Given a point on the axis of the parabola y² = 2px at a distance a from the vertex, find the abscissa of the point of the curve closest to it.
See Answer →Find the height of a right cylinder with greatest lateral surface area that may be inscribed in a given sphere of radius R.
See Answer →An open storage bin with square base and vertical sides is to be constructed from a given amount of material. Determine its dimensions if its volume is to be maximum neglecting the thickness of material and waste in constructing it.
See Answer →Show that the conical tent of given capacity will require the least amount of canvas if its height is √2 times its base radius.
See Answer →Using vectors, find the area of the triangle ABC with vertices A(1,2,3), B(2, -1, 4) and C(4,5,-1).
See Answer →If A,B,C,D are the points with position vectors , respectively. Find the projection of
along
.
If , show that
x
=
x
=
x
.
Find the angle between the vectors and
.
Find a vector of magnitude 6, which is perpendicular to both the vectors and
Show that area of a parallelogram whose diagonals are given by and
is
Also find the area of the parallelogram whose diagonals are
and
, and
find vector
such that
and
If A is a square matrix, such that A² =A, then find (I + A)³ - 7A.
See Answer →If the matrix A is both symmetric and skew-symmetric, then determine A.
See Answer →If A, B are symmetric matrices of the same order, then what will be the type of matrix (AB-BA)? Give reasons in support of your answer.
See Answer →Project planning technique
See Answer →Demand side management
See Answer →Energy efficient lighting
See Answer →