Some Algebraic Implications of Inequalities

Q.

Prove that the logarithmic function is strictly increasing on (0, ∞).

Q.

IQ of a Person Is Given by the Formula

Q.

Find two consecutive odd numbers whose sum is $128.$

Q.

The sum of three consecutive odd numbers is$69$. Find the numbers.

Q.

You need a $15\%$ acid solution for a certain test, but your supplier only ships $5\%$ solution and $17.5\%$ solution. If you need $20$ liters of $15\%$ acid solution, how many liters of $5\%$ and $17.5\%$ solution do you need?

Q.

How do you solve $\log x=-2$?

Q.

Solve the equation 2x²-5x+3=0 , by the method of completing square

Q. $\int \frac{x^3+x+1}{x^2-1}dx$

Q. Which of the following is/are not the solution of ${\log }_3\left(x^2-2\right)<{\log }_3\left(\frac{3}{2}\left|x\right|-1\right)$

1. $\left(\sqrt{2},2\right)$
2. $\left(-2,-\sqrt{2}\right)$
3. $\left(-\sqrt{2},2\right)$
4. $\left(-2,2\right)$

Q. The inequality $\sqrt{x^{{\log }_2\sqrt{x}}}\ge 2$ is satisfied by

1. only one value of x
2. $x\in (0,\frac{1}{4}]$
3. $x\in [4,\infty )$
4. $x\in \left(1,2\right)$

Q.

find the values of a and b.

(7+ root5/ 7-root5) -(7-root5/7+root5) = a+7/11root5b

Q. $\underset{0}{\overset{\infty }{\int }}\frac{1}{1+e^x}dx$ equals

(a) log 2 − 1
(b) log 2
(c) log 4 − 1
(d) − log 2

Q.

What is the integral of limits 1 to 2 of function 1/x(1+logx)2

Q.

use the rulesof the special products to find the value of 54square-50square

Q. Solve this:
Q.11. If P(A) = 0.3, P(B) = 0.4 and $P\left(A\cap B\right)=0.5$, then $P\left(B\setminus A\cup B\right)$ is
(A) 0.75
(B) 0.65
(C) 0.35
(D) 0.25

Q. The inequality $\sqrt{x^{{\log }_2\sqrt{x}}}\ge 2$ is satisfied by

1. only one value of x
2. $x\in (0,\frac{1}{4}]$
3. $x\in [4,\infty )$
4. $x\in \left(1,2\right)$

Q. Let $a={\log }_3{\log }_{3}2.$ An integer k satisfying $1<2^{\left(-k+3^{-a}\right)}<2,$ is

Q. if A, B, C are three finite sets such that n(A)=27, n(B)=23, n(C)=25 AND n(A intersection B)=14 , n(BINTERSECTION C)=9, n(C INTERSECTION A)=10 AND n(A inter B inter C)=6 ALSO n(U)=80
FIND;n(A INTER B INTER C)
n(B INTER AC)
n(C INTER A INTER B)

Q. Which of the following is/are not the solution of ${\log }_3\left(x^2-2\right)<{\log }_3\left(\frac{3}{2}\left|x\right|-1\right)$

1. $\left(\sqrt{2},2\right)$
2. $\left(-2,-\sqrt{2}\right)$
3. $\left(-\sqrt{2},2\right)$
4. $\left(-2,2\right)$