Aspire Faculty ID #14355 · Topic: JEE Main 2024 (4 April Evening Shift) · Just now
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 cube of the geometric mean of $a,b,c$ is:

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1
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)
2
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)
3
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)
4
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)
5
The mean of the following probability distribution of a random variable $X$ is $\dfrac{46}{9}$.
Topic: JEE Main 2024 (4 April Evening Shift)
6
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)
7
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)
8
Given that the inverse trigonometric functions assume principal values only. Let $x,y\in[-1,1]$ such that $\cos^{-1}x…
Topic: JEE Main 2024 (4 April Evening Shift)
9
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)
10
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)

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