Exams › JEE Main › Maths

Determine the area of the region defined by {(x, y): 0 ≤ x ≤ 9/4, 0 ≤ y ≤ 1, x ≥ 3y, x + y ≥ 2}.

1. 11/32
2. 35/96
3. 37/96
4. 13/32

Correct answer: 11/32

Solution

The feasible region is a polygon bounded by x = 3y, x + y = 2, y = 1, and x = 9/4; evaluating its area gives 11/32.

Related JEE Main Maths questions

• For every b > 1, the area enclosed by the x-axis, the graph of y = f(x), and the vertical lines x = 1 and x = b is given by √(b² + 1) − √2. Then f(x) must be:
• The graphs of y = sin x and y = cos x meet at infinitely many points, forming repeated bounded regions of equal area. The area of one such region is
• Find the area bounded by the parametric curve x = a cos³ t, y = b sin³ t together with the positive x-axis and positive y-axis.
• Find the area enclosed by the curves y = e^x, y = e^(-x), and the vertical line x = 1, measured in square units.
• A straight line of the form y = mx divides into two equal parts the region bounded by the y-axis, the horizontal line y = 3/2, and the parabola y = 1 + 4x - x². What is the value of m?
• Find the area enclosed by the curve y = cos² x, the x-axis, and the vertical lines x = 0 and x = π over the interval (0, π).

⚔️ Practice JEE Main Maths free + battle 1v1 →