List of top Mathematics Questions on Inequalities

If ∫0ax dx≤a2+6 \int_0^a x \, dx \leq \frac{a}{2} + 6 , then which of the following holds for a a ?
The solution set of the inequality ∣3x∣≥∣6−3x∣ |3x| \geq |6 - 3x| is: 
The solution region of the inequality 2x+4y≤9 2x + 4y \leq 9 is:
The real valued function f:R→[52,∞) f: \mathbb{R} \to \left[ \frac{5}{2}, \infty \right) defined by f(x)=∣2x+1∣+∣x−2∣ f(x) = \left| 2x + 1 \right| + \left| x - 2 \right| is:
If 1⋅3⋅5+3⋅5⋅7+5⋅7⋅9+… 1 \cdot 3 \cdot 5 + 3 \cdot 5 \cdot 7 + 5 \cdot 7 \cdot 9 + \dots (n terms) = n(n+1)f(n)−3n n(n + 1)f(n) - 3n , then f(1)= f(1) = :
If 3f(x)−2f(1x)=x, 3f(x) - 2f\left(\frac{1}{x}\right) = x, then f′(2) f'(2) is:
The set of all values of kk for which the inequality x2−(3k+1)x+4k2+3k−3>0x^2 - (3k+1)x + 4k^2 + 3k - 3>0 is true for all real values of xx is
If A⊆Z A \subseteq \mathbb{Z} and the function f:A→R f: A \to \mathbb{R} is defined by f(x)=164−(0.5)24+x−x2 f(x) = \frac{1}{\sqrt{64 - (0.5)^{24+x- x^2} }} then the sum of all absolute values of elements of A A is:
The set of all real values of xx satisfying the inequality 7x2−5x−182x2+x−6<2\frac{7x^2 - 5x - 18}{2x^2 + x - 6}<2 is
If 8+3x<∣8+3x∣,x∈R 8 + 3x < |8 + 3x|, x \in \mathbb{R} , then x x lies in : 
Match List I with List II

LIST I

LIST II

A.The solution set of the inequality
5x−8>2x+3,x∈R is,5x-8\gt2x+3,x\in R\ is,		I.(−∞,65](-\infin,\frac{6}{5}]
B.The solution set of the inequality
3x−4<5x+7,x∈R is,3x-4\lt5x+7,x\in R\ is,		II.(65,∞)(\frac{6}{5},\infin)
C.The solution set of the inequality
4x+15≤3(1−2x)is,4x+15\le3(1-2x)is,		III.[10,∞)[10,\infin)
D.The solution set of the inequality
7x−8≥2(1+3x)is,7x-8\ge2(1+3x)is,		IV.(−112,∞)(-\frac{11}{2},\infin)

Choose the correct answer from the options given below:
The graph of the inequality 3x - 2y > 6 is
The solution set of inequalities :
x + 3 ≤ 0 and 2x + 5 ≤ 0; if x ∈ R is :
If 2−x4−4+x6≥10 \frac {2-x}{4}-\frac{4+x}{6}\geq10  then :
The region represented by the system of inequalities x, y≥0, y≤8, x + y≤4 is: