Questions asked by Raj

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• What is the angle between two lines whose direction ratios satisfy following equations?
  
• Find the coordinates of the vertices and foci, eccentricity? #x^2-8x+2y+7=0#
  
• Prove that the paraboloids #x^2/a_1^2+y^2/b_1^2=(2z)/c_1# ; #x^2/a_2^2+y^2/b_2^2=(2z)/c_2#; #x^2/a_3^2+y^2/b_3^2=(2z)/c_3# Have a common tangent plane if?
  
• Using the discriminant, give the nature of the roots of #7x^3+x^2-35x=5#?
  
• Solve the equation #x^4+4x^3+8=0#?
  
• Give a real life situation problem which is mathematically translated into #2x+y+2z=18#?
  
• Find the values and roots of the equation #z^4-2z^3+7z^2-4z+10=0#?
  
• Let #a, b > 0, a+b = 1, n>1# Show that #(a+1/a)^n + (b+1/b)^n >= 5^n/n^(n-1)#?
  
• Find all the #8^(th)# roots of #3i-3#?
  
• How to solve the linear system with Cramer's Rule?
  
• Find the cubic equation whose roots are the cubes of the roots of #x^3+ax^2+bx+c=0#,#a,b,cinRR#?
  
• Find the condition under which the line #xcosalpha+ysinalpha=p# will be a tangent to the conic #3x^2+4y^2=5#?
  
• How to find solution set in #RR^3# of #x-pi=5#?
  
• Find the equation of the enveloping cylinder of the sphere #x^2+y^2+z^2-2x+4y=1# with its lines parallel to #x/2=y/3,z=0#?
  
• #int sin theta sin2theta sin3theta# ?
  
• Find the area of triangle in parabola #x^2=8y#?
  
• Find the equations of the hyperbolas that intersect #3x^2-4y^2=5xy# and #3y^2-4x^2=2x+5#?
  
• The tangent and the normal to the conic #x^2/a^2+y^2/b^2=1# at a point #(acostheta, bsintheta)# meet the major axis in the points #P# and #P'#, where #PP'=a# Show that #e^2cos^2theta + costheta -1 = 0#, where #e# is the eccentricity of the conic?
  
• Prove that the paraboloids: #x^2/a_1^2+y^2/b_1^2=(2z)/c_1#; #x^2/a_2^2+y^2/b_2^2=(2z)/c_2#; #x^2/a_3^2+y^2/b_3^2=(2z)/c_3# Have a common tangent plane if: #|(a_1^2 a_2^2 a_3^2), (b_1^2 b_2^2 b_3^2), (c_1 c_2 c_3)|=0#?
  
• Using mean value theorem show that: #x< sin^-1x#, for #x>0#?
  
• The normal at a point #P# of the ellipsoid #x^2/a^2+y^2/b^2+z^2/c^2=1# meets the coordinate planes in #A,B,C#. Show that #AP:BP:CP::a^2:b^2:c^2#?
  
• Show that the path traced by the point of intersection of three mutual perpendicular tangent planes to the ellipsoid #ax^2+by^2+cz^2=1# is a sphere with the same centre as that of the ellipsoid.?
  
• Find the domain of the function #f# defined by #f(x) = 1/sqrt(5x-x^2-6)#?
  
• Find the area of a loop of the curve #r=a sin3theta#?
  
• #lim_(x->3) (sqrt3x-3)/(sqrt(2x-4) - sqrt2)# Evalute?
  
• Differentiate #tan^-1 ((2x)/(1-x^2))# with respect to #sin^-1 ((2x)/(1+x^2))#?
  
• Find the maximum and minimum values for the function #f# defined by #f(x) = 2sinx + cos2x# in the interval #[0, pi/2]#?
  
• If #u_n = int (sin nx)/sinx dx, >= 2#, prove that #u_n = (2sin(n-1)x)/(n-1)+u_(n-2)# Hence evaluate: #int_0^(pi/2) (sin5x)/ sinx dx#?
  
• Show that #ln(1+x) < x-(x^2)/(2(1+x)), AA x>0#?
  
• Find #a, b# so that the system #x+y+z=6#, #x+2y+3z=10#, #x+2y+az=b# has an unique solution?
  
