The value of $a$ such that $f(x) = \sqrt{3} \sin x - \cos x - 2ax + b$ decreases for all real values of $x$ is given by:

The horizontal and vertical displacements of a projectile at time $t$ are $x=36 t$ and $y=48 t-4.9 t^2$,respectively. Initial velocity of the projectile in $m/s$ is

The coefficient of static friction,$\mu_s$ between block $A$ of mass $2\,kg$ and the table as shown in the figure is $0.2$. What would be the maximum mass value of block $B$ so that the two blocks do not move (in $,kg$)? The string and the pulley are assumed to be smooth and massless. $(g = 10\,m/s^2)$

Compound $X$ is the anhydride of sulphuric acid. The number of $\sigma$-bonds and the number of $\pi$-bonds present in $X$ are,respectively:

The wavelength of the light used in Young's double slit experiment is $\lambda$. The intensity at a point on the screen is $I$,where the path difference is $\lambda/6$. If $I_0$ denotes the maximum intensity,then the ratio of $I$ and $I_0$ is

An ideal transformer has $500$ and $5000$ turns in primary and secondary windings respectively. If the primary voltage is connected to a $6\,V$ battery, then the secondary voltage is.......$V$.