Vexillary aestivation is a characteristic feature of the family .........

The roots of the equation $x^3-14x^2+56x-64=0$ are in

$A$ spring balance is attached to the ceiling of a lift. $A$ man hangs his bag on the spring and the spring balance reads $49 ~N$,when the lift is stationary. If the lift moves downward with an acceleration of $5 ~m/s^2$,the reading of the spring balance will be (in $N$)

Dividing the interval $[0,6]$ into $6$ equal parts and by using the trapezoidal rule, the value of $\int_0^6 x^3 dx$ is approximately:

Light waves producing interference have their amplitudes in the ratio $3: 2$. The intensity ratio of maximum and minimum of interference fringes is

$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ horizontal force $F$ is applied at one end of the rod perpendicular to its length. The acceleration of the centre of mass of the rod is: