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: 2017-2018

Date: June 2018

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(1) Question no. 1 is compulsory.

(2) Attempt any 3 questions from remaining five questions.

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

Chapter: [5] Complex Numbers

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

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

Chapter: [7] Matrices

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`

Chapter: [8] Partial Differentiation

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

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

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

Chapter: [6.01] Successive Differentiation

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

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

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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`

Chapter: [6.01] Successive Differentiation

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

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

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.

Chapter: [7] Matrices

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

Chapter: [8] Partial Differentiation

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)]`

Chapter: [6.02] Logarithm of Complex Numbers

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

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

Chapter: [8] Partial Differentiation

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

“ALL IS WELL” .

Chapter: [7] Matrices

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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`

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

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`

Chapter: [8] Partial Differentiation

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

Chapter: [5] Complex Numbers

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

Chapter: [6.02] Logarithm of Complex Numbers

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

Chapter: [5] Complex Numbers

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

Chapter: [5] Complex Numbers

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

Chapter: [5] Complex Numbers

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

Chapter: [7] Matrices

Obtain the root of 𝒙^{𝟑}−𝒙−𝟏=𝟎 by Regula Falsi Method

(Take three iteration).

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

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