A homogeneous shaft PQR with fixed supports at both ends is subjected to a torsional moment T at point Q, as shown in the figure. The polar moments of inertia of the portions PQ and QR of the shaft with circular cross-sections are $J_1$ and $J_2$, respectively. The torsional moment reactions at the supports P and R are $T_P$ and $T_R$, respectively.

If $T_P/T_R = 4$ and $J_1/J_2 = 2$, the ratio of the lengths $L_1/L_2$ is:

The plane frame shown in the figure has fixed support at joint A, hinge support at joint F, and roller support at joint I. In the figure, A to I indicate joints of the frame.

If the axial deformations are neglected, the degree of kinematic indeterminacy is _________ (in integer).

The plane truss shown in the figure has 13 joints and 22 members. The truss is made of a homogeneous, prismatic, linearly elastic material. All members have identical axial rigidity. A to M indicate the joints of the truss. The truss has pin supports at joints A and L and roller support at joint K. The truss is subjected to a 10 kN vertically downward force at joint H and a 10 kN horizontal force in the rightward direction at joint B as shown.

The magnitude of the reaction (in kN) at the pin support L is __________ (rounded off to 1 decimal place).

A car is travelling at a speed of 60 km/hr on a section of a National Highway having a downward gradient of 2%. The driver of the car suddenly observes a stopped vehicle on the car path at a distance 130 m ahead, and applies brake. If the brake efficiency is 60%, coefficient of friction is 0.7, driver’s reaction time is 2.5 s, and acceleration due to gravity is $9.81 \text{ m/s}^2$, the distance (in meters) required by the driver to bring the car to a safe stop lies in the range