1
JEE Main 2025 (Online) 29th January Evening Shift
Numerical
+4
-1
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If $\lim\limits _{t \rightarrow 0}\left(\int\limits_0^1(3 x+5)^t d x\right)^{\frac{1}{t}}=\frac{\alpha}{5 e}\left(\frac{8}{5}\right)^{\frac{2}{3}}$, then $\alpha$ is equal to ________________.
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2
JEE Main 2025 (Online) 29th January Evening Shift
Numerical
+4
-1
Change Language

Let $a_1, a_2, \ldots, a_{2024}$ be an Arithmetic Progression such that $a_1+\left(a_5+a_{10}+a_{15}+\ldots+a_{2020}\right)+a_{2024}=2233$. Then $a_1+a_2+a_3+\ldots+a_{2024}$ is equal to _________.

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3
JEE Main 2025 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
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JEE Main 2025 (Online) 29th January Evening Shift Physics - Center of Mass and Collision Question 15 English

Three equal masses $m$ are kept at vertices $(A, B, C)$ of an equilateral triangle of side a in free space. At $t=0$, they are given an initial velocity $\overrightarrow{V_A}=V_0 \overrightarrow{A C}, \overrightarrow{V_B}=V_0 \overrightarrow{B A}$ and $\overrightarrow{V_C}=V_0 \overrightarrow{C B}$. Here, $\overrightarrow{A C}, \overrightarrow{C B}$ and $\overrightarrow{B A}$ are unit vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the net angular momentum of the system at the point of collision is :

A
$\frac{1}{2}$ a $\mathrm{mV}_0$
B
3 a $\mathrm{mV}_0$
C
$\frac{3}{2}$ a $\mathrm{mV}_0$
D
$\frac{\sqrt{3}}{2}$ a $\mathrm{m}V_0$
4
JEE Main 2025 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

In an experiment with photoelectric effect, the stopping potential,

A

is $\left(\frac{1}{e}\right)$ times the maximum kinetic energy of the emitted photoelectrons

B

increases with increase in the intensity of the incident light

C

decreases with increase in the intensity of the incident light

D

increases with increase in the wavelength of the incident light

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