XAT Functions Practice Questions With Solutions

Consider the equation $\log_5(x - 2) = 2 \log_{25}(2x - 4)$, where x is a real number.
For how many different values of x does the given equation hold?

The roots of the polynomial $P(x) = 2x^3 - 11x^2 + 17x - 6$ are the radii of three concentric circles.
The ratio of their area, when arranged from the largest to the smallest, is:

Given $A = |x + 3| + | x - 2 | - | 2x -8|$. The maximum value of $|A|$ is:

ABC is a triangle and the coordinates of A, B and C are (a, b-2c), (a, b+4c) and (-2a,3c) respectively where a, b and c are positive numbers.
The area of the triangle ABC is:

Consider $a_{n+1} =\frac{1}{1+\frac{1}{a_{n}}}$ for $n = 1,2, ....., 2008, 2009$ where $a_{1} = 1$. Find the value of $a_{1}a_{2} + a_{2}a_{3} + a_{3}a_{4} + ... + a_{2008}a_{2009}$.

Raju and Sarita play a number game. First, each one of them chooses a positive integer independently. Separately, they both multiply their chosen integers by 2, and then subtract 20 from their resultant numbers. Now, each of them has a new number. Then, they divide their respective new numbers by 5. Finally, they added their results and found that the sum is 16. What can be the maximum possible difference between the positive integers chosen by Raju and Sarita?

The sum of the cubes of two numbers is 128, while the sum of the reciprocals of their cubes is 2.

Consider the real-valued function $f(x)=\frac{\log{(3x-7)}}{\sqrt{2x^{2}-7x+6}}$ Find the domain of f(x).

Let $f(x) = \frac{x^2 + 1}{x^2 - 1}$ if $x \neq 1, -1,$ and 1 if x = 1, -1. Let $g(x) = \frac{x + 1}{x - 1}$ if $x \neq 1,$ and 3 if x = 1.
What is the minimum possible values of $\frac{f(x)}{g(x)}$ ?

The topmost point of a perfectly vertical pole is marked A. The pole stands on a flat ground at point D. The points B and C are somewhere between A and D on the pole. From a point E, located on the ground at a certain distance from D, the points A, B and C are at angles of 60, 45 and 30 degrees respectively. What is AB : BC : CD?