Share
Notifications

View all notifications
Advertisement

Applied Mathematics 1 CBCGS 2017-2018 BE Biotechnology Semester 1 (FE First Year) Question Paper Solution

Login
Create free account


      Forgot password?
Applied Mathematics 1 [CBCGS]
Marks: 80Academic Year: 2017-2018
Date: June 2018

(1) Question no. 1 is compulsory.
(2) Attempt any 3 questions from remaining five questions.


[20]1
[3]1.a

If `tan(x/2)=tanh(u/2),"show that" u = log[(tan(pi/4+x/2))] `

Concept: Inverse Hyperbolic Functions
Chapter: [5] Complex Numbers
[3]1.b

Prove that the following matrix is orthogonal & hence find 𝑨−𝟏.

A`=1/3[(-2,1,2),(2,2,1),(1,-2,2)]`

Concept: Transpose of a Matrix
Chapter: [7] Matrices
[3]1.c

State Euler’s theorem on homogeneous function of two variables and if `u=(x+y)/(x^2+y^2)` then evaluate `x(delu)/(delx)+y(delu)/(dely`

Concept: Euler’s Theorem on Homogeneous functions with two and three independent variables (with proof)
Chapter: [8] Partial Differentiation
[3]1.d

If `u=r^2cos2theta, v=r^2sin2theta. "find"(del(u,v))/(del(r,theta))`

Concept: Jacobian
Chapter: [9] Applications of Partial Differentiation , Expansion of Functions
[4]1.e

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

Concept: nth derivative of standard functions
Chapter: [6.01] Successive Differentiation
[4]1.f

Evaluate : `lim_(x->0)((2x+1)/(x+1))^(1/x)`

Concept: L‐ Hospital Rule
Chapter: [10] Indeterminate Forms, Numerical Solutions of Transcendental Equations and System of Linear Equations
[20]2
[6]2.a

Solve  `x^4-x^3+x^2-x+1=0.`

Concept: D’Moivre’S Theorem
Chapter: [5] Complex Numbers
Advertisement
[6]2.b

If `y=e^(tan^(-1)x)`.Prove that

`(1+x^2)y_(n+2)+[2(n+1)x-1]y_(n+1)+n(n+1)y_n=0`

Concept: Leibnitz’S Theorem (Without Proof) and Problems
Chapter: [6.01] Successive Differentiation
[8]2.c

Examine the function `f(x,y)=xy(3-x-y)` for extreme values & find maximum and minimum values of `f(x,y).`

Concept: Maxima and Minima of a Function of Two Independent Variables
Chapter: [9] Applications of Partial Differentiation , Expansion of Functions
[20]3
[6]3.a

Investigate for what values of 𝝁 𝒂𝒏𝒅 𝝀 the equation x+y+z=6; x+2y+3z=10; x+2y+𝜆z=𝝁 have
(i)no solution,
(ii) a unique solution,
(iii) infinite no. of solution.

Concept: consistency and solutions of homogeneous and non – homogeneous equations
Chapter: [7] Matrices
[6]3.b

If u =`f((y-x)/(xy),(z-x)/(xz)),` show that `x^2(delu)/(delx)+y^2(delu)/(dely)+z^2(delu)/(delz)=0`.

Concept: Euler’s Theorem on Homogeneous functions with two and three independent variables (with proof)
Chapter: [8] Partial Differentiation
[8]3.c

Prove that `log((a+ib)/(a-ib))=2itan^(-1)  b/a      &    cos[ilog((a+ib)/(a-ib))=(a^2-b^2)/(a^2+b^2)]`

Concept: Separation of Real and Imaginary Parts of Logarithmic Functions
Chapter: [6.02] Logarithm of Complex Numbers
[20]4
[6]4.a

If `u=sin^(-1)((x+y)/(sqrtx+sqrty))`,Prove that

`x^2u_(x x)+2xyu_(xy)+y^2u_(yy)=(-sinu.cos2u)/(4cos^3u)`

Concept: Euler’s Theorem on Homogeneous functions with two and three independent variables (with proof)
Chapter: [8] Partial Differentiation
[6]4.b

Using encoding matrix `[(1,1),(0,1)]`encode and decode the message

“ALL IS WELL” .

