JEE Main 2026 (Online) 8th April Evening Shift

The stored charge in the capacitor in steady state of the following circuit is $\_\_\_\_$ $\mu \mathrm{C}$.

' $x$ ' is the product which is obtained from benzene by reacting it with carbon monoxide and hydrogen chloride in the presence of cuprous chloride. ' $y$ ' is the major product obtained from the benzene by reacting it with ethanoyl chloride in the presence of anhydrous $\mathrm{AlCl}_3$. Product (major) obtained by heating $x$ and $y$ in the presence of alkali is $z$. Total number of $\pi$ (pi) electrons in $z$ is $\_\_\_\_$ .

The sum of squares of all the real solutions of the equation

$\log _{(x+1)}\left(2 x^2+5 x+3\right)=4-\log _{(2 x+3)}\left(x^2+2 x+1\right)$ is equal to $\_\_\_\_$ .

Some distant star is to be observed by some telescope of diameter of objective lens $a$, at an angular resolution of $3.0 \times 10^{-7}$ radian. If the wavelength of light from the star reaching the telescope is 500 nm , the minimum diameter of the objective lens of the telescope is $\_\_\_\_$ cm. (nearest interger)

Number of paramagnetic complexes among the following is $\_\_\_\_$ .

$$\begin{aligned} & {\left[\mathrm{MnBr}_4\right]^{2-},\left[\mathrm{NiCl}_4\right]^{2-},\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-},\left[\mathrm{Ni}(\mathrm{CO})_4\right],\left[\mathrm{CoF}_6\right]^{3-},\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{4-},\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-},\left[\mathrm{Ti}(\mathrm{CN})_6\right]^{3-},} \\ & {\left[\mathrm{Cu}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+},\left[\mathrm{Co}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-}} \end{aligned}$$

Consider the circle C : $x^2+y^2-6 x-8 y-11=0$. Let a variable chord AB of the circle C subtend a right angle at the origin. If the locus of the foot of the perpendicular drawn from the origin on the chord AB is the circle $x^2+y^2-\alpha x-\beta y-\gamma=0$, then $\alpha+\beta+2 \gamma$ is equal to $\_\_\_\_$ .