List of top Mathematics Questions on linear inequalities in one variable asked in KEAM

In a right-angled trapezium $ABCD$, $\angle A = 90^\circ$, $\angle D = 90^\circ$, $AB = 7a + 1$, $CD = 3a + 1$ and $AD = 3a$. If the perimeter of the trapezium is greater than 56 but less than 92, then the range of possible values of $a$ is

The solution set of the inequality $6(2x + 3) + x > 53 - 2x$ is

The set of all \(x\) satisfying the inequality \(8 + 3x > 4(x - 3) + 2\) is

Let A and P be the area and perimeter of a rectangle respectively. The length and breadth of the rectangle are (x + 2) cm and (x - 2) cm. If \(A \leq 140 cm^2\) and \(P \geq 20 cm\), then the range of possible values of x is

Let $x$ be a real number such that $5<|x - 1|<15$. Then

The coefficient of \( x^3 \) in \( (2+x)^n \) is 160. Find the coefficient of \( x^6 \) in \( (2-x^2)^n \).

Number of words that can be formed starting and ending with the same letter from the word BANANA.

Let $x$ be a real number such that $x+\frac{x}{4}+\frac{x}{3}<13$. Then the solution set is ________.

The solution set for $-12x > 38$, where $x$ is a natural number, is ________.

Let $x$ be a real number such that $\frac{3(x+3)}{7} \le \frac{6(x-1)}{5}$. Then the solution set of the inequality is:

Let $x$ be a real number such that $7x+4 < 9x+8$. Then the solution set of the inequality is:

\( -5<x \le -1 \) implies \( -21<5x + 4 \le b \), the least value of \( b \) is

The set of all \( x \) satisfying the inequalities \( -4 \le 2 - 3x<7 \) is

The set of all \(x\) satisfying the inequality \(|3 - 4x| \leq 11\) is

If \[ \frac{x}{4} + \frac{x}{3} < 13, \text{ then } x \in \]

Solution set of \( -12x > 38 \text{ for } x \in \mathbb{N} \) \[ -12x > 38 \]

The smallest prime number satisfying the inequality $\frac{2n-3}{3}\ge\frac{n-1}{6}+1$ is

The number of integers satisfying the inequality \(|n^{2}-100|<50\) is

The solution set of the rational inequality $\frac{x+9}{x-6}\le0$ is

The set of all real numbers satisfying the inequality \( x - 2 < 1 \) is:

The least integer satisfying \( \frac{396}{10} - \frac{19-x}{10}<\frac{376}{10} - \frac{19-9x}{10} \) is:

If \( |x-3| < 2x+9 \), then \(x\) lies in the interval

The number of solutions of the inequation \( |x - 2| + |x + 2| < 4 \) is:

The number of solutions of the inequation \( |x - 2| + |x + 2| < 4 \) is:

The number of solutions of the inequation \( |x - 2| + |x + 2| < 4 \) is: