B.C.A. Mathematics
491 videos • 330 views • by Doctor of Mathematics
1
If A=[1 tanx, -tanx 1],then show that A'.A-1=[cos2x -sin2x, sin2x cos2x]
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2
1.Scalar,Vector,Representation,Addition,Substraction of vectors;Triangular and Parallelogram law,Dis
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3
2-Distribution Law for vectors:Vecor Analysis
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4
Find the asymptotes of curve x^2.y^2-x^2.y-x.y^2+x+y+1=0
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5
Prove that the asymptotes of the curve (x^2-y^2).y-2ay^2+5x-7=0 form a triangle of area a^2.
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6
condition that xcosα+ysinα=p should touch x^m.y^n=a^(m+n) is p^(m+n).m^m.n^n=(m+n)^(m+n).a^m+n.sin^α
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7
Find the condition that the line x.cosα+y.sinα=p may touch the curve x^m/a^m+y^m/b^m=1
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8
If the normal at any point to the curve x^2/3+y^2/3=a^2/3 makes angle phi with x-axis ,show that its
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9
If the tangent at (x1,y1) to the curve x^3+y^3=a^3 meets the curve again in (x2,y2),show that x2/x1+
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10
State and prove Euler's theorem.If u=sin-1(x+y)/(√x+√y) then show that xdelu/delx+ydelu/dely=1/2sinu
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11
If y=e^m.cos-1x,then show that (1-x^2)yn+2-(2n+1)x.yn+1-(n^2+m^2)yn=0
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12
E-1:Solve : (x^3-3xy^2)dx=(y^3-3x^.2y)dy differential equation
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13
Solve D.E. (x^2-y^2)dx+2xydy=0
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14
Lt x tends to 0 logx^2/logcot^2x
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15
Find the asymptotes of the curve (x^2-y^2)(x+2y+1) +x+y+1=0.
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16
Find the differential equation of all circles passing through the origin and having their centre on
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17
Solve (2x+3y-5)dy/dx+(3x+2y-5)=0
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18
Prove that AUB=BUA (commutatuve law in union of sets)
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19
❌Lt x tends to 0 sinx.logx[I committed a mistake so differentiation of cosec x =-cosecx.cotx]
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20
Lt x tends to 0. [1/2x^2-1/2xtanx]
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21
Expand tan-1x in terms of (x-1) upto non-zero three terms||Top Mathematics channel on YouTube||Best
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22
Find the radius of curvature of curve x^3+y^3=3axy
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23
Idempotent Law in sets i.e. AUA=A
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24
A is subset of B implys that AUB=B
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25
Solve (D^2+9)y=sec3x
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26
Asssociative Law (AB)C=A(BC) intersections of sets
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27
Find the volume of solid formed by revolution of ellipse x^2/a^2+y^2/b^2=1 about x-axis.
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28
part 2:Length of arc along parabola y^2=4ax from vertex to on extrimity of latus rectum part2/2
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29
part 1:Length of arc along parabola y^2=4ax from vertex to on extrimity of latus rectum part1/2
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30
Trace thw curve y^2=x.(x-1)^2 and find the area of the loop.
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31
If y=sin(sinx); prove that d^2y/dx^2+tanx.dy/dx+y.cos^2x=0
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32
Analyse the equation 2x^2-3x+5y+4=0 and sketch the curve
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33
Find (x^2.e^x.cosx)n.
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34
Solve: (2D^2D'-3DD'^2+D'3)z=0
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35
If A and B are hermitian or skew-hermitian ,so is also A+B.
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36
Find the general solution of the D.E. y''+2y'+3y=e^x ||Top Mathematics YouTube channel
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37
Find the general solution of the y''-3y'+4y=0.
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38
Find the equation of the tangent at the point (x1,y1) of ellipse x^2/a^2+y^2/b^2=1.
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39
limit x tends to a log(x-a)/log(e^x-e^a
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40
Show that the area included between curve y^2=x^2(a+x)/(a-x) and its asymptote is 1/2(pi+4)a^2.
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41
Find the rank of the matrix A=[1. 2. 3.,2. 4. 6, 7. 8. 10]
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42
Find the whole area of the curve r=a(1-cosθ).
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43
Solve initial value problem dy/dx+y.tanx=sin2x,y (0)=1
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44
Solve (D^2-3DD'+2D'^2)z=e^2x-y
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45
Solve x(1+y^2)dx-y(1+x^2)dy=0
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46
If z=f(x^2.y); where f is defferentiable ,then show that xdelz/delx=2ydelz/dely
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47
The loop of the curve 2ay^2=x(x-a)^2 revlved about the x-axis .Find the volume of the solid so gener
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48
Part1:Sketch the curve y^2(4-x)x^3 and find the area bounded by the curve and its asymptote.
