If the curves $y^2=6x$ and $9x^2+by^2=16$ intersect each other at right angles,then the value of $b$ is

Three rods of equal length $l$ are joined to form an equilateral triangle $PQR.$ $O$ is the midpoint of $PQ.$ The distance $OR$ remains the same for a small change in temperature. The coefficient of linear expansion for $PR$ and $RQ$ is the same,i.e.,$\alpha_2,$ but that for $PQ$ is $\alpha_1.$ Then the relation between $\alpha_1$ and $\alpha_2$ is:

$A$ galvanometer of resistance $50\,\Omega$ is connected to a battery of $3\,V$ along with a resistance of $2950\,\Omega$ in series. $A$ full-scale deflection of $30$ divisions is obtained in the galvanometer. In order to reduce this deflection to $20$ divisions,the resistance in series should be.......$\Omega$.

The centre of mass of a body

$\sum_{k=1}^5 \frac{1^3+2^3+\ldots+k^3}{1+3+5+\ldots+(2k-1)}$ is equal to (in $.5$)

Who among the following is known as the 'Father of Taxonomy'?