Consider a particle moving along a straight line, whose position as a function of time is given by $s(t)=\alpha t^{2}-\beta t+\gamma$, where $\alpha=1~ms^{-2}$ $\beta=6~ms^{-1}$ and $\gamma=5m.$ The average speed of the particle, in $ms^{-1}$ from $t=0$ to $t=6$ s is:

Symbiotic association between fungi and algae are called

For a salt XY, which is a strong electrolyte, the plot of $\Lambda_{m}$ versus $\sqrt{c}$ has a slope of $-90.0~S~cm^{2}mol^{-3/2}L^{1/2}$ at 298 K. At 0.01 M concentration of XY, the value of $\Lambda_{m}$ is $145.0~S~cm^{2}mol^{-1}$. The limiting molar conductivity of $Y^{-}$ ion $(\lambda_{Y^{-}}^{0}$, in $S~cm^{2}~mol^{-1}$) at 298 K will be (Given : $\lambda_{X^{+}}^{0}=74.0~S~cm^{2}mol^{-1})$

A frictionless circular wire of unit radius is fixed on the horizontal plane. Two-point particles of unit mass start moving simultaneously from point $A(\theta=\frac{\pi}{2})$ with identical uniform angular speeds in opposite directions, and meet again at point $B(\theta=-\frac{\pi}{2})$. During this time, which of the following figures schematically represent the magnitude of the total linear momentum P of the system, as a function of $\theta$? [Image Placeholder]

A thin horizontal disc is rotating about a vertical axis passing through its fixed centre O. Its angular momentum is $L_{A}$ and $L_{B}$ computed about points A and B, respectively, with $OB=2\times OA.$ The value of $\frac{L_{A}}{L_{B}}$ is: