JEE MAIN 2025 ONLINE 7TH APRIL MORNING SHIFT

A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is $1727^{\circ} \mathrm{C}$ and power radiated by the wire is 94.2 W . Its emissivity is $\frac{x}{8}$ where $x=$ _________.

(Given $\sigma=6.0 \times 10^{-8} \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-4}, \pi=3.14$ and assume that the emissivity of wire material is same at all wavelength.)

Thyroxine, the hormone has given below structure

The percentage of iodine in thyroxine is __________ %. (nearest integer)

(Given molar mass in $\mathrm{g} \mathrm{mol}^{-1} \mathrm{C}: 12, \mathrm{H}: 1, \mathrm{O}: 16, \mathrm{~N}: 14, \mathrm{I}: 127$ )

The number of relations on the set $A=\{1,2,3\}$, containing at most 6 elements including $(1,2)$, which are reflexive and transitive but not symmetric, is __________.

For ac circuit shown in figure, $\mathrm{R}=100 \mathrm{k} \Omega$ and $\mathrm{C}=100 \mathrm{pF}$ and the phase difference between $\mathrm{V}_{\text {in }}$ and $\left(\mathrm{V}_{\mathrm{B}}-\mathrm{V}_{\mathrm{A}}\right)$ is $90^{\circ}$. The input signal frequency is $10^x \mathrm{rad} / \mathrm{sec}$, where ' $x$ ' is __________ .

The number of paramagnetic complexes among $\left[\mathrm{FeF}_6\right]^{3-},\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-},\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-}$, $\left[\mathrm{Co}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-},\left[\mathrm{MnCl}_6\right]^{3-}$, and $\left[\mathrm{CoF}_6\right]^{3-}$, which involved $\mathrm{d}^2 \mathrm{sp}^3$ hybridization is _________.

For $n \geq 2$, let $S_n$ denote the set of all subsets of $\{1,2, \ldots, n\}$ with no two consecutive numbers. For example $\{1,3,5\} \in S_6$, but $\{1,2,4\} \notin S_6$. Then $n\left(S_5\right)$ is equal to ________