The total revenue in Rupees received from the sale of $x$ units of a product is given by $R(x) = 13x^2 + 26x + 15$. Find the marginal revenue when $x = 7$.

$A$ particle is moving in a straight line. At time $t$, the distance of the particle from its starting point is given by $x = t^3 - 6t^2 + t$. Its acceleration will be zero at

Consider a rectangle whose length is increasing at the uniform rate of $2 \, m/sec$,breadth is decreasing at the uniform rate of $3 \, m/sec$ and the area is decreasing at the uniform rate of $5 \, m^2/sec$. If after some time the breadth of the rectangle is $2 \, m$,then the length of the rectangle is ........ $m$.

$A$ particle covers a distance $x$ in time $t$ given by $x = t^3 - 9t^2 + 24t + 6$. When the acceleration of the particle is $6$,its velocity is .... units.

By dropping a stone in a quiet lake,a wave in the form of a circle is generated. The radius of the circular wave increases at the rate of $2.1 \text{ cm/sec}$. Then the rate of increase of the enclosed circular region,when the radius of the circular wave is $10 \text{ cm}$,is (Given $\pi = \frac{22}{7}$)

The distance $s$ in meters travelled by a particle in $t$ seconds is given by $s = \frac{2 t^3}{3} - 18 t + \frac{5}{3}$. The acceleration when the particle comes to rest is (in $m/s^2$)