If $\left(1+\frac{3}{1}\right)\left(1+\frac{5}{4}\right)\left(1+\frac{7}{9}\right) \ldots\left(1+\frac{2n+1}{n^2}\right)=121$,then $n=$

$A$ metal rod of length $2 \text{ m}$ has cross-sectional areas $2A$ and $A$ as shown in the figure. The ends are maintained at temperatures $100^{\circ}\text{C}$ and $70^{\circ}\text{C}$. The temperature at the middle point $C$ is...... $^{\circ}\text{C}$

The $pH$ of $0.1 \ M$ solution of the following salts increases in the order

$A$ body of mass $M \ kg$ is at the top point of a smooth hemisphere of radius $5 \ m$. It is released to slide down the surface of the hemisphere. It leaves the surface when its velocity is $5 \ m/s$. At this instant,the angle made by the radius vector of the body with the vertical is: (Acceleration due to gravity $g = 10 \ m/s^2$) (in $^{\circ}$)

$A$ man measures the period of a simple pendulum inside a stationary lift and finds it to be $T \ s$. If the lift accelerates upwards with an acceleration $g/4$,then the period of the pendulum will be

The potential energy for a force field $\vec{F}$ is given by $U(x, y) = \cos(x + y)$. The force acting on a particle at the position given by coordinates $(0, \pi/4)$ is: