List of practice Questions

For all real numbers $ x $, the condition $ |3x - 20| + |3x - 40| = 20 $ necessarily holds if

If 3x+2|y|+y=7 and x+|x|+3y=1, then x+2y is
For all possible integers n satisfying 2.25 ≤ 2 + 2n + 2 ≤ 202, the number of integer values of 3 + 3n + 1 is
The number of distinct pairs of integers (m, n) satisfying |1+mn| < |m+n| < 5 is
If r is a constant such that \(|x^2-4x-13| = r\) has exactly three distinct real roots, then the value of r is
\(f(x) = \) \(\frac{x^2+2x−15}{x^2−7x−18}\) is negative if and only if

If n is a positive integer such that \((10−−√7)(10−−√7)2…(10−−√7)n > 999\), then the smallest value of n is

The number of distinct pairs of integers (m, n) satisfying \(|1+mn| < |m+n| < 5\) is
For all possible integers n satisfying \(2.25 ≤ 2 + 2^{n + 2} ≤ 202\), the number of integer values of \(3 + 3^{n + 1}\) is
The number of integers \( n \) that satisfy the inequalities \( |n - 60| < |n - 100| < |n - 20| \) is 
If x and y are positive real numbers satisfying \(x+y=102\), then the minimum possible value of \(2601(1+\frac 1x)(1+\frac 1y)\) is
[This Question was asked as TITA]
The number of real-valued solutions of the equation \(2^x+2^{-x}=2-(x-2)^2\) is
For real \(x\), the maximum possible value of \(\frac{x}{\sqrt{1+x^4}}\) is
In how many ways can a pair of integers \((x , a)\) be chosen such that \(x^2-2|x|+|a-2|=0\) ?
If \(x\) and \(y\) are positive real numbers satisfying \(x+y=102\), then the minimum possible value of \(2601\bigg(1+\frac{1}{x}\bigg)\bigg(1+\frac{1}{y}\bigg) \)is