The fundamental frequency of a sonometer wire is $n$. If the length and diameter of the wire are doubled while keeping the tension constant,what is the new fundamental frequency?

If $x$ is a solution of the equation $\sqrt{2x+1} - \sqrt{2x-1} = 1$ for $x \geq \frac{1}{2}$,then $\sqrt{4x^2-1}$ is equal to:

$A$ film of water is formed between two straight parallel wires of length $10\,cm$ each,separated by $0.5\,cm$. If their separation is increased by $1\,mm$ while still maintaining their parallelism,how much work will have to be done? (Surface tension of water = $7.2 \times 10^{-2}\,N/m$)

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?

Which one of the following is used in the preparation of cellulose nitrate?

The value of $a$ for which the system of equations $a^3x + (a + 1)^3y + (a + 2)^3z = 0$,$ax + (a + 1)y + (a + 2)z = 0$,$x + y + z = 0$ has a non-zero solution is