Recent questions tagged inequality

0 votes
1 answer
1
Consider the following inequalities$$\begin{aligned}& p^2-4 q<4 \\& 3 p+2 q<6\end{aligned}$$where $p$ and $q$ are positive integers.The value of $(p+q)$ is __________.$2$...
1 votes
1 answer
3
1 votes
1 answer
4
Which one of the following is a representation (not to scale and in bold) of all values of $x$ satisfying the inequality $2 - 5x \leq - \dfrac{6x - 5}{3}$ on the real num...
1 votes
1 answer
5
Consider the following inequalities.$2x – 1 7$$2x – 9 < 1$Which one of the following expressions below satisfies the above two inequalities?$x \leq – 4$$ – 4 < x...
2 votes
2 answers
9
Let$$\begin{array}{} V_1 & = & \frac{7^2+8^2+15^2+23^2}{4} – \left( \frac{7+8+15+23}{4} \right) ^2, \\ V_2 & = & \frac{6^2+8^2+15^2+24^2}{4} – \left( \frac{6+8+15+24...
0 votes
1 answer
10
0 votes
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11
The smallest positive number $K$ for which the inequality $\mid \sin ^2 x – \sin ^2 y \mid \leq K \mid x-y \mid$ holds for all $x$ and $y$ is$2$$1$$\frac{\pi}{2}$there ...
1 votes
2 answers
12
Let $S=\{6,10,7,13,5,12,8,11,9\},$ and $a=\sum_{x\in S}(x-9)^{2}\:\&\: b=\sum_{x\in S}(x-10)^{2}.$ Then$a<b$$a>b$$a=b$None of these
0 votes
1 answer
13
For natural numbers $n,$ the inequality $2^{n}>2n+1$ is valid when$n\geq 3$$n<3$$n=3$None of these
2 votes
1 answer
14
Let $0.01^x+0.25^x=0.7$ . Then$x\geq1$$0\lt x\lt1$$x\leq0$no such real number $x$ is possible.
0 votes
1 answer
15
1 votes
0 answers
16
1 votes
2 answers
17
The inequality $\frac{2-gx+x^{2}}{1-x+x^{2}}\leq 3$ is true for all the value of $x$ if and only if$1\leq g\leq 7$$-1\leq g\leq 1$$-6\leq g\leq 7$$-1\leq g\leq 7$
12 votes
4 answers
19
If $a, b,$ and $c$ are constants, which of the following is a linear inequality?$ax+bcy=0$$ax^{2}+cy^{2}=21$$abx+a^{2}y \geq 15$$xy+ax \geq 20$
14 votes
3 answers
20
Which of the following is true ?$\sqrt{3}+\sqrt{7}=\sqrt{10}$$\sqrt{3}+\sqrt{7}\leq \sqrt{10}$$\sqrt{3}+\sqrt{7}< \sqrt{10}$$\sqrt{3}+\sqrt{7} \sqrt{10}$
4 votes
1 answer
21
In which of the following options will the expression $P < M$ be definitely true? $M < R P S$ $M S < P < F$ $Q < M < F = P$ $P = A < R < M$
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