$A$ ball is thrown on a lawn in such a way that it initially slides with a speed $v_0$ without rolling. It gradually picks up rotational motion. Find the speed of the ball at which there will be rolling without slipping.

If $C, R, L$ and $I$ denote capacity,resistance,inductance and electric current respectively,the quantities having the same dimensions of time are :
$(1)$ $C R$
$(2)$ $\frac{L}{R}$
$(3)$ $\sqrt{L C}$
$(4)$ $L I^2$

Read the following five statements $(1-5)$ carefully and answer the question that follows.
$(1)$ In $Equisetum$,the female gametophyte is retained on the parent sporophyte.
$(2)$ In $Ginkgo$,the male gametophyte is not independent.
$(3)$ The sporophyte of $Polytrichum$ is more developed than that of $Riccia$.
$(4)$ Sexual reproduction in $Volvox$ is isogamous.
$(5)$ Spores of slime molds lack a cell wall.
How many of the above statements are correct?

In the circuit shown,the current in the $1\,\Omega$ resistor is

The area (in sq units) of the region bounded by $x=-1, x=2, y=x^2+1$ and $y=2x-2$ is

An ink mark is made on a piece of paper on which a glass slab of thickness $t$ is placed. The ink mark appears to be raised up through a distance $x$ when viewed at nearly normal incidence. If the refractive index of the material of the glass slab is $\mu$,then the thickness of the glass slab is given by: