The behaviour of the function $f(x)=\sin \left(2 x+\frac{\pi}{4}\right)$ on $\left(\frac{3 \pi}{8}, \frac{5 \pi}{8}\right)$ is:
Strictly increasing on $\left(\frac{3 \pi}{8}, \frac{5 \pi}{8}\right)$
Strictly increasing on $\left(\frac{\pi}{8}, \frac{3 \pi}{8}\right)$
Strictly decreasing on $\left(\frac{3 \pi}{8}, \frac{5 \pi}{8}\right)$
${\text { Strictly decreasing on }}\left(\frac{\pi}{8}, \frac{5 \pi}{8}\right)$
$$ \text { The particular solution of the equation } \sin \left(\frac{d y}{d x}\right)=a \text {, where } a \in \mathbb{R} \text { and } y=2 \text { when } x=0 \text { is } $$
$$ \sin \left(\frac{y-2}{x}\right)=a $$
$$ \sin \left(\frac{x-2}{y}\right)=a $$
$$ \sin \left(\frac{y+2}{x}\right)=a $$
$$ \sin \left(\frac{x}{y-2}\right)=a $$
$$ \begin{aligned} &\text { Find the co-ordinates of the orthocentre of the triangle formed by the lines }\\ &\begin{aligned} & L_1: y-x=2 \\ & L_2: y+2 x=8 \\ & L_3: 3 y-x=18 \end{aligned} \end{aligned} $$
$$ \left(\frac{10}{7}, \frac{40}{7}\right) $$
(6, 8)
An atom has a single electron. Its ground state energy is -30 eV and its first excited state energy is -8 eV . The atom is bombarded with a stream of photons, each of energy 15 eV .
Assuming the atom being in the ground state, which of the following statements is correct?
A. Atom gets excited to the first excited state and later emit photons of 22 eV
B. Atom absorbs energy continuously until 22 eV is accumulated and then gets excited
C. Atom will not get excited, and the transmitted light will have the same frequency as the incident light
D. Atom will absorb the photon and re-emit a photon of lower energy
A
B
D
C
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