Let $A = \{ x: x \in R, |x| < 1 \}$ and $B = \{ x: x \in R, |x - 1| \ge 1 \}$. If $A \cup B = R - D$,then the set $D$ is:

The spring balance $A$ reads $2 \ kg$ with a block $m$ suspended from it. $A$ balance $B$ reads $5 \ kg$ when a beaker with liquid is placed on the pan of the balance. The two balances are now arranged such that the hanging mass is inside the liquid in the beaker as shown in the figure. In this situation:

Which of the following is not correct?

Which of the following factors increase the heart rate?
$(a)$ Sympathetic nerve signals
$(b)$ Parasympathetic nerve signals
$(c)$ Adrenal medullary hormones
$(d)$ Vagus nerve
$(e)$ Thyroxine hormone
$(f)$ Acetylcholine

Mass $M$ is divided into two parts $xM$ and $(1-x)M$. For a given separation,the value of $x$ for which the gravitational attraction between the two pieces becomes maximum is

Using the digits $0, 2, 4, 6, 8$ not more than once in any number,the number of $5$-digit numbers that can be formed is: