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If $P_1, P_2, P_3$ are the perimeters of the three circles $x^2+y^2+8x-6y=0$,$4x^2+4y^2-4x-12y-186=0$,and $x^2+y^2-6x+6y-9=0$ respectively,then

Along the $x$-axis,three charges $\frac{q}{2}, -q$ and $\frac{q}{2}$ are placed at $x=0, x=a$ and $x=2a$ respectively. The resultant electric potential at a point $P$ located at a distance $r$ from the charge $-q$ (where $r > a$) is ($\varepsilon_0$ is the permittivity of free space):

Which of the following is an example of a ketohexose?

$15 \text{ mL}$ of aqueous solution of $Fe^{2+}$ in acidic medium completely reacted with $20 \text{ mL}$ of $0.03 \text{ M}$ aqueous $Cr_2O_7^{2-}$. The molarity of the $Fe^{2+}$ solution is $.......... \times 10^{-2} \text{ M}$ (Round off to the Nearest Integer).

If $\tan (\pi \cos \theta)=\cot (\pi \sin \theta)$,then a value of $\cos \left(\theta-\frac{\pi}{4}\right)$ among the following is

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