The arc $PQ$ of a circle subtends a right angle at its centre $O$. The midpoint of the arc $PQ$ is $R$. If $\overrightarrow{OP}=\vec{u}$, $\overrightarrow{OR}=\vec{v}$ and $\overrightarrow{OQ}=\alpha\vec{u}+\beta\vec{v}$, then $\alpha,\ \beta^{2}$ are the roots of the equation:
Previous 10 Questions — JEE Main 2023 (10 April Morning Shift)
Nearest first
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The coefficient of $x^{7}$ in $\left(ax-\dfrac{1}{bx^{2}}\right)^{13}$ and the coefficient of $x^{-5}$ in $\left(ax+\df…
Topic: JEE Main 2023 (10 April Morning Shift)
The function is $f(x)=\dfrac{(\tan 1^\circ)x+\log_e(123)}{x,\log_e(1234)-(\tan 1^\circ)},; x>0$.
Then the least value o…
Topic: JEE Main 2023 (10 April Morning Shift)
Let O be the origin and the position vector of the point P be $ - \widehat i - 2\widehat j + 3\widehat k$. If the posit…
Topic: JEE Main 2023 (10 April Morning Shift)
Let the ellipse $E:{x^2} + 9{y^2} = 9$ intersect the positive x and y-axes at the points A and B respectively. Let the …
Topic: JEE Main 2023 (10 April Morning Shift)
The shortest distance between the lines $\dfrac{x+2}{1}=\dfrac{y}{-2}=\dfrac{z-5}{2}$ and $\dfrac{x-4}{1}=\dfrac{y-1}{2…
Topic: JEE Main 2023 (10 April Morning Shift)
The function $I(x)=\int e^{\sin^{2}x},(\cos x\sin 2x-\sin x),dx$ with $I(0)=1$. Then $I!\left(\dfrac{\pi}{3}\right)$ is…
Topic: JEE Main 2023 (10 April Morning Shift)
Next 10 Questions — JEE Main 2023 (10 April Morning Shift)
Ascending by ID
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Let $N$ denote the sum of the numbers obtained when two dice are rolled. If the probability that $2^{N} < N!$ is $\dfra…
Topic: JEE Main 2023 (10 April Morning Shift)
The square tin of side $30\ \text{cm}$ is made into an open-top box by cutting a square of side $x$ from each corner an…
Topic: JEE Main 2023 (10 April Morning Shift)
$96\cos\frac{\pi}{33},\cos\frac{2\pi}{33},\cos\frac{4\pi}{33},\cos\frac{8\pi}{33},\cos\frac{16\pi}{33}$ is equal to:
Topic: JEE Main 2023 (10 April Morning Shift)
The system of linear equations
$2x - y + 3z = 5$
$3x + 2y - z = 7$
$4x + 5y + \alpha z = \beta,$
which of the following…
Topic: JEE Main 2023 (10 April Morning Shift)
A line segment $AB$ of length $\lambda$ moves such that the points $A$ and $B$ remain on the periphery of a circle of r…
Topic: JEE Main 2023 (10 April Morning Shift)
The function $f$ is differentiable and satisfies $x^{2}f(x)-x=4\displaystyle\int_{0}^{x} t f(t),dt$, with $f(1)=\dfrac{…
Topic: JEE Main 2023 (10 April Morning Shift)
The first term $\alpha$ and common ratio $r$ of a geometric progression are positive integers. If the sum of squares of…
Topic: JEE Main 2023 (10 April Morning Shift)
The complex number $z=x+iy$ is such that $\dfrac{2z-3i}{2z+i}$ is purely imaginary. If $x+y^{2}=0$, then $y^{4}+y^{2}-y…
Topic: JEE Main 2023 (10 April Morning Shift)
