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`?