteration method
2𝒙 + 12y + z – 4w = 13
13𝒙 + 5y - 3z + w = 18
2𝒙 + y – 3z + 9w = 31
3𝒙 - 4y + 10z + w = 29
Chapter: [10] Indeterminate Forms, Numerical Solutions of Transcendental Equations and System of Linear Equations
If y = log `[tan(pi/4+x/2)]`Prove that
I. tan h`y/2 = tan pi/2`
II. cos hy cos x = 1
Chapter: [6.02] Logarithm of Complex Numbers
If U `=sin^(-1)[(x^(1/3)+y^(1/3))/(x^(1/2)+y^(1/2))]`prove that `x^2(del^2u)/(del^2x)+2xy(del^2u)/(delxdely)+y^2(del^2u)/(del^2y)=(tanu)/144[tan^2"U"+13].`
Chapter: [8] Partial Differentiation
Expand 2 𝒙3 + 7 𝒙2 + 𝒙 – 6 in power of (𝒙 – 2) by using Taylors Theorem.
Chapter: [9] Applications of Partial Differentiation , Expansion of Functions
Expand sec x by McLaurin’s theorem considering up to x4 term.
Chapter: [9] Applications of Partial Differentiation , Expansion of Functions
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University of Mumbai previous year question papers Semester 1 (FE First Year) Applied Mathematics 1 with solutions 2018 - 2019
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