GATE IN 2021 Question Paper (06-Feb-2021) (Shift 1)

Given below is the diagram of a synchronous sequential circuit with one J-K flip-flop and one T flip-flop with their outputs denoted as A and B respectively, with J${}_A$ = (Aʹ + Bʹ), K${}_A$ = (A + B), and T${}_B$ = A.



Starting from the initial state (AB = 00), the sequence of states (AB) visited by the circuit is

Consider that X and Y are independent continuous valued random variables with uniform PDF given by X ~ U(2, 3) and Y ~ U(1, 4). Then P(Y ≤ X) is equal to __________ (rounded off to two decimal places).

Given A = ≤ft( {*20c 2&5\\ 0&3 } ). The value of the determinant |A⁴ -5A³ + 6A² + 2I| = ______

The figure below shows an electrically conductive bar of square cross-section resting on a plane surface. The bar of mass of 1 kg has a depth of 0.5 m along the y direction. The coefficient of friction between the bar and the surface is 0.1. Assume the acceleration due to gravity to be 10 m/s². The system faces a uniform flux density B = −1 ẑ T. At time t = 0, a current of 10 A is switched onto the bar and is maintained.



When the bar has moved by 1 m, its speed in metre per second is ____ (rounded off to one decimal place).

A toroid made of CRGO has an inner diameter of 10 cm and an outer diameter of 14 cm. The thickness of the toroid is 2 cm. 200 turns of copper wire is wound on the core. μo = 4π × 10⁻⁷ H/m and μr of CRGO is 3000. When a current of 5 mA flows through the winding, the flux density in the core in millitesla is ________