IPM Indore 2022

In how many ways can the letters of the word MANAGEMENT be arranged such that no two vowels appear together?

The set of all possible values of f(x) for which $$(81)^{x} + (81)^{(f(x)} = 3$$ is

The value of k for which the following lines
x-y-1=0
2x+3y-12=0
2x-3y+k=0
are concurrent is

The curve represented by the equation

$$\frac{x^{2}}{\sin \sqrt{2} - \sin \sqrt{3}} + \frac{y^{2}}{\cos \sqrt{2} - \cos \sqrt{3}} = 1$$

Let A = {1, 2, 3} and B = {a, b}. Assuming all relations from set A to set B are equally likely, what is the probability that a relation from A to B is also a function?

In a 400-metre race, Ashok beats Bipin and Chandan respectively by 15 seconds and 25 seconds. If Ashok beats Bipin by 150 metres, by how many metres does Bipin beat Chandan in the race?

The sum of the squares of all the roots of the equation $$x^{2} + |x + 4| + |x − 4| − 35 = 0$$ is

If $$f(x^{2} + f(y)) = xf(x) + y$$ for all non-negative integers x and y, then the value of $$[f(0)]^{2} + f(0)$$ equals________.

The Set of real values of x for which the inequality $$\log_{27}8\leq \log_{3}x < \frac{1}{9\log_{2}3}$$ holds

A set of all possible values the function $$f(x) = \frac{|x|}{|x|}$$, where $$x \neq 0$$ takes is, where x ≠ 0, takes is