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49
Find the length of an arc of the parabola y^2=4ax measured from the vertex to one extremity of the
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50
Solve the initial value problem d^2x/dt^2-3dx/dt+2x=0 ;x(0)=2;x'(0)=0
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51
Solve p-2q=3x^2sin(y-2x)
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52
Show that the entire area of x^2/3+y^2/3=a^2/3 is 3/8.πa^2.
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53
The sum of three positive number is unity.What is the maximum value of their product.
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54
Solve dy/dx+ay=e^mx
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55
Evaluate the double integral √x^2+y^2 dy dx x=0 to1 and y=0 to x
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56
Evaluate the area of the region that lies inside circle r=acosθ and outside cardioid r=a(1-cosθ)
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57
Show that f(x)=cos(1/x) when x≠0,f(0)=0 is discontinuous at origin.
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58
Show that the following function is discontinuous at the origin: f(x)=1/1+e^1/x
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59
Examine the following function for continuity at x=2, f(x)=(x^2-4)/(x-2),f(2)=0
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60
With usual notations,for any curve prove d^2r/ds^2=sin^2(ϕ)/r-sin(ϕ)/ρ ;d^2r/ds^2=sin^2ϕ/r-sinϕ/ρ
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61
The segment of curve x=a.sin^2t,y=a.cos^2t,t is in between 0 to π/2 is revolved about y-axis,find th
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62
If A and B are symmetric and AB=BA show that AB is symmetric.
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63
e^ax.sinbx=bx+abx^2+(3a^2b-b^3)x^3/3!+....
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64
IF u=(x^2+y^2+z^2)^-1 then prove that del^2u/delx^2+del^2u/del^2y+del^2u/delz^2=
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65
Evaluate Double integration of 1/√x^2+y^2+1 w.r.t. y and x with limits
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66
Double integration of 1/√x^2+y^2+1 w.r.t. y and x with limits
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67
Find the radius of curvature at the point (r,θ) on the curve θ=√r^2-a^2/a-cos-1(a/r)
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68
Show that the functions u=x+y-z,v=x-y+z,w=x^2+y^2+z^2-2yz are not independentof one another.Also fin
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69
If N=[0 1+2i; -1+2i 0],obtain the matrix (I-N)(I+N)^-1, and show that it is unitary.
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70
If A=[3 1; -1 2] express 2A^5-3A^4-A^2-4I as a linear polynomial in A.
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71
The rank of a matrix does not change by pre or post multiplication with a non-singular matrix.
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72
Solve: (D^2+2D+1)y=2x+x^2 differential equation
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73
Using (,) epsilen-delta definition show that lim x tends to x.sin(1/x)=0
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74
Prove that the rank of product of two matrix can not exceed the rank of either of the matrices
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75
If y=x^2.sinx,prove that D^n(y)=(x^2-n^2+n)sin(x+n.π/2)-2nxcos(x+n.π/2).
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76
Trace the curve (Cissoid) r=a.sin^2θ/cosθ
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77
B.Sc. Mathematics : Show that the whole length of the cardiod r=a (1+cos@) is 8a.
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78
Find the area of circle of radius 'a' using Green's theorem.||Best Mathematics Channel on YouTube||
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79
If y=sin-1x/√1-x^2, prove that (1-x^2)yn+1-(2n+1)xyn-n^2yn=0
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80
Find the surface of the solid generated by revolving the arc of the parabola y^2=4ax bounded by its
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81
Integrate (Sin-1x)^4 with respect to x
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82
Apply Maclaurin theorem to obtain the term upto x^4 in the expansion of log(1+sin^2)
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83
Solve:(D+D'-1) (D+D'-3) (D+D')z =e^x+y.sin(2x+y) non-homogeneous Partial Differential Equation.
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84
grad(a.b)=ax curl b+bx curl a+(a.del)b +(b.del)a
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85
If a is a constant vector, then prove that del(a.u) =(a.del)u +axcurl u
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86
del. (axu) =-a.curl u
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87
The rank of matrix A and it's transpose are same.
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88
Find the radius of curvature at any point 't' on the curve x=a.cost, y=b.sint.
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89
If x=cosh(1/m.logy) , prove that (x^2-1) yn+2+(2n+1) xyn+1+(n^2-m^2) yn=0
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90
Explanation of Shab-e-miraj and Isra on basis on special theory of relativity
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91
Find the length of curve y=log[tanh(x/2) ] from x=1 to x=2.
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92
Find the length of the arc of the curve y=x(2-x) as x varies 0 to 2.
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93
Show that the functions u=x/y-z, v=y/z-x, w=z/x-y are not independent of one another. find relation
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94
Find the length of the arc of the curve x=t^2.cost, y=t^2.sint from origin to t I. e. 0 to t.
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95
Show that the functions u=x^3+x^2y+x^2z-z^2(x+y+z),v=z+x,w=x^2-z^2+xy-zy are not independent.find re
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96
Find maximum and minimum of x^3y^2(1-x-y)
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97
Find the length of the curve y=x^3/2 from x=0 to x=4.
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98
Evaluate integration of coshx+sinhx.sinx/1+cosx
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99
G-74:prove that curl r=0 vector. del x r=0
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100
If the directional derivative Φ=axy^2+byz+cz^2x^3 at (-1,1,2) has maximum magnitude of 32 units
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101
Solve: (1-x^2)dy/dx+xy=ax
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102
Find the area included between the curve y^2(a-x) =x^3, and it's asymptote. cissoid
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103
Prove that del r =vector r/r
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104
To prove that a.cosbx+b.sinbx/a^2+b^2=cos(bx-tan-1b/a) /squ.roota^2+b^2=
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105
Find pedal equation of the curve x^2/3+y^2/3=a^2/3
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106
dr/dθ+r/=aθ^n
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107
Integrate e^x.(1-x/1+x) ^2dx
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108
Grad 1/r
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109
Show that [a+b b+c c+a]=2[a b c] all vectors (Vector Algebra)
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110
ax(bxc) +bx(cxa) +cx(axb) =0 all vectors
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111
Using Taylor's Theorem show that tan(π/4+x) =1+2x+2x²+8/3x^3+....
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112
Using Taylor's theorem show that tan(π/4+x) =1+2x+2x^2+8/3.x^3+....
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113
Integrate Cos^3/e^3x w.r.t. x
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114
Find the radius of curvature of curve the cardiod r=a(1-cosθ)
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115
Expand log[cos(x+π/4)]
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116
Show value of the solid by revolving area included between y^2=x^3 and x^2=y^3 about x- axis 5π/28.
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117
Trace the curve a^2.y^=x^3.(2a-x)
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118
Lt x tends to infinity x^n/e^x ; n being a positive integer.
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119
B(m+1,n) /B(m, n)
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120
J-10:Integrate from θ=0 to θ=π/2 sin^7θ.√cosθ in term of beta function.
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121
Evaluate:B(1/2,1/2) where B is beta function
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122
If (1+x)y=ln(1+x) then show that(1+x)^2yn+2+(2n+3) (1+x) yn+1+(n+1)^2yn=0
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123
Show that arc of the upper half of the curve r=a(1-cosθ) is bisected by θ=2π/3.
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124
Find the volume of the paraboloid generated by devolving the parabola y^2=4ax about its axis cut by
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125
Find the area included between the parabolae y^2=4ax and x^2=4by||Top mathematics channel on YouTube
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126
Evaluate Integral ∫1/x^2dx.||Top mathematics channel for YouTube
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127
Find the whole length of the cardioid r=a(1+cosθ).||Top mathematics channel on YouTube
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128
Find the surface area generated by the curve y=as in(x/a)||Top mathematics channel on YouTube
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129
Show that volume generated by revolution of curve y(a^2+x^2)=a^3 about it'sAsymptote is 1/2π^3a^3Top
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130
Find the area situated outside the circle r=2acosθ and inside the cardioid r=a(1+cosθ).||Top Channel
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131
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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132
If aij=aji, show that A=[aij] is symmetric matrix.
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133
Check the following function for x=05, f(x)=e^1/x-1/e^1/x+1
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134
Test the continuity and differentiabelity of the function f(x) at x=2 where f(x)=1+x for x less than
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135
Evaluate limit (3x+|x|)/(7x-5|x|)
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136
Show that limit sinax/sinbx=a/b
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137
The part of the parabola y^2=4ax cut off by its latus rectum revolves about the tangent at the verte
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138
Pedal equation of r=a(1-cosθ)
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139
Lagrange's conditions for maxima and minima (Unique Solution)
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140
With suitable substitution evaluate the integral ∫√x/(x+1)dx
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141
State Lagrange's mean value theorem
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142
If y=ae^mx+be^-mx then show that y2=m^2y
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143
Evaluate: ∫1/(1+x^2) √(1-x^2) dx
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144
Evaluate: ∫1/(1+x^3)dx
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145
limit (a^xsinbx-b^xsinax) /(tannx-tanax)
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146
limit a tends to b (a^xsinbx-b^xsinax) /(tannx-tanax)
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147
Limit (x,y) tends to (0,0) xy/x+y
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148
Geometrical meaning of a differential equation
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149
If y=sin-1x/√1-x^2 , show that (1-x^2)yn+2-(2n+3)xyn+1-(n+1)^2yn=0
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150
If y=e^tan-1x , prove that (1+x^2) yn+2+{2(n+1)x-1}yn+1+n(n+1)yn=0
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151
Derivative of sinh-1x
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152
If y=cos(logx) prove that x^2yn+2+(2n+1)xyn+1+(n^2+1)yn=0
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153
∫x^7/√(a^2-x^2) =16/35a^7 limit x=0 to x=a
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154
Prove that: (axb)x(cxd)+(axc)x(dxb)+(axd)x(bxc) =2[b d c]a ||Top B Sc.Mathematics on YouTube free
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155
Lim [1/4n^2+1+2/4n^2+2^2+3/4n^2+3^2....n/4n^2+n^2]
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156
If u=f(z), z being a homogenous function of degree n in x, y, prove that
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157
Find the radius of curvature at any point of the curve r=a(1+cosθ)
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158
If f=x^2zi-2y^3z^2j+xy^2zk, find curl f at point (1,-1,1).
