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: जून 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 𝒙𝟑−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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