$A$ transverse harmonic wave on a string is described by $y = 3 \sin(36t + 0.018x + \frac{\pi}{4})$,where $x$ and $y$ are in $cm$ and $t$ is in $s$. The least distance between two successive crests in the wave is .... $m$. (in $.5$)

The equation of the common tangent to the circle $x^2 + y^2 = 2$ and the parabola $y^2 = 8x$ is

In the figure $(a)$,half of the meter scale is made of wood while the other half is made of steel. The wooden part is pivoted at $O$. $A$ force $F$ is applied at the end of the steel part. In figure $(b)$,the steel part is pivoted at $O'$ and the same force is applied at the wooden end (in a horizontal plane).

If $3$ is a root of $x^2+kx-24=0$,then it is also a root of which of the following equations?

The major product of the following reaction is

Which of the following is a redox reaction?