Let $y$ be the solution of the differential equation with the initial conditions given below. If $y(x=2)=A \ln 2$, then the value of $A$ is _________ (rounded off to 2 decimal places).

$$ x^2 \frac{d^2 y}{d x^2}+3 x \frac{d y}{d x}+y=0 \quad y(x=1)=0 \quad 3 x \frac{d y}{d x}(x=1)=1 $$

A truss structure is loaded as shown in the figure below. Among the options given, which member in the truss is a zero-force member?

Consider two identical tanks with a bottom hole of diameter $d$. One tank is filled with water and the other tank is filled with engine oil. The height of the fluid column $h$ is same in both the cases. The fluid exit velocity in the two tanks are $V_1$ and $V_2$. Neglecting all losses, which one of the following options is correct?

In a laboratory experiment using a scaled down model to measure scour at a bridge pier, the Froude number is important. The ratio of the prototype length to the model length is 100 . If the velocity of the model is $1 \mathrm{~m} \mathrm{~s}^{-1}$, the velocity (in $\mathrm{m} \mathrm{s}^{-1}$ ) of the prototype is