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:

In which of the following molecules/ions are all the bonds not equal?

If $f(x) = \int \frac{5x^8 + 7x^6}{(x^2 + 1 + 2x^7)^2} dx, (x \ge 0)$ and $f(0) = 0$,then the value of $f(1)$ is

$A$ body is projected from the earth at an angle of $30^{\circ}$ with the horizontal with some initial velocity. If its range is $20 \ m$,the maximum height reached by it is (in meters):

If $u=\log \left(x^3+y^3+z^3-3 x y z\right)$, then $(x+y+z)(u_x+u_y+u_z)$ is equal to

One end each of a resistance $r$,a capacitor $C$,and a resistance $2r$ are connected together. The other ends are respectively connected to the positive terminals of batteries $P, Q,$ and $R$ having emf's $E, E,$ and $2E$. The negative terminals of the batteries are then connected together. In this circuit,with steady current,the potential drop across the capacitor is: