If $f(x) = \sin^6 x + \cos^6 x$ for $x \in R$,then $f(x)$ lies in the interval

Select the correct statement.

$A$ thin circular ring of mass $M$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Four objects,each of mass $m$,are placed gently at the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be:

The reading of a spring balance corresponds to $100 N$ while situated at the north pole and a body is kept on it. The weight record on the same scale if it is shifted to the equator, is $...........\,N$

(take, $g =10 m / s ^2$ and radius of the earth, $R =6.4 \times 10^3 m$ )

Which among the following is a pair of monocarboxylic acids?

If the pair of straight lines given by $A x^2+2 H x y+B y^2=0$ $(H^2>A B)$ forms an equilateral triangle with the line $a x+b y+c=0$,then $(A+3 B)(3 A+B)$ is equal to :