Concept: Application of Inverse of a Matrix to Coding Theory
Chapter: [7] Matrices
Advertisement
[8]4.c

Solve the following equation by Gauss Seidal method:

`10x_1+x_2+x_3=12`
`2x_1+10x_2+x_3-13`
`2x_1+2x_2+10x_3=14`

Concept: Gauss Seidal Iteration Method
Chapter: [10] Indeterminate Forms, Numerical Solutions of Transcendental Equations and System of Linear Equations
[20]5
[6]5.a

If `u=e^(xyz)f((xy)/z)` where `f((xy)/z)` is an arbitrary function of `(xy)/z.`

Prove that: `x(delu)/(delx)+z(delu)/(delz)=y(delu)/(dely)+z(delu)/(delz)=2xyz.u`

Concept: Partial Derivatives of First and Higher Order
Chapter: [8] Partial Differentiation
[6]5.b

Prove that `sin^5theta=1/16[sin5theta-5sin3theta+10sintheta]`

Concept: Expansion of sinnθ, cosnθ in powers of sinθ, cosθ
Chapter: [5] Complex Numbers
[8]5.c
[4]5.c.i

Prove that `log(secx)=1/2x^2+1/12x^4+.........`

Concept: Logarithmic Functions
Chapter: [6.02] Logarithm of Complex Numbers
[4]5.c.ii

Expand `2x^3+7x^2+x-1` in powers of x - 2

Concept: Expansion of sinn θ, cosn θ in terms of sines and cosines of multiples of θ
Chapter: [5] Complex Numbers

Prove that `sin^(-1)(cosec  theta)=pi/2+i.log(cot  theta/2)`

Concept: Expansion of sinn θ, cosn θ in terms of sines and cosines of multiples of θ
Chapter: [5] Complex Numbers
[20]6
[6]6.a

Prove that `sin^(-1)(cosec  theta)=pi/2+i.log(cot  theta/2)`

Concept: Expansion of sinn θ, cosn θ in terms of sines and cosines of multiples of θ
Chapter: [5] Complex Numbers
Advertisement
[6]6.b

Find non singular matrices P and Q such that A = `[(1,2,3,2),(2,3,5,1),(1,3,4,5)]`

Concept: PAQ in normal form
Chapter: [7] Matrices
[8]6.c

Obtain the root of 𝒙𝟑−𝒙−𝟏=𝟎 by Regula Falsi Method
(Take three iteration).

Concept: Regula – Falsi Equation
Chapter: [10] Indeterminate Forms, Numerical Solutions of Transcendental Equations and System of Linear Equations

Request Question Paper

If you dont find a question paper, kindly write to us





      View All Requests

Submit Question Paper

Help us maintain new question papers on Shaalaa.com, so we can continue to help students




only jpg, png and pdf files

University of Mumbai previous year question papers Semester 1 (FE First Year) Applied Mathematics 1 with solutions 2017 - 2018

     University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 question paper solution is key to score more marks in final exams. Students who have used our past year paper solution have significantly improved in speed and boosted their confidence to solve any question in the examination. Our University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1 question paper 2018 serve as a catalyst to prepare for your Applied Mathematics 1 board examination.
     Previous year Question paper for University of Mumbai Semester 1 (FE First Year) Applied Mathematics 1-2018 is solved by experts. Solved question papers gives you the chance to check yourself after your mock test.
     By referring the question paper Solutions for Applied Mathematics 1, you can scale your preparation level and work on your weak areas. It will also help the candidates in developing the time-management skills. Practice makes perfect, and there is no better way to practice than to attempt previous year question paper solutions of University of Mumbai Semester 1 (FE First Year).

How University of Mumbai Semester 1 (FE First Year) Question Paper solutions Help Students ?
• Question paper solutions for Applied Mathematics 1 will helps students to prepare for exam.
• Question paper with answer will boost students confidence in exam time and also give you an idea About the important questions and topics to be prepared for the board exam.
• For finding solution of question papers no need to refer so multiple sources like textbook or guides.
Advertisement
View in app×