List of top Mathematics Questions on inequalities

Solve the inequality: \( \log_2(x^2 - 5x + 6) >1 \)
let \(S\) be the set of positive integral values of a for which \(\frac {ax^2+2(a+1)x+9a+4}{x^2+8x+32}< 0,\) \(∀x∈R\). Then, the number of elements in \(S\) is
Let A=\(\begin{pmatrix} 2 &-1  &-1 \\   1&0  &-1 \\   1&-1  &0  \end{pmatrix}\) and B=A–I. If ω=\(\frac{\sqrt3 i-1}{2}\), then the number of elements in the set {n∈{1,2,⋯,100}:\(A^n+(ωB)^n\)=A+B} is equal to _______.
If the maximum value of the term independent of t in the expansion of (t2x\(^{\frac{1}{5}}\)+\(\frac{(1−x)^{\frac{1}{10}}}{t}\)),x≥0 is K, then 8 K is equal to__________.
Which is the correct order for a given number \(\alpha\) in increasing order?
The number of integral solution of \(\frac{x + 1}{x^2 + 2}>\frac{1}{4}\) is
If \(3^x + 2^{2x} \ge 5^x\), then the solution set for \(x\) is
If the equation \(x^2 + px + q = 0\) and \(x^2 + qx + p = 0\) have a common root then \(p + q + 1\) is equal to
The value of \(a \ge b\) for which the sum of the cubes of the roots of \(x^2 - (a - 2)x + (a - 3) = 0\) assumes the least value, is
The number of real solutions of the equation \(1 + |e^x - 1| = e^x(e^x - 2)\) is

Solve the given inequality for real\(x:\frac{ x}{3} > \frac{x}{2} +1\).

Solve the given inequality for real \(x: \frac{3(x - 2)}{5} ≤ \frac{5(2 - x)}{3}\).

Solve the given inequality for real\(x: \frac{1}{2}(\frac{3x}{5}+4) ≥ \frac{1}{3}(x-6)\).

Solve the given inequality for real x: 2(2x + 3) - 10 < 6 (x - 2).
Solve the given inequality for real x: 37 – (3x + 5) ≥ 9x – 8(x – 3)

Solve the given inequality for real\(x: \frac{x}{4} < \frac{(5x-2)}{3} -\frac{ (7x-3)}{5}\).

Solve the given inequality for real \(x:\frac{ (2x -1)}{3} ≥ \frac{(3x -2)}{4} - \frac{(2-x)}{5}\).

Ravi obtained 70 and 75 marks in first two unit test. Find the minimum marks he should get in the third test to have an average of at least 60 marks.
To receive Grade 'A' in a course, one must obtain an average of 90 marks or more in five examinations (each of 100 marks). If Sunita's marks in first four examinations are 87, 92, 94 and 95, find minimum marks that Sunita must obtain in fifth examination to get grade 'A' in the course.
Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.
Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23.
The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.
A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5 cm longer than the second?
Solve the inequality 2 ≤ 3x – 4 ≤ 5
Solve the inequality 6 ≤ –3(2x – 4) < 12.