Suppose the gravitational force varies inversely as the $n^{th}$ power of distance. Then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to

If $1, 2, 3$ and $4$ are the roots of the equation $x^4+ax^3+bx^2+cx+d=0$,then $a+2b+c$ is equal to

The value of $\lambda$ such that $\lambda x^2-10 x y+12 y^2+5 x-16 y-3=0$ represents a pair of straight lines is:

Let $P(3, 2, 6)$ be a point in space and $Q$ be a point on the line $\vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \mu(-3\hat{i} + \hat{j} + 5\hat{k})$. Then the value of $\mu$ for which the vector $\vec{PQ}$ is parallel to the plane $x - 4y + 3z = 1$ is:

Four particles $A, B, C$ and $D$ of equal mass $m$ are placed at the four corners of a square. They move with equal uniform speed $v$ towards the intersection of the diagonals. After the collision,particle $A$ comes to rest,particle $B$ traces its path back with the same speed $v$,and particles $C$ and $D$ move with equal speeds $v'$. What is the velocity of particle $C$ after the collision?

Haversian canals are found in