Domain & Range — CAT Previous-Year Questions

f(x) = $\frac{x^2+2x-15}{x^2-7x-18}$ is negative if and only if

The area of the region satisfying the inequalities |x| - y ≤ 1, y ≥ 0 and y ≤ 1 is

The shortest distance of the point (1/2,1) from the curve y = |x - 1| + |x + 1| is

The graph of y – x against y + x is as shown below. (All graphs in this question are drawn to scale and the same scale has been used on each axis). Then, which of the options given shows the graph of y against x.

In the X-Y plane, the area of the region bounded by the graph of |x + y| + |x – y| = 4 is

When the curves, y = log₁₀ x and y = x⁻¹ are drawn in the X-Y plane, how many times do they intersect for values of x ≥ 1?

The function f(x) = |x − 2| + |2.5 − x| + |3.6 − x|, where x is a real number, attains a minimum at

Consider the following two curves in the X-Y plane

y = x³ + x² + 5

y = x² + x + 5

Which of the following statements is true for −2 ≤ x ≤ 2?