Competishun Header
Competishun
Contact Us
Back

Report Issue

JEE Advanced 2023
Paper-1
Question
Let $a$ and $b$ be two nonzero real numbers. If the coefficient of $x^5$ in the expansion of $\left(a x^2+\frac{70}{27 b x}\right)^4$ is equal to the coefficient of $x^{-5}$ in the expansion of $\left(\mathrm{ax}-\frac{1}{\mathrm{bx}^2}\right)^7$, then the value of $2 b$ is
Write Your Answer
✓ 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
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 $$ \mathbf{M}\left[\begin{array}{l} 0 \\ 1 \\ 0 \end{array}\right]=\left[\begin{array}{c} -1 \\ 2...
JEE AdvanceMathematicsEasy
View Solution→
QJEE ADVANCE 20112011
Let $y^{\prime}(x)+y(x) g^{\prime}(x)=g(x) g^{\prime}(x), y(0)=0, x \in \mathbb{R}$, where $f^{\prime}(x)$ denotes $\frac{d f(x)}{d x}$ and $g(x)$ is a given nonconstant...
JEE AdvanceMathematicsEasy
View Solution→
QJEE Advance 20082008
Let $a, b, c, p, q$ be real numbers. Suppose $\alpha, \beta$ are the roots of the equation $...
JEE AdvanceMathematicsEasy
View Solution→
QJEE Advance 20082008
STATEMENT-1: $\quad \mathrm{Pb}^{4+}$ compounds are stronger oxidizing agents than $\mathrm{Sn}^{4+}$ compounds. and STATEMENT-2: The higher oxidation states for the group...
JEE AdvanceChemistryEasy
View Solution→
QJEE Advance 20082008
STATEMENT-1: Bromobenzene upon reaction with $\mathrm{Br}_2 / \mathrm{Fe}$ gives 1,4 - dibromobenzene as the major product. and STATEMENT-2: In bromobenzene,...
JEE AdvanceChemistryEasy
View Solution→
QJEE ADVANCE 20112011
The number of distinct real roots of $x^4-4 x^3+12 x^2+x-1=0$ is
JEE AdvanceMathematicsEasy
View Solution→
QJEE ADVANCE 20112011
Let $\omega=\mathrm{e}^{\mathrm{i} \mathrm{x} / 3}$, and $\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{x}, \mathrm{y}, \mathrm{z}$ be non-zero complex numbers such that $$ \begin{aligned}...
JEE AdvanceMathematicsEasy
View Solution→
QJEE Advance 20082008
STATEMENT-1: The plot of atomic number ( y -axis) versus number of neutrons ( x -axis) for stable nuclei shows...
JEE AdvanceChemistryEasy
View Solution→
QJEE ADVANCE 20112011
The straight line $2 x-3 y=1$ divides the circular region $x^2+y^2 \leq 6$ into two parts. If $$ S=\left\{\left(2, \frac{3}{4}\right),\left(\frac{5}{2},...
JEE AdvanceMathematicsEasy
View Solution→
QJEE ADVANCE 20112011
Let $\mathrm{a}=-\hat{\mathrm{i}}-\hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=-\hat{\mathrm{i}}+\mathrm{j}$ and $\dot{\mathrm{c}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$ be three given vectors. If $\dot{\mathrm{r}}$ is a vector such that $...
JEE AdvanceMathematicsEasy
View Solution→
QJEE Advance 20082008
STATEMENT-1: For every chemical reaction at equilibrium, standard Gibbs energy of reaction is zero. and STATEMENT-2: At constant temperature and...
JEE AdvanceChemistryEasy
View Solution→
QJEE Advance 20082008
Let the function $\mathrm{g}:(-\infty, \infty) \rightarrow\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ be given by $\mathrm{g}(\mathrm{u})=2 \tan ^{-1}\left(\mathrm{e}^{\mathrm{u}}\right)-\frac{\pi}{2}$. Then, g is
JEE AdvanceMathematicsEasy
View Solution→
QJEE ADVANCE 20112011
Let L be a normal to the parabola $\mathrm{y}^2=4 \mathrm{x}$. If L passes through the point $(9,6)$, then L is...
JEE AdvanceMathematicsEasy
View Solution→
QJEE ADVANCE 20112011
Let E and F be two independent events. The probability that exactly one of them occurs is $\frac{11}{25}$ and the...
JEE AdvanceMathematicsEasy
View Solution→
QJEE ADVANCE 20112011
Let $f:(0,1) \rightarrow \mathbb{R}$ be defined by $f(x)=\frac{b-x}{1-b x}$, where be is a constant such that $0
JEE AdvanceMathematicsEasy
View Solution→
QJEE ADVANCE 20112011
If $f(x)=\left\{\begin{array}{cc}-x-\frac{\pi}{2}, & x \leq-\frac{\pi}{2} \\ -\cos x, & -\frac{\pi}{2}1\end{array}\right.$ then
JEE AdvanceMathematicsEasy
View Solution→