$A$ father with $8$ children takes them $3$ at a time to the Zoological gardens,as often as he can without taking the same $3$ children together more than once. The number of times he will go to the garden is

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=x-[x]$ and $g(x)=[x]$ for $x \in R$,where $[x]$ is the greatest integer not exceeding $x$,then for every $x \in R, f(g(x))$ is equal to

Osteomalacia is caused by the deficiency of . . . . . . .

If $x$ and $y$ are acute angles such that $\cos x + \cos y = \frac{3}{2}$ and $\sin x + \sin y = \frac{3}{4}$,then $\sin(x+y)$ is equal to

The chemical formula of feldspar is

$A$ bimetallic strip consists of metals $X$ and $Y$. It is mounted rigidly at the base as shown in the figure. The metal $X$ has a higher coefficient of linear expansion compared to that of metal $Y$. When the bimetallic strip is placed in a cold bath, what happens?