The structural formula of $2$-methyl-$2$-butene is:

Two identical balls $A$ and $B$ are released from the positions shown in the figure. They collide elastically on the horizontal portion $MN$. The ratio of the heights attained by $A$ and $B$ after the collision will be: (neglect friction)

In the given circuit,the readings of voltmeters $V_1$ and $V_2$ are $300 \, V$ each. The readings of voltmeter $V_3$ and ammeter $A$ are respectively:

In which stage does the condensation of chromosomes reach its maximum level?

$A$ uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. $A$ block of mass $m_2$ is attached to the free end of the rope. $A$ transverse pulse of wavelength $\lambda_1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $\lambda_2$. The ratio $\lambda_2/\lambda_1$ is

Let $f:[-1, 3] \to R$ be defined as $f(x) = \begin{cases} |x| + [x], & -1 \le x < 1 \\ x + |x|, & 1 \le x < 2 \\ x + [x], & 2 \le x \le 3 \end{cases}$ where $[t]$ denotes the greatest integer function. Then $f$ is discontinuous at: