Algebra Review Test - 2

The number of solutions of

\( \dfrac{\log 5+\log(y^2+1)}{\log(y-2)}=2 \) is

Information for Questions 2 and 3: Given below are two graphs labeled F(x) and G(x). Compare the graphs and give the answer in accordance to the options given below:

Q.

Information for Questions 2 and 3: Given below are two graphs labeled F(x) and G(x). Compare the graphs and give the answer in accordance to the options given below:

Q.

If a is a natural number which of the following statements is always true?

In the figure below, equation of the line PQ is

For which of the following functions is

\( \dfrac{f(a)-f(b)}{a-b} \) ​constant for all the numbers ‘a’ and ‘b’, where a ≠ b?

Given that \( f(a,b,c)=\dfrac{a+b+c}{3} \), then

(a) \( f(a,b,c)\ge\dfrac{\lvert a\rvert+\lvert b\rvert+\lvert c\rvert}{3} \)

(b) \( f(a,b,c)\ge\max(a,b,c) \)

(c) \( \lvert f(a,b,c)\rvert\ge\dfrac{\lvert a+b+c\rvert}{3} \)

(d) \( \lvert f(a,b,c)\rvert\le\dfrac{\lvert a\rvert+\lvert b\rvert+\lvert c\rvert}{3} \)

We are given two variables \( x \) and \( y \). The values of the variables are

\( x=\dfrac{1}{a+b} \) and \( y=\dfrac{3}{c+x} \). Find the value of the expression \( \dfrac{7y}{x} \)

(a) \( \dfrac{21(a+b)^2}{ca+cb+1} \)

(b) \( \dfrac{3(a+b)}{7ab+ac} \)

(c) \( \dfrac{7}{3(ca+cb+1)} \)

(d) None of these

If \( p=\dfrac{12-\lvert x-3\rvert}{12+\lvert x-3\rvert} \) the maximum value that ‘p’ can attain is:

Refer to the graph. What does the shaded portion represent?