AILET entrance exam Question Bank Solutions for Mathematics

Solve the following question and mark the best possible option.
A swimming pool has dimensions 10 m x 26 m. At the deep end of the pool, the depth is 4.4 m and it uniformly decreases till the shallow end with a depth of 1.6 m What is the volume of the pool (in m³)? (in numerical value).

The area of the region bounded by the curve y = sin²x, x-axis and the lines x = 0, x = ππ² is

If the volume of a balloon is increasing at the rate of 25 cm³/ sec. then if the radius of the balloon is 5 cm. then the rate of the surface area is:

If the vertices of a parallelogram are (0, 0) , (2, 1), (1, 3) and (1, 2) then the angle between their diagonals will be:

The unit vector perpendicular to the vector 6i + 2j – 2k will be:

The area of the region bounded by the curves y² = 4ax, x = 0 and x = a is 

The height of the cylinder of maximum volume that can be inscribed in a sphere of radius r is:

If two vertices of a triangle are (6, 4), (2, 6) and its centroid (4, 6) then its theird vertex will be:

The slop of the tangent to the parabola y² = 4 ax point (at², 2at) will be: 

A stone is thrown in silent water, the ripples are moving at the rate of 6 cm0/sec. then the rate of change of the area when the radius of the unite is 10 cm. at the time when radius of the circle is 10 cm, then the rate at which its area increases is :

If three vertices of a square are 3i, 1 + i and 3 + 2i then its fourth vertex will be :

If a, b, c and u, v, w are complex numbers representing the vertices of two triangles such that c = (1 – r) a + b and w = ( 1 – r) u + rv, where e is a complex number, then the two triangles.

Surface area of hollow cylinder with radius ‘r’ and height ‘h’ is measured by

A polygon having 8 sides is called

A polygon having 10 sides is called

Perimeter of a rectangle with base ‘b’ and height ‘h’ is measured by

A triangle that has no equal sides and no equal angles is known as

A line going through midpoint from one side to other side of a circle is called

Area of a rectangle with base ‘b’ and height ‘h’ is measured by

Exterior angles of any polygon sum up to