B.Sc. Honour 1st year
64 videos • 372 views • by Doctor of Mathematics
1
Prove that the inverse of a non-singular matrix is unique.
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2
prove that the necessary and sufficient conditions for the existence of the inverse of a square matr
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3
Show that cosπ/7, cos3π/7 and cos5π/7 are the roots of the equation,8x^3-4x^2-4x+1=0 and deduce the
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4
Solve the equation x^9+1=0
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5
If Aα=[cosα sinα; -sinα cosα] prove that (Aα)^n=[cosnα sinnα ; -sinnα cosnα]
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6
Prove that the equation cos2θ+a.cosθ+b.sinθ+c=0 has the sum of the four roots is a multiple of 2π.
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7
Find A-1,if A=[1 -2 -2, 2 3 1, 0 5 -2]
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8
If A=[1 2 3 0, 2 4 3 2, 3 2 1 3, 6 8 7 5],Find rank of A.
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9
(D^2+6D+9)y=2e^(-3x) Solve Differential Equation
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10
(1-1/2^2)(1-1/3^2)(1-1/5^2)(1-1/7^2).......=6/π^2,where 2,3,5,7,.....are all prime numbers.
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11
Prove that 1/1^2+1/2^2+1/3^2+......=π^2/6
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12
Prove that 1-1/3^3+1/5^3+..........=π^3/32
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13
State and prove De Moivre's Theorem
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14
Prove that tan−1n+cot−1 (n+1) = tan−1 (n 2 +n+1) and if tan−1 x+tan−1 y+tan−1 z = π/2
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15
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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16
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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17
Separate Cosh(x+iy) into real and imaginary parts.
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18
Separate sin(x+iy) into real and imaginary parts
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19
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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20
If α,β,gamma are the roots of the cubic equation x^3+px^2+qx+r=0;then find the value of sigm
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21
Find the asymptotes of the curve (x^2-y^2)(x+2y+1) +x+y+1=0.
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22
Find the centre,vertices,foci,eccentricity,directrix and asymtotes of hyperbila x^2-4y^2-2x+8y-2=0
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23
Lt x tends to 0. [1/2x^2-1/2xtanx]
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24
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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25
Trace thw curve y^2=x.(x-1)^2 and find the area of the loop.
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26
Find (x^2.e^x.cosx)n.
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27
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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28
limit x tends to a log(x-a)/log(e^x-e^a
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29
Find the whole area of the curve r=a(1-cosθ).
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30
Solve initial value problem dy/dx+y.tanx=sin2x,y (0)=1
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31
whether the function f(x,y)=xy/√(x^2+y^2); (x,y)≠(0,0); 0,(x,y)=(0,0) is continuous at the origin?J
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32
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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33
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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34
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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35
Solve the initial value problem d^2x/dt^2-3dx/dt+2x=0 ;x(0)=2;x'(0)=0
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36
Solve p-2q=3x^2sin(y-2x)
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37
Show that the entire area of x^2/3+y^2/3=a^2/3 is 3/8.πa^2.
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38
Find the limit n tends to infinity of the series n^2/(n+1)^3+n^2/(n+2)^3+....+1/8n
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39
Evaluate integration from 0 to infinity tan-1ax/x(1+x^2) where a greater than 1.
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40
Find the maximum and minimum value of u=x^2+y^2+z^2 subject to the condition that ax^2+by^2+cz^2=1.
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41
The sum of three positive number is unity.What is the maximum value of their product.
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42
Integrate w.r.t x (1+x^2)/(1-x^2).√(1+x^2+x^4)
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43
Evaluate integration of sin(mx)/x from limit 0 to infinity
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44
Explanation of Shab-e-miraj and Isra on basis on special theory of relativity
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45
Find the radius of curvature of curve the cardiod r=a(1-cosθ)
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46
If p=cisθ and q=cisΦ, prove that (p+q) (pq-1) /(p-q) (p-q+1) =sinθ+sinΦ/sinθ-sinΦ
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47
Trace the curve a^2.y^=x^3.(2a-x)
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48
Find the volume of solid generated by revolution of one arc of the cycloid x=a(θ-sinθ);y=a(1-cosθ)
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49
Lt x tends to infinity x^n/e^x ; n being a positive integer.
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50
Front Hand Easy Arabic Henna Design For Ramzan | Stylish & Beautiful Mehndi Design
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51
Find the Laplace transform of F(t) =t when t greater than 0 and less than 4;5 if t greater than 4.
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52
Integrate x. e^x.sin^2x with respect to x
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53
Test the convergence of the following series 1+3/7.x+3.6/7.10.x^2+3.6.9/7.10.13.x^3+...............
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54
Define commutative and associative binary operation on a set and give examples
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55
Integrate(2x-2) /_/x^2-2x+5 with respect to x
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56
Integrate (e^x-1) /(e^x+1) w. r. t. x
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57
∫ logx.sin-1x dx
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58
Show that the pedal equation of the lemniscate r^2=a^2.cos2θ is r^3=a^2p.
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59
Evaluate the integral:∫[√(3x+2)-1/x+2]dx
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60
Subtangent and subnormal
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61
Find the subtangent, subnormal, tangent and it's intercept on the cycloid x=a(t+sint),y=a(1-cost).
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62
Integration of 1/(sin2x-sinx) w.r.t. x
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63
Prove that the line x + y - 3= 0 touches the conic x^2+ 4xy + 3y^2 - 4x - 10 y +7 = 0.
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64
Prove that the line x + y - 3= 0 touches the conic 2x^2+ 4xy + 3y^2 - 4x - 10 y +7 = 0.
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