If three vectors $a, b, c$ satisfy $a + b + c = 0$ and $|a| = 3, |b| = 5, |c| = 7$,then the angle between $a$ and $b$ is ............ $^\circ$.

When a body of mass $1.0 ~kg$ is suspended from a certain light spring hanging vertically,its length increases by $5 ~cm$. By suspending a $2.0 ~kg$ block to the spring,if the block is pulled through $10 ~cm$ and released,the maximum velocity in $m/s$ is: (Acceleration due to gravity $= 10 ~m/s^2$)

In the following diagram,the charge and potential difference across $8\, \mu F$ capacitance will be nearly

If $ad \neq 0$ and two of the lines represented by $ax^3+3bx^2y+3cxy^2+dy^3=0$ are perpendicular,then

Observe the following reaction: $2A + B \longrightarrow C$. The rate of formation of $C$ is $2.2 \times 10^{-3} \ mol \ L^{-1} \ min^{-1}$. What is the value of $-\frac{d[A]}{dt}$ (in $mol \ L^{-1} \ min^{-1}$)?

If the transverse and conjugate axes of a hyperbola are equal,then its eccentricity is