U. P. T. G. T. Mathematics
457 videos • 269 views • by Doctor of Mathematics
1
Prove that log(x+iy) =1/2log(x^2+y^2) +itan-1y/x
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2
Find the rank of the matrix A=[1. 2. 3.,2. 4. 6, 7. 8. 10]
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3
Prove that the points (x1,y1),(x2,y2)and(x3,y3) are collinear if and only if the rank of the matrix
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4
Find the rank of matrix (Normal Form)
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5
Find the rank of matrix by reducing it into Normal form
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6
The system AX=B of non-homogeneous linear equations is consistent if and only if rank A=rank [AB]
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7
Find the unit vector normal to the surface x2.y+2xz=4 at the point (2,-2,3).
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8
If u=tan-1y/x, prove that x∂u/∂x+y∂u/∂y=0
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9
If u=sin-1(x+y/√x+√y) , prove that xdelu/delx+ydelu/dely=1/2.tanu
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10
ax(bxc) +bx(cxa) +cx(axb) =0 all vectors
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11
Grad 1/r
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12
Integrate 1/(1+x) √1+3x+3x^2 w. r. t. x
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13
Non-Collinear Vectors
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14
Position Vector
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15
Coplanar and non-coplanar Vectors
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16
Show that the pedal equation of the lemniscate r^2=a^2.cos2θ is r^3=a^2p.
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17
Evaluate the integral:∫x^4/(a^2+x^2)^4dx from limit 0 to a
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18
Evaluate the integral:∫sin^4θ.cos^2θdθ
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19
Evaluate the integral:∫[√(3x+2)-1/x+2]dx
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20
Find the limit as n tends to infinity of the sum n^1/2/n^3/2+n^1/2/(n+3)^3/2+n^1/2/(n+6)^3/2+..to n
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21
Determine the position and nature of the double points of the curve x^3-y^2-7x^2+4y+15x-13=0
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22
Subtangent and subnormal
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23
Find the subtangent, subnormal, tangent and it's intercept on the cycloid x=a(t+sint),y=a(1-cost).
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24
Evaluate:B(1,2)+B(2,1) (Beta function)
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25
B(m+1,n) /B(m, n)
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26
J-10:Integrate from θ=0 to θ=π/2 sin^7θ.√cosθ in term of beta function.
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27
Evaluate:B(1/2,1/2) where B is beta function
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28
Find the volume of the paraboloid generated by devolving the parabola y^2=4ax about its axis cut by
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29
Express log{log(cosθ+sinθ)} in the form of A+iB.||Top Mathematics channel on YouTube
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30
Find the area included between the parabolae y^2=4ax and x^2=4by||Top mathematics channel on YouTube
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31
Evaluate Integral ∫1/x^2dx.||Top mathematics channel for YouTube
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32
Find the centre, eccentricity, foci, directrices and the length of the transverse and conjugate axes
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33
Prove that integration from 0 to 2a f(x)=2 x integration from 0 to a of f(x) w. r. t. x P6(Prop.)
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34
With suitable substitution evaluate the integral ∫√x/(x+1)dx
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35
Evaluate: ∇^2(1/r) del^2(1/r) or div.(grad1/r)
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36
To prove: Gamma(1/2)=√π or Γ1/2
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37
Find the volume of the solid generated by the revolution of an arc of the catenary y=ccosh(x/c) abou
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38
Find the whole area of the curve a^2y^2=x^3(2a-x)
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39
Relation between polar and Cartesian coordinates
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40
Separation of (a+ib)^(x+iy) into real and imaginary parts
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41
If u(x,y,z)=1/(x^2+y^2+z^2), find the value of d^2u/dx^2+d^2u/dy^2+d^2u/dz^2 all partial differentia
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42
Find curl V,where V=e^xyz(i+j+k)
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43
Find the partial differential equation by the elimination of a and b from z=ax+by+ab
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44
∫x^4e-xdx from 0 to infinity
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45
Evaluate ∫e-4x.x^3/2dx from 0 to infinity
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46
Evaluate ∫∫rsinθdθdr ,θ=0 to π/2;r=0 to r=acosθ
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47
Evaluate ∫ tan^nxdr,from x=0 to π/2
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48
Prove that in triangle ABC,. Area(ABC)=abc/4R
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49
Find the asymptotes of the curve:y^3+x^2y-y+1=0
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50
Find the area of the surface of revolution formed by revolving the curve r=a(1+cosθ) about the init
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51
Test the convergence of the series whose general term is given by 1/n.(logn)^p
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52
Prove: div.r=3. or ∇.r=3
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53
Solve: y=(1+p)x+ap^2
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54
I-55:Prove that 2itan-1[itan(π/4-θ)]=logtanθ
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55
Expand log(1+x) by Maclaurin's theorem.
