Find a basis and degree of the field extension Q(2½ ,3½) over Q #fieldtheory #basis #degree

Solve the differential equation [y(1+1/x)+cos y]dx+[x+log x - x×sin y]dy =0 #differentialequation

Solve [1+e^(x/y)]dx + e^(x/y) [1-x/y]dy =0 #exactequations #differentialequation #exam

Show that Q(2½,3½)is a simple extension of Q #fieldtheory#algebricexpression#mostimportantquestions

Solve the differential equation (cos x .cos y - cot x)dx -(sin x .sin y) dy=0 Exact Differential

Let K/F and L/K be fields. If [K:F] & [L:K] are finite, then [L:F] is also finite & [L:F]=[L:K][K:F]

Beal's Method , Quatric Programing Problem #mscmathematics #nonlinear #mostimportantquestions

Wolfe Method , Quatric Programing Problem #mscmathematics #nonlinear #mostimportantquestions

A=(-9 4 4 , -8 3 4 , -16 8 7)Is A diagonalizable?Then find matrix P s.t P^(-1)AP is a diagonal matri

Find the eigen values and eigen vectors of A( 3 10 5 , -2 -3 -4 , 3 5 7 ) Also verify that G.M of..

Find the Laplace of sin²t #laplacetransformation #mostimportantquestions#punjabuniversity

Find L{f(t)} , where f(t)={ 0 if greater and equal t less than 1 And f(t)={ (t-1)² if greaterthan 1

Find the derivative of y = sin Inverse [(1-tan²theta)/(1+tan²theta)]#derivative #boardexam #maths

Find the derivative of y = tan Inverse [cos x /(1+sin x) ] #derivatives #class12 #trigonometry

The principal value of (-1)^(-2i/pi) is? (a) e² (b) e^(2pi) (c) e^(-2pi) (d) e^(-2)#complexanalysis

The number 2½e^(i pi)is (a)Rational (b)Transcendental number (c)Irrational (d)Imaginary #complex

Which of the following is the imaginary part of a possible value of log(i½) ? #complexanalysis

Find L{sin t^1/2}#laplacetransformation #questionpaper #punjabuniversity #mostimportantquestions

Prove that e^{(x/2)*(t-1/t)} is generating function for Jn(x) #specialfunction #mscmathematics

Rodrigue's Formula :-Pn(x)=1/(2^n (n!)) differentiation w.r.t 'x' n times (x²-1)^n#specialfunctions

Orthogonal properties of legendre's polynomial || #specialfunctions #mostimportantquestions

Show that J1/2(x)=(√2/√πx)(sin x) || Bessel's Functions #specialfunctions #mscmathematics

Prove that Jn(x) =(-1)^n J-n(x) || Bessel's Functions #specialfunctions#mscmathematics

J-3/2(x) = - (√2/√πx)(sin x + cos x/x)|| Recurrence Relation || Bessel's Functions#specialfunctions

J3/2(x) = (√2/√πx)(sin x/x - cos x)|| Recurrence Relation || Bessel's Functions #specialfunctions

Find the directional derivative of f(x,y,z)=3 x+4 y+5z² at(1,1,1) in the direction of y-axis#vector

Find extremals of integration(y'²+z'²-2yz)dx ; y(0)=0,y(π/2)=1,z(0)=0,z(π/2)=1 |using Euler Lagrange

Find the directional derivative of x²yz+4xz² at (1,-2,-1) in the direction of 2 i - j -2 k .#vector

Find the extremals of integration (y'²+z²+z'²)dx ; y(1)=1,y(2)=2,z(1)=0,z(2)=1 |using Euler Lagrange

(D²-DD'-2D'²)z=( 2x²+xy-y²) sin(xy) - cos(xy)|| Partial differential equations of 2nd & higher order

Some of the standard methods to solve Differential equation || variable separable, homogeneous...

(i) If u=3x²y-y³z² ,then find grad u .(ii) If grad u=2r⁴. vector r, find u #gradient#vectoranalysis

Bending of light Decoded #refraction #light #physics

Partial differentiation of vector function #differentiation #partialdifferentiation #vector

Find the rational canonical form of A over Q where A =[(1,5,7),(0,4,3),(0,0,1)] #algebra #exam

Find the Invariant factor of A over Q[x] , where A=[(-3-x,2,0),(1,-x,1),(1,-3,-2-x)]#algebra #exam

Statement and Prove Euler's Summation Formula (Number Theory) #theorems #exam #importantquestion

Integration dx / (3+4 cosh x) #calculus #hyperbolicfunctions #integration #importantquestions #exam

Integration {tanh^(-1)x (1-x²)³/² dx #calculus #integration #hyperbolicfunctions #importantquestion

Integration {cosh^(-1)x((1+x² )/(1-x²))}dx, |x| less than 1#calculus#integration#hyperbolicfunctions

Find the area of the region bounded by the curve : y=x²+1, y=x , x=0 , x=0 , y=2 .#calculus

Find the area above the x-axis included between the curves y²=2ax-x² and y²=ax #calculus#quadrature

Green's Theorem in the plane to evaluate..C is boundary of surface enclosed by x-axis & semi-circle

Find the directional derivative of f=xy+yz+zx in the direction of vector i+2j+2k at the point(1,2,0)

Find a unit vector normal the surface x⁴ -3xyz + z²+1=0 at the point (1,1,1) .#vectoranalysis

Prove that \frac{1}{3}\int\vec{r}\cdot\vec{n}dS is the volume of the space enclosed by the surface S

Integrate (sinh(sqrt(x)))/(sqrt(x)) dx #hyperbolicfunctions #integration#mostimportant #calculus

Integrate e^x * log (cosh 2x + sinh 2x) dx || #hyperbolicfunctions #calculus #importantquestions

Integrate 1/(3sinh(x)+5cosh(x)) dx || #hyperbolicfunctions #calculus #importantquestions

Find the Laplace Transforms of t*e^(at)*sin (at) ||Important question || Multiplication by t^n

Evaluate :- integrate x*sinh^(-1) x dx || #hyperbolicfunctions#integration#mostimportant #calculus

Multiplication By t^(n) , (i) L\{t*sin at\} (ii) L\{t^2*sin at\} ,Laplace transforms #mostimportant

Evaluate L \{\int_{0}^{t}e^{-z}cos(z)dz\} Laplace transforms of integrals || First Shifting property

Find the Laplace transforms :- e^(- t) * (3sinh(2t) - 5cosh(2t)) | First Shifting Property#question

Integrate (cosh^- 1 x)/((x ^ 2 - 1)^(3/2)) dx || Hyperbolic Function #calculus #importantquestions

Prove that :- (i) \int_{0}^{\infty}sin~x^2 dx=√(π/8) (ii)\int_{0}^{\infty}cosx^2 dx=√(π/8)#laplace

Integrate sinh(x) * sinh(2x) * sinh(3x) dx || Hyperbolic Function #calculus #importantquestions

Prove that \int_{0}^{\infty}\frac{e^{-6t}-e^{-3t}}{t}dt=log\frac{1}{2} || Laplace Transforms

Find the least positive integer that yields the remainder 1,3,5 when divided by 5,7,9 respectively.

The remainder when 2^50 is divided by 7 ? 🤔|| #csirnet #mscmathematics #numbertheory