If the normal to the curve $y(x) = \int_0^x (2t^2 - 15t + 10) dt$ at a point $(a, b)$ is parallel to the line $x + 3y = -5$ for $a > 1$,then the value of $|a + 6b|$ is equal to ...........

Opening of floral buds into flowers is a type of

$A$ thin circular ring of mass $M$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Two objects,each of mass $m$,are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity:

If the lines $4x + 3y - 1 = 0$,$x - y + 5 = 0$,and $kx + 5y - 3 = 0$ are concurrent,then $k$ is equal to:

Let $R_1$ be a relation defined by $R_1 = \{(a, b) | a \geq b, a, b \in \mathbb{R}\}$. Then $R_1$ is

$A$ ladder is leaned against a smooth wall and it is allowed to slip on a frictionless floor. Which figure represents the track of its centre of mass?