The sum of the distinct real values of $\mu$,for which the vectors $\mu \hat{i}+\hat{j}+\hat{k}$,$\hat{i}+\mu \hat{j}+\hat{k}$,and $\hat{i}+\hat{j}+\mu \hat{k}$ are coplanar is

Which role is played by Lactobacillus in our stomach?

$A$ reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by $62^{\circ} C$,the efficiency of the engine is doubled. The temperatures of the source and sink are

An iron sphere of mass $20 \times 10^{-3} \ kg$ falls through a viscous liquid with terminal velocity $0.5 \ ms^{-1}$. The terminal velocity (in $ms^{-1}$) of another iron sphere of mass $54 \times 10^{-2} \ kg$ is (in $.5$)

The equation of the locus of $z$ such that $\left|\frac{z-i}{z+i}\right|=2$,where $z=x+iy$ is a complex number,is

If an electron in a hydrogen atom jumps from the $3^{\text{rd}}$ orbit to the $2^{\text{nd}}$ orbit,it emits a photon of wavelength $\lambda$. When it jumps from the $4^{\text{th}}$ orbit to the $3^{\text{rd}}$ orbit,the corresponding wavelength of the photon will be