$A$ hollow insulated conducting sphere is given a positive charge of $10\,\mu C$. What will be the electric field at the centre of the sphere if its radius is $2\,m$?

If a point $P$ moves such that its distances from the point $A(1,1)$ and the line $x+y+2=0$ are equal,then the locus of $P$ is

$\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \log \left(\frac{2-\sin \theta}{2+\sin \theta}\right) d \theta$ is equal to

If $ab \neq 0$ and the sum of the coefficients of $x^7$ and $x^4$ in the expansion of $\left(\frac{x^2}{a}-\frac{b}{x}\right)^{11}$ is $0$,then

Two long parallel wires are at a distance $2d$ apart. They carry steady equal currents flowing out of the plane of the paper,as shown. The variation of the magnetic field $B$ along the line $XX'$ is given by

Which of the following $statement(s)$ is/are not correct?
$(i)$ Reproduction is the production of progeny possessing features dissimilar to their parents.
$(ii)$ The fungi,the filamentous algae,the protonema of mosses,all multiply by budding.
$(iii)$ Many organisms like mules,sterile worker bees do not reproduce.
$(iv)$ Reproduction is not an all-inclusive defining characteristic of living organisms.