Given that the inverse trigonometric functions assume principal values only. Let $x,y\in[-1,1]$ such that $\cos^{-1}x-\sin^{-1}y=\alpha$, with $-\dfrac{\pi}{2}\le\alpha\le\pi$. Then, the minimum value of $x^{2}+y^{2}+2xy\sin\alpha$ is:
Previous 10 Questions — JEE Main 2024 (4 April Evening Shift)
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The area (in sq. units) of the region described by $\{(x,y):y^{2}\le2x,\;y\ge4x-1\}$ is:
Topic: JEE Main 2024 (4 April Evening Shift)
Let $f(x)=\int_{0}^{x}\left(t+\sin(1-e^{t})\right)dt,\;x\in\mathbb{R}$.
Then, $\displaystyle\lim_{x\to0}\dfrac{f(x)}{…
Topic: JEE Main 2024 (4 April Evening Shift)
Let $f(x)=3\sqrt{x-2}+\sqrt{4-x}$ be a real-valued function.
If $\alpha$ and $\beta$ are respectively the minimum and…
Topic: JEE Main 2024 (4 April Evening Shift)
Let $P$ be the point of intersection of the lines
$\dfrac{x-2}{1}=\dfrac{y-4}{5}=\dfrac{z-2}{1}$ and $\dfrac{x-3}{2}=…
Topic: JEE Main 2024 (4 April Evening Shift)
If the function
$
f(x)=
\begin{cases}
\dfrac{7^{x}-9^{x}-8^{x}+1}{\sqrt{2}-\sqrt{1+\cos^{2}x}}, & x\neq0,\\[6pt]
a\log…
Topic: JEE Main 2024 (4 April Evening Shift)
The value of $\dfrac{1\times2^2+2\times3^2+\ldots+100\times(101)^2}{1\times3+2\times4+3\times5+\ldots+100\times101}$ is:
Topic: JEE Main 2024 (4 April Evening Shift)
If the coefficients of $x^4$, $x^5$, and $x^6$ in the expansion of $(1+x)^n$ are in arithmetic progression,
then the …
Topic: JEE Main 2024 (4 April Evening Shift)
Consider a hyperbola $\text{H}$ having centre at the origin and foci on the x-axis.
Let $C_1$ be the circle touching …
Topic: JEE Main 2024 (4 April Evening Shift)
Next 10 Questions — JEE Main 2024 (4 April Evening Shift)
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For $\lambda>0$, let $\theta$ be the angle between the vectors
$\vec a=\hat i+\lambda\hat j-3\hat k$ and $\vec b=3\ha…
Topic: JEE Main 2024 (4 April Evening Shift)
Let $y=y(x)$ be the solution of the differential equation
$(x^{2}+4)^{2}\,dy+(2x^{3}y+8xy-2)\,dx=0.$
If $y(0)=0$, then …
Topic: JEE Main 2024 (4 April Evening Shift)
The mean of the following probability distribution of a random variable $X$ is $\dfrac{46}{9}$.
Topic: JEE Main 2024 (4 April Evening Shift)
Let $C$ be a circle with radius $\sqrt{10}$ units and centre at the origin.
Let the line $x+y=2$ intersect the circle…
Topic: JEE Main 2024 (4 April Evening Shift)
Let $PQ$ be a chord of the parabola $y^{2}=12x$ and the midpoint of $PQ$ be at $(4,1)$.
Then, which of the following …
Topic: JEE Main 2024 (4 April Evening Shift)
The area (in sq. units) of the region
$S = \{\, z \in \mathbb{C} : |z - 1| \le 2,\ (z + \bar{z}) + i(z - \bar{z}) \le …
Topic: JEE Main 2024 (4 April Evening Shift)
If $\displaystyle \int_{-1}^{1}\frac{\cos(\alpha x)}{1+3x^{2}},dx=\frac{2}{\pi}$, then a value of $\alpha$ is:
Topic: JEE Main 2024 (4 April Evening Shift)
If $a,b,c$ are in AP and $a+1,; b,; c+3$ are in GP. Given $a>10$ and the arithmetic mean of $a,b,c$ is $8$, then the cu…
Topic: JEE Main 2024 (4 April Evening Shift)
Let a relation $R$ on $\mathbb N\times\mathbb N$ be defined by $(x_1,y_1),R,(x_2,y_2)$ iff $x_1\le x_2$ or $y_1\le y_2$…
Topic: JEE Main 2024 (4 April Evening Shift)
Let $\vec a=\hat i+\hat j+\hat k,;\vec b=2\hat i+4\hat j-5\hat k$ and $\vec c=x\hat i+2\hat j+3\hat k,;x\in\mathbb R$.
…
Topic: JEE Main 2024 (4 April Evening Shift)
