List of top Quantitative Aptitude Questions on Linear Inequalities

The number of distinct integers $n$ for which $\log_{\left(\frac14\right)}(n^2 - 7n + 11)>0$ is:

For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is:

If \(c=\frac{16x}{y}+\frac{49y}{x} \)for some non-zero real numbers x and y,then c cannot take the value
The largest real value of a for which the equation\( |x+a|+|x−1|=2\) has an infinite number of solutions for x is
The number of distinct pairs of integers (m, n) satisfying |1+mn| < |m+n| < 5 is
The number of distinct pairs of integers (m, n) satisfying \(|1+mn| < |m+n| < 5\) is

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

If \(x_0 = 1, x_1 = 2, and \space x_{n + 2} =\frac{ 1+x_{n+1}}{x_n}, n = 0, 1, 2, 3,...,\) then \(x_{2021}\) is equal to?
If r is a constant such that \(|x^2-4x-13| = r\) has exactly three distinct real roots, then the value of r is
The number of integers \( n \) that satisfy the inequalities \( |n - 60| < |n - 100| < |n - 20| \) is 
Let t1, t2,… be real numbers such that t1+t2+…+tn = 2n2 +9n+13, for every positive integer n ≥ 2. If tk=103, then k equals