If $(1+x)^{15}=a_0+a_1 x+\ldots+a_{15} x^{15}$,then $\sum_{r=1}^{15} r \frac{a_r}{a_{r-1}}$ is equal to

If a line makes angles $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with the $X$-axis and $Y$-axis respectively, then the angle made by the line with the $Z$-axis is

The basic unit of classification for plants and animals is ....

The slope of the tangent to the curve $x=t^{2}+3t-8, y=2t^{2}-2t-5$ at the point $(2,-1)$ is

Two soap bubbles of radii $r_1 = 4 \, cm$ and $r_2 = 5 \, cm$ are touching each other over a common surface $S_1S_2$ (as shown in the figure). The radius of curvature of this common surface will be ....... $cm$.

The locus of the centre of a circle which always passes through the fixed points $(a, 0)$ and $(-a, 0)$ is