# JEE Main & Advanced Mathematics Other Series Question Bank

### done Logarithmic series

• A) $\frac{1}{2}-{{\log }_{e}}\frac{2}{3}$

B) $-{{\log }_{e}}\frac{2}{3}$

C) $\frac{1}{2}+{{\log }_{e}}\left( \frac{2}{3} \right)$

D) None of these

• A) $\frac{x}{1+x}-{{\log }_{e}}(1-x)$

B) $\frac{x}{1+x}+{{\log }_{e}}(1-x)$

C) $\frac{x}{1-x}-{{\log }_{e}}(1-x)$

D) $\frac{x}{1-x}+{{\log }_{e}}(1-x)$

• A) ${{\log }_{e}}x$

B) ${{\log }_{e}}(1+x)$

C) ${{\log }_{e}}(1-x)$

D) ${{\log }_{e}}\frac{x}{1+x}$

• A) ${{\log }_{e}}\sqrt{2}$

B) ${{\log }_{e}}2-\frac{1}{2}$

C) ${{\log }_{e}}2$

D) ${{\log }_{e}}4$

• A) $2-{{\log }_{e}}2$

B) $2+{{\log }_{e}}2$

C) ${{\log }_{e}}4$

D) None of these

• A) ${{\log }_{e}}\frac{1}{2}$

B) $2\,\left[ x+\frac{{{x}^{3}}}{3}+\frac{{{x}^{5}}}{5}+.....\infty \right]$

C) $2\,\left[ {{x}^{2}}+\frac{{{x}^{4}}}{4}+\frac{{{x}^{6}}}{6}+.....\infty \right]$

D) None of these

• A) ${{\log }_{e}}\left( 1+\frac{1}{x} \right)$

B) ${{\log }_{e}}\left( 1-\frac{1}{x} \right)$

C) ${{\log }_{e}}\left( \frac{x}{x+1} \right)$

D) None of these

• A) $2\,\left[ x+\frac{{{x}^{3}}}{3}+\frac{{{x}^{5}}}{5}+......\infty \right]$

B) $\,\left[ x+\frac{{{x}^{3}}}{3}+\frac{{{x}^{5}}}{5}+......\infty \right]$

C) $2\,\left[ \frac{1}{x}+\frac{1}{3{{x}^{3}}}+\frac{1}{5{{x}^{5}}}+...\infty \right]$

D) $\,\left[ \frac{1}{x}+\frac{1}{3{{x}^{3}}}+\frac{1}{5{{x}^{5}}}+...\infty \right]$

• A) ${{\log }_{e}}(a-b)$

B) ${{\log }_{e}}\left( \frac{a}{b} \right)$

C) ${{\log }_{e}}\left( \frac{b}{a} \right)$

D) ${{e}^{\left( \frac{a-b}{a} \right)}}$

• A) ${{\log }_{b}}a$

B) ${{\log }_{a}}b$

C) ${{\log }_{e}}a-{{\log }_{e}}b$

D) ${{\log }_{e}}a+{{\log }_{e}}b$

• A) ${{\log }_{e}}\frac{4}{5}$

B) ${{\log }_{e}}\frac{\sqrt{5}}{2}$

C) $2{{\log }_{e}}\frac{\sqrt{5}}{2}$

D) None of these

• A) $\frac{{{x}^{2}}}{2}+\frac{{{x}^{4}}}{4}+\frac{{{x}^{6}}}{6}+....\infty$

B) $\frac{{{x}^{2}}}{1.2}+\frac{{{x}^{4}}}{3.4}+\frac{{{x}^{6}}}{5.6}+....\infty$

C) $2\,\,\left[ \frac{{{x}^{2}}}{1.2}+\frac{{{x}^{4}}}{3.4}+\frac{{{x}^{6}}}{5.6}+..\infty \right]$

D) None of these

• A) 1/2

B) $-1$

C) 1

D) None of these

• A) $\log \,(2/e)$

B) $\log \,(e/2)$

C) 2/e

D) e/2

• A) ${{\log }_{e}}a$

B) ${{\log }_{e}}b$

C) $a$

D) ${{e}^{a}}$

• A) ${{\log }_{e}}\frac{4}{e}$

B) ${{\log }_{e}}\frac{e}{4}$

C) ${{\log }_{e}}4$

D) ${{\log }_{e}}2$

• A) ${{\log }_{e}}(2\sqrt{3})$

B) $2\,\,{{\log }_{e}}2$

C) ${{\log }_{e}}2$

D) ${{\log }_{e}}\left( \frac{2}{\sqrt{3}} \right)$

• A) $2\,{{\log }_{e}}2-1$

B) ${{\log }_{e}}2-1$

C) ${{\log }_{e}}2$

D) None of these

• A) ${{\log }_{e}}3$

B) ${{\log }_{e}}2$

C) $2\,{{\log }_{e}}2$

D) None of these

• A) $\frac{1}{x}-\frac{1}{2{{x}^{2}}}+\frac{1}{3{{x}^{3}}}-.....\infty$

B) $\frac{1}{x}+\frac{1}{2{{x}^{2}}}+\frac{1}{3{{x}^{3}}}+.....\infty$

C) $2\,\left( \frac{1}{x}+\frac{1}{3{{x}^{3}}}+\frac{1}{5{{x}^{5}}}+...\infty \right)$

D) $2\,\left( \frac{1}{x}-\frac{1}{3{{x}^{3}}}+\frac{1}{5{{x}^{5}}}-...\infty \right)$

• A) $2{{\log }_{e}}\frac{4}{5}$

B) ${{\log }_{e}}\frac{5}{4}$

C) 1

D) 0

• A) ${{\log }_{e}}\left( \frac{{{n}^{2}}}{{{n}^{2}}+1} \right)$

B) ${{\log }_{e}}\left( \frac{{{n}^{2}}+1}{{{n}^{2}}} \right)$

C) ${{\log }_{e}}\left( \frac{{{n}^{2}}}{{{n}^{2}}-1} \right)$

D) None of these

• A) ${{\log }_{e}}\left( \frac{m}{n} \right)$

B) ${{\log }_{e}}\left( \frac{n}{m} \right)$

C) ${{\log }_{e}}\left( \frac{m-n}{m+n} \right)$

D) $\frac{1}{2}{{\log }_{e}}\left( \frac{m}{n} \right)$

• A) ${{\log }_{e}}\sqrt{\frac{3}{2}}$

B) ${{\log }_{e}}\sqrt{3}$

C) ${{\log }_{e}}\sqrt{\frac{1}{2}}$

D) ${{\log }_{e}}3$

• A) ${{x}^{2}}y=2x-y$

B) ${{x}^{2}}y=2x+y$

C) $x=2{{y}^{2}}-1$

D) ${{x}^{2}}y=2x+{{y}^{2}}$

• A) All real x

B) All negative real $x\ne 1$

C) All positive real $x\ne 0$

D) $a\ge e$

• A) ${{\log }_{e}}1$

B) ${{\log }_{e}}n$

C) ${{\log }_{e}}(1+n)$

D) ${{\log }_{e}}(1-n)$

• A) ${{\log }_{e}}\left( \frac{n+1}{n} \right)$

B) ${{\log }_{e}}\left( \frac{n}{n+1} \right)$

C) ${{\log }_{e}}\left( \frac{n-1}{n} \right)$

D) ${{\log }_{e}}\left( \frac{n}{n-1} \right)$

• A) ${{e}^{2}}$

B) ${{\log }_{e}}2$

C) ${{\log }_{e}}3-2$

D) $1-{{\log }_{e}}2$

• A) ${{\log }_{3}}2$

B) ${{\log }_{2}}3$

C) $2{{\log }_{3}}2$ v

D) None of the se

• A) ${{\log }_{e}}\frac{3}{2}$

B) ${{\log }_{10}}\frac{1}{2}$

C) ${{\log }_{e}}n\,!$

D) ${{\log }_{e}}\frac{1}{2}$

• A) $\frac{{{(-1)}^{n-1}}}{n}$

B) $\frac{{{(-1)}^{n-1}}}{n}{{\log }_{a}}e$

C) $\frac{{{(-1)}^{n-1}}}{n}{{\log }_{e}}a$

D) $\frac{{{(-1)}^{n}}}{n}{{\log }_{a}}e$

• A) $\frac{1}{r\,{{\log }_{e}}10}$

B) $-\frac{1}{r{{\log }_{e}}10}$

C) $-\frac{1}{r!{{\log }_{e}}10}$

D) None of these

• A) ${{(-1)}^{n}}\left[ \frac{{{2}^{n}}+1}{n} \right]$

B) $\frac{{{(-1)}^{n+1}}}{n}[{{2}^{n}}+1]$

C) $\frac{{{2}^{n}}+1}{n}$

D) None of these

• A) 1

B) 0

C) $\sqrt[1999]{1999}$

D) - 1

• A) $\log x$
B) $\log (x-1)$