• What is the equation of the tangent planes to #7x^2-3y^2-z^2+21=0# which passes through the line #7x-6y+9=0#,#z=3#?
  
• Solve the equation #3x^4-25x^3+50x^2-50x+12=0# given that the product of two of its roots is 2?
  
• For #z_1 = -3 + 2i# and #z_2=4+3i#, write #z_1/z_2# in polar form. In which quadrant will it lie in an Argand Diagram?
  
• Solve #lim_(xrarrprop) (sqrt(x+sqrt(x+sqrt(x)))-sqrtx)#?
  
• #d/dx[int_1^tanx sqrt(tan^-1t)dt]#?
  
• If #y=e^(mtan^-1x)#, check whether the equation #(1+x^2)y_(n+1)+(2nx-m)+n(n+1)y_(n-2) = 0# ?
  
• Evalute #lim_(x->oo) [sqrt(x^2+x+2) - sqrt(x^2-3x-5)]#?
  
• Prove that #cosx >= 1-x^2/2 AA x in RR# ?
  
• How to find the area of the loop of the curve #x(x^2+y^2)=a(x^2-y^2)#?
  
• Find the point of inflection of the curve, #y=xe^x, x in RR#, if any. What is it's radius of curvature at #x = 2#?
  
• Please make the Ask Question modal only close while click on Close button. Not the overlay area. I wrote a long question and trying to write a description while accidentally clicked the blank overlay and all gone :( ?
  
• Find #a, b# so that the system has unique solution: ? #x+y+z=6# #x+2y+3z=10# #x+2y+az=b#
  
• How to solve the equation set ? #3x+y-2z=-7# #5x-3y+2z=5# #9x-11y+10z=29#
  
• Find the equation of the cylinder whose base is circle #x^2+y^2=9, z=0# and the axis is #x/4=y/3=z/5#?
  
• What is the equations of the tangents of the conic #x^2+4xy+3y^2-5x-6y+3=0# which are parallel to the line #x+4y=0#?
  
• If the tangents at two points of a parabola are at right angles, then show that they intersect at a point on the directrix?
  
• Show that the points #(2, 0, 1), (0,4,-3)# and #(-2, 5, 0)# are non-collinear. Hence find the equation of plane passing through them ?
  
• Is the mean value theorem can be applied to #f(x)= 1/x# in the interval #[-1, 1]#?
  
• How to trace the curve #(x^2+y^2)x=ay^2, a>0# stating all the properties used in the process?
  
• If #y=e^(msin^-1x)#, then show that #(1-x^2)y_2-xy_1=m^2y#?
  
• Identify the type of conic #4(x-2y+1)^2+9(2x+y+2)^2=25# ?
  
• What surface represented by #x^2+y^2=9z#? Obtain the section of this surface by the plane #y=0# ?
  
• What is the equation of the right circular cone when the straight line #2y+3z=6, x=0# revolve about the #z# axis?
  
• Does the equation #2/r=3cos(theta - pi/4)+2sin(theta+pi/4)# represents a straight line?
  
• Find the new equation of the curve #(x-2)^2=y(y-1)^2# by transforming to parallel axes through the point #(2, 1)#?
  
• How to solve #x^4+2x^3-25x^2-26x+120=0# given that the product of two of its roots is 8?
  
• Solve #x^4-2x^3+4x^2+6x-21=0#?
  
• Check whether the rectangle of maximum area which can be inscribed in a circle is a square?
  
• Is the curve #(x^2-a^2)(y^2-b^2)+2xy+3x+4y=7# has only 2 asymptotes parallel to coordinate axes?
  
• If #I_n=int_(pi/4)^(pi/2) cot^n x dx#, then prove that #(n-1)(I_n+I_(n-2))=1#?
  
• Find the equation of the tangent planes to the conicoid #7x^2-3y^2-z^2+21=0#, which pass through the line #7x-6y+9=0, z=3#?
  
• Show by induction, that #AA n >= 1#, #1^2+3^2+5^2+...+(2n-1)^2=n/3(4n^2-1)#?
  
• #int_0^(pi/2) dx/(1+2sinx+cosx)#?
  
• What are the roots of #3x^4-28x^3-3x^2+112x-36=0#?
  
• #int (1+x^2)/(1+7x^2+x^4)dx#?
  
• Find the equation of the tangent and normal to the curve #x^2+y^2+4x+3y-25=0# at #(-3, 4)#?
  
• #int sqrt((a+x)/(a-x))dx#?
  
• Solve #(x+1)(x+3)(x+4)(x+6)=112#?
  
• I have in my purse 5, 10 and 20 rupee notes totalling 500 rupees. Total number of notes is 45. The total number of 5 and 10 rupee notes is 15 more than the number of 20 rupee notes. Find their numbers by Cramer's Rule?
  
• #Arg(z) = -Arg(z^-1)# for any #zinC, z!=0# How to prove it?
  
• #int_0^(pi/2) dx/(5+4cosx)#?
  
• #y=sin(msin^-1x)#, then check whether or not #(1-x^2)y_(n+2)-(2n+1)xy_(n+1)+(m^2-n^2)y_n=0#, also find #y_n(0)#?
  
• Differentiate #tan^-1((sinx-cosx)/(sinx+cosx))# with respect to #x/2#?
  
• If #y=ln[x+sqrt(x^2+1)]#, check whether #(1+x^2)y_(n+2) + (2n+1)xy_(n+1) - n^2y_n=0# is true or not?
  
• Find the derivative of #(tanx)^secx + (secx)^cotx# W.R.T. x?
  
• #int (x^2-1)/(x^4+x^2+1) dx#?
  
• #y=sin^-1[x(sqrt(x-1)) - sqrtx sqrt(1-x^2)]#, find #dy/dx#?
  
• #int 1/(3+5sinx+3cosx)dx#?
  
• Find the equation of tangents to the curve #y=x^3# which are parallel to the line #12x-y-3=0#?
  
• Find the volume of the solid of revolution obtained by rotating the curve #x=3cos^3theta# , #y=3sin^3theta# about the #x# axis?
  
• Find the equations of tangent planes to the conicoid #x^2+2y^2+z^2=4# which passes through the line #x+y+z+1=0#, #2x+3y+2z-3=0#?
  
• #y^2+z^2=16# is this represents a circle in 3-Dimensional space? Or 2-Dimensional Space?
  
• How to find directions ratios of the line #(x-1)/2=(y+3)/1, z=2#?
  
• Show that the plane #2x-4y-z+9=0# touches the sphere which passes through #(1,1,6)# and whose centre is #(2,-3,4)#. Also, find the point of contact.?
  
• Find the equation of the cone whose vertex is at the origin and base is the circle #x=a#, #y^2+z^2=b^2#?
  
• Find the equation of the line which is parallel to the line #3x+4y=1# and passes through the midpoint of the line segment joining #(1,2)# and #(-2,1)#. Find the distance of this line from the given line.?
  
• Find the equation of the cylinder whose base is the circle #x^2+y^2+z^2=4#, #x+y+2z=3#?
  
• Check if the line #x+1=1-y=-5z# lies on the plane #2x+3y-5z=1#?
  
• Prove that #(x+1)(2n+1)>= 6(n!)^(2/n)#?
  
• Prove by Mathematical Induction #1/1.2+1/2.3+...+1/(n(n+1))=n/(n+1)#?
  
• A enjoyed two types of games, #type A# and #type B#, at the game studio. Each time he played #type A#, it cost #Rs. 3 # and each time she played #type B#, it cost #Rs. 4#. If the number of #type B # games played was the half of the number of #type A#..?
  
• A circle cuts the parabola #y^2=4ax# in the points #(at_i^2, 2at_i)# for #i=1, 2, 3, 4#. Prove that #t_1+t_2+t_3+t_4=0#?
  
• A plane meets the coordinate axes #A, B, C# such that the centroid of the triangle #ABC# is the point #(a, b, c)#, show that the equation of the plane is #x/a+y/b+z/c=3#?
  
• Find the equation of the plane through the line of intersection of the planes #ax+by+cz+d=0, a_1x+b_1y+c_1z+d_1=0# and perpendicular to the #XY# plane?
  
• Find the equation of the plane through #(2, 3, -4)# and #(1, -1, 3)# parallel to the x-axis.?
  
• What is the distances between the parallel planes #2x-2y+z+3=0# and #4x-4y+2z+5=0#?