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56
Find the area of the loops of the curve r=a.sin3θ.[Three leaved rose]
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57
solve: dx/x=dy/y=dz/z #B.Sc.maths #B.Tech. math
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58
A particle of mass m moves in the xy-plan , r=acos(wt)i+bsin(wt)j.(a)The particle moves in ellipse
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59
r=acos(wt)i+bsin(wt)j (b)The force acting on the particle is always directed toward the origin
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60
For the Heaviside's unit step function f(t-a)={1,t greater than a;0,t less than a,prove that L[F(t
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61
Find L{sinht/t} Laplace transform
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62
Prove that ∫t^3.e^-t.sintdt from t=0 to t=♾️ infinity
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63
If L{2√(t/π)}=1/p^3/2,then prove that L{1/√(πt)}=1/p^1/2
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64
If F(t) is a periodic function with period w,then L{F(t)}=1/(1-e^-pw)∫e^-pt.F(t)dt, from t=0 to t=w.
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65
Find Laplace transform of ∫(1-e-2x/x)dx from x=0 to x=t.
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66
Find L-1{1/(s-2)+1/(s+5)+6/s^4}
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67
Evaluate:L-1{1/s^2(s^2+1)}
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68
Evaluate:L-1{(3p+1)/(p+1)(p^2+1)}.
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69
Proof of Euler's theorem and prove x^2del^2u/delx^2+2xydel^2u/delxdelu+y^2del^2u/dely^2=n(n-1)u
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70
Prove that ∫e^-x^2dx=√π/2
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71
Find:L-1{1/(p^2+8p+16)}
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72
First Shifting Property:If L-1{f(x)}=F(t),then L-1{f(p-a)}=e^at.F(t).
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73
Find L-1{1/(p+3)^7/2}
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74
second shifting property: If L-1{f(p)}=F(t),then L-1{e^-ap.f(p)}=G(t),where G(t)={F(t-a), greater th
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75
Test the convergence of the series whose n th term is √(n^3+1)-√n^3.
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76
Test for convergence the series: 1^2.2^2/1!+2^2.3^2/2!+.....+n^2.(n+1)^2/!
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77
Prove that the set R of real numbers is uncountable.
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78
Solve: xys=1
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79
Solve:(y+z)p+(z+x)q=x+y
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80
Solve by method of variation of parameters x^2d^2y/dx^2+xdy/dx-y=x^2e^x.
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81
यदि u=f(r)तथा x=cos,y=rsin तो सिद्ध करें del^2/delx^2+del^2u/dely^2=f(r)+1/rf'(r)
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82
यदि r=ae^nt+be^nt जहां a तथा b सदिश स्थिरांक हैं तब सिद्ध करो कि d^2r/dt^2-n^2r=0.
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83
If da/dt=rxa,db/dt=rxb,then prove that d(axb)/dt=rx(axb)
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84
If u=sinθi+cosθj+θk,v=cosθ i-sinθj-3,w=2i+3j-k,find d/dθ[ux(vxw) at θ=0
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85
वक्र r=4ti+t^2j+2t^3k के बिंदुओं t=1तथा t=2 पर स्पर्श रेखाओं के बीच का कोण ज्ञात करो.
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86
Show that :∫x^c/c^xdx=c+1/l(ogc)^c+1
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87
Prove that gamma n/c^n=∫e^-cy.y^n-1dy
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88
If m and n are positive real numbers,prove that ∫x^m-1(log1/x)^n-1dx.
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89
Solve by Monge's Method r+5s+6t=0
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90
Transformation of Gamma functions:Prove that gamma n =∫(log1/y)^n-1dy.
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91
Legendre's Duplication Formula:Γn Γ(n+1/2)=√π/2^2n-1Γ2n
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92
आव्यूह परिवर्तत ज्ञात कीजिए Find the transpose of a matrix
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93
यदि A=[0 1 2, 1 0 -1,2 -1 0]हो तो A^2 ज्ञात करो l
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94
Relation between beta and gamma functions
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95
Complement Formula
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96
वक्र r=t^2i+2tj-t^3 k के बिंदुओं t=1तथा t=-1 पर खींची गई स्पर्श रेखाओं के बीच का कोण ज्ञात कीजिए
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97
एक कण वक्र x=2तथा के अनुदेश गतिशील है तो सदिश केअनुदिश वेग तथा त्वरण के वियोजित भाग ज्ञात करें जबकि
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98
Verify that the adjoint of a diagonal matrix of order 3 is a diagonal matrix.
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99
Integration of 1/(sin2x-sinx) w.r.t. x
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100
यदि r=।r। और r=xi+yj+zk then find del r=r/r
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101
Null matrix और उसके rank लिखो
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102
A-B ज्ञात करो ,यदि A=[4 2, 3 5],B=[3 7,2 5]
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103
L[4cos^2(2t)] का मान ज्ञात करो।
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104
If A be a square matrix then prove that adjA'=(adjA)'
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105
Define homomorphic image of G.
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106
Define Homomorphism function
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107
Gamma Function की परिभाषा लिखो।
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108
L-1[1/√p] को हल करो।
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109
If A=[1-2i 2+3i 3-4i;4+5i 5-6i 6+7i ;8 7-8i 9].Find conjugate transpose
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110
If u=x^2tan-1y/x-y^2tan-1x/y show that del^2u/delx.dely=(x^2-y^2)/((x^2+y^2)
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111
समघातीय फलन की परिभाषा उदाहरण सहित लिखो। Homogeneous Function in two varieties
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112
यदि x=rcosθ,y=rsinθ हो तो दिखाइए del(r,θ)/del(x,y)
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113
Solve:(D^2-2D+4)y=e^x.sin^2x
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114
निम्न के लिए Euler's Theorem को सत्यापित करो-. u=(x^1/4+y^1/4)/(x^1/5+y^1/5)
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115
Solve:(D^2-1)y=cos^2x
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116
निर्धारित आव्यूह का अभिलाक्षणिक मूल ज्ञात करो।Find the characteristics roots(Eigen values)
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117
Test for convergence of the series (1-1/n)^n^2
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118
आव्यूह [1 2 -1 4,2 4 3 4,1 2 3 4,-1 -2 6]को Normal रूप में परिवर्तित कर Rank को ज्ञात करोl
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119
यदि r=t^3i+(2t^3-1/5t^2)j तो दर्शाइए कि rxdr/dt=k (vector)
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120
Solve: d^2y/dx^2-2dy/dx=e^x.sinx
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121
Find the divergence of r/r
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122
Solve (y-xdy/dx)=a(y^2+dy/dx)
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123
Lt x tends to 0 logx^2/logcot^2x
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124
What is the degree of the given differential equation:(d^2y/dx^2)+(dy/dx)^2=log(dy/dx)
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125
Solve (2x+3y-5)dy/dx+(3x+2y-5)=0
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126
dy/dx=sin(x+y)+cos(x+y) Solve differential Equation
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127
(D^2+D)y=1+coshx,D=d/dx;solved differentual Equation
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128
(D^2+6D+9)y=2e^(-3x) Solve Differential Equation
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129
(D^2-3D+2)y=e^x Solve differential equation
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130
Solve Differential Equation (6x-5y+4)dy+(y-2x-1)dx=0
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131
Solve: (D^2-5D+6)y=3sinx
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132
Solve:(D^3+1)y=(e^x+1)^2 को हल कीजिए।
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133
(dy/dx)-ytanx=e^x को हल करो। Solve:(dy/dx)-ytanx=e^x, Linear differential equation
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134
(2p^3+2p^2+4p+1)/(p^2+1)(p^2+p+1) काLaplace Inverse ज्ञात करो। Find Inverse Laplace transform of
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135
सिद्ध करो कि del(u,v)/del(x,y).del(x,y)/del(u,v)=1
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136
Find surface area of solid formed by revolution about axis of y of curve ay^2=x^3 from x=0 to x=4a
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137
solve x^2d^2y/dx^2-xdy/dx+2y=x^-1. (x^2D^2-xD+2)y=x^-1
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138
Solve:r+2s+t=0.
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139
Solve:x^2d^2y/dx^2-xdy/dx+2y=xlogx
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140
Solve:dy/dx-y/x=x^2y^2.(Bernoulli'Equation)
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141
Find area inside the circle r=asinθ and outside cardioid r=a(1-cosθ).
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142
Solve:(D^2+1)y=x^2+e^x.sinx
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143
Show that rxdr=rxdr/r^2, where r=।r। (vectors)
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144
If y=tan-1x,find the value of (yn)0 and show that when n=2p,4p+1,4p+3 then its value is 0,n-1!,-n-1!
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145
Solve:p^2-5p+6=0. Linear differential equation of first order but not first degree
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146
Solve:(xdx+ydy)/(xdy-ydx)=√[(a^2-x^2-y^2)/(x^2+y^2)]
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147
Find the equation to sphere passing through the points (0,-2,-4),(2,-1,-1) and having its centre on
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148
Find the centre and radius of circle x^2+y^2+z^2-8x+4y+8z-45=0,x-2y+2z=3.