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159
If u=log(x^3+y^3+z^3-3xyz ), show that del^2u/del2+del^2u/dely^2+del^2u/delz^2=-3/(x+y+z)^2
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160
Find the volume of a sphere of radius 'a' by the method of integration.
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161
Prove that the surface area of a sphere of radius 'a' is 4πa^2 by method of integration.
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162
Find the eigen values and corresponding eigen vectors of the matrix [1 1 1,1 2 3,-1 1 0]
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163
Separate real and imagine parts exp(siniθ)
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164
If In=∫^nxdx from 0 to π/4, show that In+In-2=1/n-1
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165
Find area inside the circle r=asinθ and outside cardioid r=a(1-cosθ).
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166
If a function f(x)=|x| , x=/ 0 and f(x)=0, x=0.Examine for continuity at x=0.
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167
If y=(x^2-1)^m , prove that y2m=2m!.
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168
Evaluate Sigma r^2/n^3+r^3 as n tends to infinite
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169
Evaluate Sigma n^2/n^3+r^3 as n tends to infinite
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170
Evaluate limit secπx/tan3πx
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171
as If u=(1-2xy+y^2)^-1/2, prove that xdelu/d elx-y delu/dely=y^2u^3
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172
If u=(1-2xy+y^2)^-1/2 , prove that del/delx[(1-x^2)delu/delx]+del/dely[y^2delu/dely]=0
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173
To prove: Gamma(1/2)=√π or Γ1/2
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174
Find the whole area of the curve a^2y^2=x^3(2a-x)
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175
Ifz=(x+y)+(x+y)Φ(y/x), then prove that x(d^2z/dx^2-d^2z/dxdy)=y(d^2y/dy^2-d^2z/dxdy) all partial
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176
Relation between polar and Cartesian coordinates
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177
If z(z^2+3x)+3y=0, prove that d^2z/dx^2+d^2z/dy^2=2z(x-1)/(z^2+x)^3 all partial doffferentiation
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178
Evaluate ∫dθ/(1-sin^4θ)
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179
If x+y=1,prove that d^n(x^ny^n)/dx^n=n![y^n-(nC1)^2y^n-1x+(nC2)^2y^n-2x^2+.....+]
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180
If z^3-3yz-3x=0,. show that zdz/dx=dx/dy,z[d^2z/dxdy+(dx/dx)^2]=d^2z/dy^2 all partial differentiatio
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181
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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182
∫x^4e-xdx from 0 to infinity
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183
Evaluate ∫e-4x.x^3/2dx from 0 to infinity
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184
Evaluate ∫∫rsinθdθdr ,θ=0 to π/2;r=0 to r=acosθ
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185
Evaluate ∫ tan^nxdr,from x=0 to π/2
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186
Find the area of the surface of revolution formed by revolving the curve r=a(1+cosθ) about the init
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187
Prove: div.r=3. or ∇.r=3
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188
Expand log(1+x) by Maclaurin's theorem.
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189
Find the area of the loops of the curve r=a.sin3θ.[Three leaved rose]
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190
Find the coordinates of the centre of the conic 41x^2+24xy+9y^2-130ax-60ay+116a^2=0
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191
Prove that E=(1-∇)^-1
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192
Prove that Δ x^(n)=nhx^(n-1) #numericalanalysis
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193
Find the value of Δ^2(x+cosx)
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194
Prove that √2 is irrational number.
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195
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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196
Prove that ∫e^-x^2dx=√π/2
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197
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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198
If da/dt=rxa,db/dt=rxb,then prove that d(axb)/dt=rx(axb)
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199
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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200
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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