The Levi type-A train illustrated in the figure has gears with module $m = 8 \text{ mm/tooth}$. Gears 2 and 3 have 19 and 24 teeth respectively. Gear 2 is fixed and internal gear 4 rotates at 20 rev/min counter-clockwise. The magnitude of angular velocity of the arm is _________ rev/min. (rounded off to 2 decimal places)
![GATE ME 2024 Theory of Machines - Gears and Gear Trains Question 4 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lx728omu/b990fedc-12de-4cb9-a5c4-42e0d84885aa/01c4c560-261b-11ef-a279-4f9760cfcb83/file-6y3zli1lx728omv.png?format=png)
At the instant when OP is vertical and AP is horizontal, the link OD is rotating counter clockwise at a constant rate ω = 7 rad/s. Pin P on link OD slides in the slot BC of link ABC which is hinged at A, and causes a clockwise rotation of the link ABC. The magnitude of angular velocity of link ABC for this instant is _________ rad/s (rounded off to 2 decimal places).
![GATE ME 2024 Theory of Machines - Analysis of Plane Mechanisms Question 5 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lx72lrug/4d5c05c3-a576-4382-a54a-26b9241980de/6dc4ab80-261c-11ef-a279-4f9760cfcb83/file-6y3zli1lx72lruh.png?format=png)
A vibratory system consists of mass $m$, a vertical spring of stiffness $2k$ and a horizontal spring of stiffness $k$. The end $A$ of the horizontal spring is given a horizontal motion $x_A = a \sin \omega t$. The other end of the spring is connected to an inextensible rope that passes over two massless pulleys as shown.
Assume $m = 10 kg$, $k = 1.5$ kN/m, and neglect friction.
The magnitude of critical driving frequency for which the oscillations of mass $m$ tend to become excessively large is _____ rad/s (answer in integer).
![GATE ME 2024 Theory of Machines - Vibrations Question 6 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lx72qtvm/344f0fe8-4fa7-4f37-b0aa-a0dd0cc0372a/fa624a20-261c-11ef-a279-4f9760cfcb83/file-6y3zli1lx72qtvn.png?format=png)
A furnace can supply heat steadily at 1200 K at a rate of 24000 kJ/min. The maximum amount of power (in kW) that can be produced by using the heat supplied by this furnace in an environment at 300 K is