AILET entrance exam Question Bank Solutions

The following question is based on the diagram given below. Study the diagram carefully and answer the question

How many players are neither artists nor doctors?

The following question is based on the diagram given below. Study the diagram carefully and answer the question

How many artists are players?

The following question is based on the diagram given below. Study the diagram carefully and answer the question

How many artists are neither doctors nor players?

The following question is based on the diagram given below. Study the diagram carefully and answer the question

How many doctors are neither players nor artists?

The following question is based on the diagram given below. Study the diagram carefully and answer the question

How many doctors are players and artists both?

Read the following information carefully and answer the question
The circle represents poor boys, the square represents educated boys, the triangle represents the boys who are employed somewhere and the rectangle represents those who help in the family business. Each section of the diagram is numbered. Now, answer the questions given below on the basis of this diagram.

Which section does number 3 represent?

Read the following information carefully and answer the question
The circle represents poor boys, the square represents educated boys, the triangle represents the boys who are employed somewhere and the rectangle represents those who help in the family business. Each section of the diagram is numbered. Now, answer the questions given below on the basis of this diagram.

Which number represents the group of educated poor boys who are employed somewhere but do not help in the family business?

Read the following information carefully and answer the question
The circle represents poor boys, the square represents educated boys, the triangle represents the boys who are employed somewhere and the rectangle represents those who help in the family business. Each section of the diagram is numbered. Now, answer the questions given below on the basis of this diagram.

Which number represents those poor boys who help in the family business but are not educated or employed elsewhere?

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.