Competishun Header
Competishun
Contact Us
Back

Report Issue

JEE Advance 2008
Paper-2
Question
Let $g(x)=\log f(x)$ where $f(x)$ is a twice differentiable positive function on $(0, \infty)$ such that $f(x+1)= \mathrm{x} \mathrm{f}(\mathrm{x})$. Then, for $\mathrm{N}=1,2,3, \ldots$,
Select the correct option:
A
$-4\left\{1+\frac{1}{9}+\frac{1}{25}+\ldots+\frac{1}{(2 \mathrm{~N}-1)^2}\right\}$
B
$4\left\{1+\frac{1}{9}+\frac{1}{25}+\ldots+\frac{1}{(2 \mathrm{~N}-1)^2}\right\}$
C
$-4\left\{1+\frac{1}{9}+\frac{1}{25}+\ldots+\frac{1}{(2 \mathrm{~N}+1)^2}\right\}$
D
$4\left\{1+\frac{1}{9}+\frac{1}{25}+\ldots+\frac{1}{(2 \mathrm{~N}+1)^2}\right\}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Solution Image
Question Tags
JEE Advance
Mathematics
Easy
Start Preparing for JEE with Competishun
YouTube
Books
App
Tests
Filters 0
JEE Main
JEE Advance
Easy
Medium
Hard
Showing 18 questions
QJEE Advance 20082008
Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added...
JEE AdvanceChemistryEasy
View Solution→
QJEE Advance 20082008
Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added...
JEE AdvanceChemistryEasy
View Solution→
QJEE Advance 20082008
Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added...
JEE AdvanceChemistryEasy
View Solution→
QJEE Advance 20082008
Consider the lines $$ \begin{aligned} & L_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2} \\ & L_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3} \end{aligned} $$
The distance of the point...
JEE AdvanceMathematicsEasy
View Solution→
QJEE Advance 20082008
Consider the lines $$ \begin{aligned} & L_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2} \\ & L_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3} \end{aligned} $$
The shortest distance between $\mathrm{L}_1$...
JEE AdvanceMathematicsEasy
View Solution→
QJEE Advance 20082008
Consider the lines $$ \begin{aligned} & L_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2} \\ & L_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3} \end{aligned} $$
The unit vector perpendicular to...
JEE AdvanceMathematicsEasy
View Solution→
QJEE Advance 20082008
Suppose four distinct positive numbers $\mathrm{a}_1, \mathrm{a}_2, \mathrm{a}_3, \mathrm{a}_4$ are in G.P. Let $\mathrm{b}_1=\mathrm{a}_1, \mathrm{~b}_2=\mathrm{b}_1+\mathrm{a}_2, \mathrm{~b}_3=\mathrm{b}_2+ \mathrm{a}_3$ and $\mathrm{b}_4=\mathrm{b}_3+\mathrm{a}_4$. STATEMENT-1:...
JEE AdvanceMathematicsEasy
View Solution→
QJEE Advance 20082008
There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult...
JEE AdvanceChemistryEasy
View Solution→
QJEE ADVANCE 20112011
Match the statements given in Column I with the intervals/union of intervals given in Column II
JEE AdvanceMathematicsEasy
View Solution→
QJEE ADVANCE 20112011
Match the statements given in Column I with the values given in Column II
JEE AdvanceMathematicsEasy
View Solution→
QJEE Advance 20082008
Let a solution $y=y(x)$ of the differential equation $x \sqrt{x^2-1} d y-y \sqrt{y^2-1} d x=0$ satisfy $y(2)=\frac{2}{\sqrt{3}}$. STATEMENT-1 : $...
JEE AdvanceMathematicsEasy
View Solution→
QJEE Advance 20082008
There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult...
JEE AdvanceChemistryEasy
View Solution→
QJEE Advance 20082008
Consider $$ \begin{aligned} & L_1: 2 x+3 y+p-3=0 \\ & L_2: 2 x+3 y+p+3=0 \end{aligned} $$ where $p$ is a...
JEE AdvanceMathematicsEasy
View Solution→
QJEE Advance 20082008
There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult...
JEE AdvanceChemistryEasy
View Solution→
QJEE ADVANCE 20112011
Let M be a $3 \times 3$ matrix satisfying $$ \mathbf{M}\left[\begin{array}{l} 0 \\ 1 \\ 0 \end{array}\right]=\left[\begin{array}{c} -1 \\ 2...
JEE AdvanceMathematicsEasy
View Solution→
QJEE ADVANCE 20112011
Let $y^{\prime}(x)+y(x) g^{\prime}(x)=g(x) g^{\prime}(x), y(0)=0, x \in \mathbb{R}$, where $f^{\prime}(x)$ denotes $\frac{d f(x)}{d x}$ and $g(x)$ is a given nonconstant...
JEE AdvanceMathematicsEasy
View Solution→
QJEE Advance 20082008
Let $a, b, c, p, q$ be real numbers. Suppose $\alpha, \beta$ are the roots of the equation $...
JEE AdvanceMathematicsEasy
View Solution→
QJEE Advance 20082008
STATEMENT-1: $\quad \mathrm{Pb}^{4+}$ compounds are stronger oxidizing agents than $\mathrm{Sn}^{4+}$ compounds. and STATEMENT-2: The higher oxidation states for the group...
JEE AdvanceChemistryEasy
View Solution→