Competishun Header
Competishun
Contact Us
Back

Report Issue

JEE Main 2022
25-07-2022_S2
Question
Let $[t]$ denote the greatest integer less than or equal to $t$. Then the value of the integral $$ \int_{-3}^{101}\left([\sin (\pi x)]+\mathrm{e}^{[\cos (2 \pi x)]}\right) \mathrm{dx} \text { is equal to } $$
Select the correct option:
A
$\frac{52(1-e)}{e}$
B
$\frac{52}{\mathrm{e}}$
C
$\frac{52(2+e)}{e}$
D
$\frac{104}{\mathrm{e}}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Solution Image
Question Tags
JEE Main
Mathematics
Medium
Start Preparing for JEE with Competishun
YouTube
Books
App
Tests
Filters 0
JEE Main
JEE Advance
Easy
Medium
Hard
Showing 18 questions
Q JEE MAIN 20262026
Given below are two statements
Statement I: $\mathrm{H}_2 \mathrm{O}$ molecules move from the chamber 1 to chamber 2 .
Statement II:...
JEE MainChemistryMedium
View Solution→
QJEE MAIN 20222022
Let the area enclosed by the $x$-axis, and the tangent and normal drawn to the curve $...
JEE MainMathematicsMedium
View Solution→
QJEE MAIN 20222022
Let $x=\sin \left(2 \tan ^{-1} \alpha\right)$ and $y=\sin \left(\frac{1}{2} \tan ^{-1} \frac{4}{3}\right)$. If $S=\left\{\alpha \in \mathbb{Z}: y^2=1-x\right\}$, then $...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20222022
If the circles $x^2+y^2+6 x+8 y+16=0$ and $x^2+y^2+2^{(3-\sqrt{3})} x+2^{(4-\sqrt{6})} y=k+6 \sqrt{3}+8 \sqrt{6}, k>0$, touch internally at the point $\mathbf{P}(\alpha, \beta)$,...
JEE MainMathematicsMedium
View Solution→
QJEE MAIN 20222022
Let $a_n=\int_{-1}^n\left(1+\frac{x}{2}+\frac{x^2}{3}+\ldots . .+\frac{x^{n-1}}{n}\right) d x$ for every $n \in N$. Then the sum of all the elements of the...
JEE MainMathematicsMedium
View Solution→
QJEE MAIN 20222022
Let $f$ be a twice differentiable function on $R$. If $f^{\prime}(0)=4$ and $...
JEE MainMathematicsMedium
View Solution→
QJEE MAIN 20222022
Let $y=y(x)$ be the solution of the differential equation $\frac{d y}{d x}=\frac{4 y^3+2 y x^2}{3 x y^2+x^3}, y(1)=1$. If for...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20222022
The sum of the maximum and minimum values of the function $f(x)=|5 x-7|+\left[x^2+2 x\right]$ in the interval $\left[\frac{5}{4}, 2\right]$, where...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20232023
Let the function $f(x)=2 x^3+(2 p-7) x^2+3(2 p-9) x-6$ have a maxima for some value of $x<0$ and a minima...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20222022
Let $...
JEE MainMathematicsMedium
View Solution→
QJEE MAIN 20222022
Let $f(x)$ be a quadratic polynomial with leading coefficient 1 such that $f(0)=p, p \neq 0$, and $f(1)=\frac{1}{3}$. If the...
JEE MainMathematicsHard
View Solution→
QJEE MAIN 20222022
Let $A=\{1,2,3,4,5,6,7\}$. Define $B=\{T \subseteq A$ : either $1 \notin T$ or $2 \in T\}$ and $C=\{T \subseteq A: T$...
JEE MainMathematicsHard
View Solution→
QJEE MAIN 20222022
Consider the following statements : P : Ramu is intelligent. Q : Ramu is rich. R : Ramu is not...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20222022
$2 \sin \left(\frac{\pi}{22}\right) \sin \left(\frac{3 \pi}{22}\right) \sin \left(\frac{5 \pi}{22}\right) \sin \left(\frac{7 \pi}{22}\right) \sin \left(\frac{9 \pi}{22}\right)$ is equal to :
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20222022
If the mean deviation about median for the number 3, 5, 7, 2k, 12, 16, 21, 24 arranged in the...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20222022
The shortest distance between the lines $\frac{x+7}{-6}=\frac{y-6}{7}=z$ and $\frac{7-x}{2}=y-2=z-6$ is
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20222022
A plane $E$ is perpendicular to the two planes $2 x-2 y+z=0$ and $x-y+2 z=4$, and passes through the point...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20222022
Let the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{7}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{\alpha}=\frac{1}{25}$ coincide. Then the length of the latus rectum of...
JEE MainMathematicsMedium
View Solution→