Let $m_1, m_2$ be the slopes of two adjacent sides of a square of side $a$ such that $a^{2}+11a+3\left(m_{1}^{2}+m_{2}^{2}\right)=220.$ If one vertex of the square is $\big(10(\cos\alpha-\sin\alpha),\,10(\sin\alpha+\cos\alpha)\big)$, where $\alpha\in(0,\tfrac{\pi}{2})$, and the equation of one diagonal is $(\cos\alpha-\sin\alpha)x+(\sin\alpha+\cos\alpha)y=10$, then $ 72\left(\sin^{4}\alpha+\cos^{4}\alpha\right)+a^{2}-3a+13 $ is equal to:
Previous 10 Questions — JEE Main 2022 (29 July Evening Shift)
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Let $y=y(x)$ be the solution curve of the differential equation
$
\frac{dy}{dx}+\left(\frac{2x^{2}+11x+13}{x^{3}+6x^{2}…
Topic: JEE Main 2022 (29 July Evening Shift)
If the solution curve of the differential equation
$ \dfrac{dy}{dx}=\dfrac{x+y-2}{x-y} $
passes through the points $(…
Topic: JEE Main 2022 (29 July Evening Shift)
For
$
I(x) = \int \frac{\sec^{2}x - 2022}{\sin^{2022}x} \, dx,
$
if
$
I\!\left(\frac{\pi}{4}\right) = 2^{1011},
$
then
Topic: JEE Main 2022 (29 July Evening Shift)
If $[t]$ denotes the greatest integer $\leq t$, then the value of
$
\int_{0}^{1} \left[ 2x - |3x^{2} - 5x + 2| + 1 \ri…
Topic: JEE Main 2022 (29 July Evening Shift)
Which of the following matrices can NOT be obtained from the matrix
$\begin{bmatrix}-1 & 2 \\ 1 & -1\end{bmatrix}$
by…
Topic: JEE Main 2022 (29 July Evening Shift)
Let the function
$
f(x) =
\begin{cases}
\dfrac{\log_e(1+5x) - \log_e(1+\alpha x)}{x}, & x \neq 0 \\
10, & x = 0
\end{…
Topic: JEE Main 2022 (29 July Evening Shift)
If $z \neq 0$ be a complex number such that $\left|z - \frac{1}{z}\right| = 2$, then the maximum value of $|z|$ is :
Topic: JEE Main 2022 (29 July Evening Shift)
Next 10 Questions — JEE Main 2022 (29 July Evening Shift)
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Let $A(\alpha,-2)$, $B(\alpha,6)$ and $C\!\left(\dfrac{\alpha}{4},-2\right)$ be vertices of $\triangle ABC$.
If $\left…
Topic: JEE Main 2022 (29 July Evening Shift)
Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls.
One ball is tra…
Topic: JEE Main 2022 (29 July Evening Shift)
Let $S=\{\,z=x+iy:\ |z-1+i|\ge |z|,\ |z|
Topic: JEE Main 2022 (29 July Evening Shift)
Let $\vec{a},\vec{b},\vec{c}$ be three coplanar concurrent vectors such that the angles between any two of them are the…
Topic: JEE Main 2022 (29 July Evening Shift)
The domain of the function
$
f(x)=\sin^{-1}\!\left(\frac{x^{2}-3x+2}{x^{2}+2x+7}\right)
$
is:
Topic: JEE Main 2022 (29 July Evening Shift)
If the system of equations
$x+y+z=6$
$2x+5y+\alpha z=\beta$
$x+2y+3z=14$
has infinitely many solutions, then $\al…
Topic: JEE Main 2022 (29 July Evening Shift)