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149
Find the volume of solid obtained by revolving the area enclosed by one aarch of the cycloid x=a(+)
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150
Determine the position and character of double points on the curve a^4y^2=x^4(2x^2-3a^2)
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151
If α and β be the angles which a string of length l makes with the at the points of support, show th
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152
Show that L{(1+te^-t)^3}=1/s+3/(s+1)^2+6/(s+2)^3+6/(s+3)^4.
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153
Solve:(D^2-4D+4)y=(3x^2+2)e^x
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154
Find the radius of curvature at any point of the cycloid x=a(θ+sinθ),y=a(1-cosθ).
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155
Find the angle between the curves r^2=a^2cos2θ and r^2=b^2sin2θ.
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156
If a,b,c in harmonic progression than find the value of (b+a)/(b-a)+(b+c)/(b-c)
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157
Find the angle between the curves r=asin2θ and r=acos2θ .
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158
Show that the radius of curvature at any point on curve √x/a+ √y/b=1 is 2(ax+by)^3/2/ab
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159
Obtain pedal equation for the curve r^2=a^2cos2θ.
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160
Show that for the curve by^2=(x+a)^3,the square of the subtangent varies as subnormal.
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161
Show that curves ax^2+by^2=1and a'x^2+b'y^2=1cut orthogonally if 1/a-1/b=1/a'-1/b'.
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162
Find the equation to right circular cylinder whose axis x=2y=-z and radius is 4.Prove that the area
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163
Solve D. E. : x^2d^2y/dx^2-4xdy/dx+6y=x
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164
Find the intrinsic equation of the spiral r=aθ,the arc being measured from the pole.
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165
Separate tan-1(α+β) into real and imaginary parts
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166
Evaluate ∫x^3(2ax-x^2)^3/2dx
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167
3cosθ+5cos2θ+7cos3θ+........to n terms ,Find the sum of the series,(Summation of series)
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168
Solve:(x-a)p^2+(x-y)p-y=0
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169
Show that the volume of the solid generated by cycloid x=a(θ+sinθ),y=a(1-cosθ), about y-axis is πa^3
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170
∫Cos^n-2x.sinnxdx from x=0 to x=π/2
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171
Find the volume of the solid of the revolution formed by revolving the area included between the cur
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172
Solve:(D^2-1)y=cosx.coshx+a^x
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173
Solve:(D^2+4)y=xcosx
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174
Find the volume revolution of curve :x=acos^3t, y=bsin^3t, i.e.(x/a)^2/3+(y/b)^2/3about x-axis
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175
Test the convergence of the series (-1)^n+1/log(n+1),n greater 1 to infinity using Leibnitz Test
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176
If {an} be a sequence of positive terms such that for all n, an+1=√k+an where k greater than 0 and a
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177
The generators of multiplicative group{1,w,w^2},where w is the cube root of unity. #shorts
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178
The additive inverse of the element 3 of the ring {(0,1,2,3,4),+5,x5}:. #shorts
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179
Solve:d^2y/dx^2+dy/dx+y=sin2x or (D^+D+1)y=sin2x
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180
d^2y/dx^2+4y=sin3x+e^x+x^2
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181
The velocities of a particle along and perpendicular to the radius vector from a fixed origin are λr
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182
Solve:d^4y/dx^4+4y=0 or (D^4+1)y=0
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183
Define Scalar Triple Product.Give it's geometrical interpretation.
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184
Formula of radius of curvature of the curve in intrinsic form
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185
Formula of radius of curvature for Cartesian equations
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186
Formula of radius of curvature for Parametric Equations
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187
Prove that β(m+1,n)/β(m,n)=m/(m+n)
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188
Find the angle between the vectors a=i+j-k and b=i-j+k.
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189
If R is a relation on the set N,defined as R={(a,b):a=b-2,b greater than 6}, select the correct opti
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190
Find the area of the parallelogram whose adjacent sides are given by vectors a=3i+j+4k and b=i-j+k.
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191
Differentiate the function (sinx)^cosx with respect to x.
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192
Lagrange's Linear Partial differential equation
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193
The general equation of second degree in two variables
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194
Define Director Circle and find equation for it
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195
The homogeneous equation of second degree ax^2+2hxy+by^2=0
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196
If (2 3,4 6)(a 7 ,3 b)=(13 23,26 46), determine the values of a and b.
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197
The combined equation of pair of the tangents from external point to conics.
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198
इन अक्षर A, B, G, I, K, L, M, N, P, R , S और V के नाम से शुरू होनेवाले अभी देखे gharelu health tips
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199
Determine the inverse of the matrix A by using row operation. A=(1 3; 2 -4).
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200
Let a function f be defined as f(x)=sin2x/x, when x≠0;=1when x=0.Examine whether f is continuous at
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