1
JEE Main 2024 (Online) 30th January Morning Shift
Numerical
+4
-1
Change Language

Let $$\mathrm{A}=\{1,2,3, \ldots, 7\}$$ and let $$\mathrm{P}(\mathrm{A})$$ denote the power set of $$\mathrm{A}$$. If the number of functions $$f: \mathrm{A} \rightarrow \mathrm{P}(\mathrm{A})$$ such that $$\mathrm{a} \in f(\mathrm{a}), \forall \mathrm{a} \in \mathrm{A}$$ is $$\mathrm{m}^{\mathrm{n}}, \mathrm{m}$$ and $$\mathrm{n} \in \mathrm{N}$$ and $$\mathrm{m}$$ is least, then $$\mathrm{m}+\mathrm{n}$$ is equal to _________.

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2
JEE Main 2024 (Online) 30th January Morning Shift
Numerical
+4
-1
Change Language

If the function

$$f(x)= \begin{cases}\frac{1}{|x|}, & |x| \geqslant 2 \\ \mathrm{a} x^2+2 \mathrm{~b}, & |x|<2\end{cases}$$

is differentiable on $$\mathbf{R}$$, then $$48(a+b)$$ is equal to __________.

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3
JEE Main 2024 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the 5th excited state of a hydrogen atom is :

A
4
B
1
C
$$\frac{1}{2}$$
D
$$\frac{1}{4}$$
4
JEE Main 2024 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The work function of a substance is $$3.0 \mathrm{~eV}$$. The longest wavelength of light that can cause the emission of photoelectrons from this substance is approximately;

A
215 nm
B
400 nm
C
414 nm
D
200 nm
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