Thorn of $Bougainvillea$ and tendril of $Cucurbita$ are examples of

If $a$ and $b$ are odd integers,then the roots of the equation $2ax^2 + (2a + b)x + b = 0, a \ne 0,$ will be

Let $S$ be the sample space of the random experiment of throwing simultaneously two unbiased dice with six faces (numbered $1$ to $6$) and let $E_k = \{(a, b) \in S : ab = k\}$ for $k \geq 1$. If $p_k = P(E_k)$ for $k \geq 1$,then which of the following is correct?

Which of the following is a correct statement?

The ratio of rates of diffusion of gases $X$ and $Y$ is $1:5$ and that of $Y$ and $Z$ is $1:6$. The ratio of rates of diffusion of $Z$ and $X$ is

$A$ particle of mass $M$ is situated at the centre of a spherical shell of mass $M$ and radius $a$. The gravitational potential at a point situated at a distance of $\frac{a}{2}$ from the centre will be: