Competishun Header

Report Issue

JEE Advance 2022
Paper-1
Question
Let $l_1, l_2, \ldots, l_{100}$ be consecutive terms of an arithmetic progression with common difference $d_1$, and let $w_1, w_2, \ldots$, $w_{100}$ be consecutive terms of another arithmetic progression with common difference $d_2$, where $d_1 d_2=10$. For each $i=1,2, \ldots, 100$, let $R_i$ be a rectangle with length $l_i$, width $w_i$ and area $A_i$. If $A_{51}-A_{50}=1000$, then the value of $A_{100}-A_{90}$ 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
Video Solution
BY competishun
Video Solution
Watch Solution
Filters 0
JEE Main
JEE Advance
Easy
Medium
Hard
Showing 18 questions
QJEE Main 20242024
The area (in sq. units) of the region described by $\left\{(x, y): y^2 \leq 2 x\right.$, and $...
JEE MainMathematicsEasy
View Solution
QJEE Main 20242024
Let $f(x)=\int_0^x\left(t+\sin \left(1-e^t\right)\right) d t, x \in \mathbb{R}$. Then $\lim _{x \rightarrow 0} \frac{f(x)}{x^3}$ is equal to
JEE MainMathematicsEasy
View Solution
QJEE Main 20242024
The value of $\frac{1 \times 2^2+2 \times 3^2+\cdots+100 \times(101)^2}{1^2 \times 2+2^2 \times 3+\cdots+100^2 \times 101}$ is
JEE MainMathematicsEasy
View Solution
QJEE MAIN 20242024
Let ABC be an isosceles triangle in which A is at $(-1,0), \angle A=\frac{2 \pi}{3}, A B=A C$ and $B$...
JEE MainMathematicsEasy
View Solution
QJEE MAIN 20242024
If $\frac{d x}{d y}=\frac{1+x-y^2}{y}, x(1)=1$, then $5 x(2)$ is equal to :
JEE MainMathematicsEasy
View Solution
QJEE Main 20242024
Let $A=\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right]$ and $B=I+\operatorname{adj}(A)+(\operatorname{adj} A)^2+\cdots+(\operatorname{adj} A)^{10}$. Then, the sum of all the elements of...
JEE MainMathematicsEasy
View Solution
QJEE Main 20242024
Let three real numbers 𝑎, 𝑏, 𝑐 be in arithmetic progression and a +1, b, c +3 be in geometric...
JEE MainMathematicsEasy
View Solution
QJEE MAIN 20242024
The sum of squares of all possible values of $k$, for which area of the region bounded by the parabolas...
JEE MainMathematicsEasy
View Solution
QJEE Main 20242024
Let a relation R on N x N be defined as : $\left(x_1, y_1\right) R\left(x_2, y_2\right)$ if and only if...
JEE MainMathematicsEasy
View Solution
QJEE MAIN 20242024
Three points $\mathrm{O}(0,0), \mathrm{P}\left(\mathrm{a}, \mathrm{a}^2\right), \mathrm{Q}\left(-\mathrm{b}, \mathrm{b}^2\right), \mathrm{a}>0, \mathrm{~b}>0$, are on the parabola $y=x^2$. Let $S_1$ be the area of...
JEE MainMathematicsEasy
View Solution
QJEE MAIN 20242024
The lines $\mathrm{L}_1, \mathrm{~L}_2, \ldots, \mathrm{I}_{20}$ are distinct. For $\mathrm{n}=1,2,3, \ldots, 10$ all the lines $\mathrm{L}_{2 \mathrm{n}-1}$ are parallel to...
JEE MainMathematicsEasy
View Solution
Q JEE MAIN 20242024
Let $\vec{a}=\hat{\imath}+\hat{\jmath}+\hat{k}, \vec{b}=-\hat{\imath}-8 \hat{\jmath}+2 \hat{k}$ and $\overrightarrow{\mathrm{c}}=4 \hat{\imath}+\mathrm{c}_2 \hat{\jmath}+\mathrm{c}_3 \hat{\mathrm{k}}$ be three vectors such that $\vec{b} \times \vec{a}=\vec{c} \times \vec{a}$....
JEE MainMathematicsEasy
View Solution
QJEE Main 20242024
Let C be a circle with radius $\sqrt{10}$ units and centre at the origin. Let the line $x+y=2$ intersects the...
JEE MainMathematicsEasy
View Solution
QJEE Main 20242024
If $\lambda>0$, let $\theta$ be the angle between the vectors $\vec{a}=\hat{\imath}+\lambda \hat{\jmath}-3 \hat{k}$ and $\vec{b}=3 \hat{\imath}-\hat{\jmath}+2 \hat{k}$. If the vectors...
JEE MainMathematicsEasy
View Solution
QJEE Main 20242024
If the function $f(x)=\left\{\begin{array}{ll}\frac{72^x-9^x-8^x+1}{\sqrt{2}-\sqrt{1+\cos x}} & , x \neq 0 \\ \log _e 2 \log _e 3 & , x=0\end{array}\right.$...
JEE MainMathematicsEasy
View Solution
QJEE MAIN 20242024
If $y=\frac{(\sqrt{x}+1)\left(x^2-\sqrt{x}\right)}{x \sqrt{x}+x+\sqrt{x}}+\frac{1}{15}\left(3 \cos ^2 x-5\right) \cos ^3 x$, then $96 y^{\prime}\left(\frac{\pi}{6}\right)$ is equal to :
JEE MainMathematicsEasy
View Solution
QJEE Main 20242024
Vanillin compound obtained from vanilla beans, has total sum of oxygen atoms and  electrons is__
JEE MainChemistryEasy
View Solution
QJEE MAIN 20242024
Let $f:(0, \infty) \rightarrow R$ and $F(x)=\int_0^x t f(t) d t$. If $F\left(x^2\right)=\mathrm{x}^4+\mathrm{x}^5$, then $\sum_{\mathrm{r}=1}^{12} \mathrm{f}\left(\mathrm{r}^2\right)$ is equal to :
JEE MainPhysicsEasy
View Solution
Check this project | Best Developer Portfolio