The complex number $z=x+iy$ is such that $\dfrac{2z-3i}{2z+i}$ is purely imaginary. If $x+y^{2}=0$, then $y^{4}+y^{2}-y$ is equal to:
Previous 10 Questions — JEE Main 2023 (10 April Morning Shift)
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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 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)
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 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)
$96\cos\frac{\pi}{33},\cos\frac{2\pi}{33},\cos\frac{4\pi}{33},\cos\frac{8\pi}{33},\cos\frac{16\pi}{33}$ is equal to:
Topic: JEE Main 2023 (10 April Morning Shift)
The 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)
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 arc $PQ$ of a circle subtends a right angle at its centre $O$. The midpoint of the arc $PQ$ is $R$. If $\overrighta…
Topic: JEE Main 2023 (10 April Morning Shift)
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)
