Construct the Karnaugh map for the following 3-input truth table, write its Boolean expression and simplify it to obtain MSP.

A ball of mass 60g is moving due south with a speed of 50 ms^-1 at latitude 30°N. Calculate the magnitude and direction of the coriolis force on the ball.

What should be the angular velocity of the earth such that a person of mass 80 kg standing on the earth at the equator would actually fly off the earth?

Design a binary adder circuit to add 4-bit binary numbers corresponding to the decimal numbers 11 and 7.

Titan, a satellite of Saturn, has a mean orbital radius of 1.22 x 10⁹ m. The orbital period of Titan is 15.95 days. Hyperion, another satellite of Saturn, orbits at a mean radius of 1.48 x 10m. Estimate the orbital period of Hyperion.

At a crossing a truck travelling towards the north collides with a car travelling towards the east. After the collision the car and the truck stick together and move off at an angle of 30° east of north. If the speed of the car before the collision was 20 ms, and the mass of the truck is twice the mass of the car, calculate the speed of the truck before and after the collision. 

Draw the circuit of 2-input NAND gate using diodes, transistor and resistors and explain its working with the help of truth table.

A child of mass 50 kg is standing on the edge of a merry go round of mass 250 kg and radius 3.0 m which is rotating with an angular velocity of 3.0 rad s^-1. The child then starts walking towards the centre of the merry go round. What will be the final angular velocity of the merry go round when the child reaches the centre?

A girl is sitting with her dog at the left end of a boat of length 10.0 m. The mass of the girl, her dog and the boat are 60.0 kg, 30.0 kg and 100.0 kg respectively. The boat is at rest in the middle of the lake. Calculate the centre of mass of the system. If the dog moves to the other end of the boat, the girl staying at the same place, how far and in what direction does the boat move?

Convert FC₁₆ (Hex) into its binary equivalent and then divide it by 1001₂. Express the result in octal equivalent.

A horizontal rod with a mass of 10 kg and length 12 m is hinged to a wall at one end and supported by a cable which makes an angle of 30° with the rod at its other end. Calculate the tension in the cable and the force exerted by the hinge.

h-parameters of a single stage CE amplifier are given as   and   and  Calculate   and Z_out with n=10 k and rs = 100.

A wheel 2.0 m in diameter lies in the vertical plane and rotates about its central axis with a constant angular acceleration of 4.0 rad s^-2. The wheel starts at rest at 1-0 and the radius vector of a point A on the wheel makes an angle of 60° with the horizontal at this instant. Calculate the angular speed of the wheel, the angular position of the point A and the total acceleration at 1-2.0s.

A box of mass 8.0 kg slides at a speed of 10 ms^-1 across a smooth level floor before it encounters a rough patch of length 3.0 m. The frictional force on the box due to this part of the floor is 70 N. What is the speed of the box when it leaves this rough surface? What length of the rough surface would bring the box completely to rest?

Discuss the breakdown mechanisms observed in a zener diode. 

A ball having a mass of 0.5 kg is moving towards the east with a speed of 8.0 ms^-1. After being hit by a bat it changes its direction and starts moving towards the north with a speed of 6.0 ms¹. If the time of impact is 0.1 s, calculate the impulse and average force acting on the ball.

A crate of mass 30.0 kg is pulled by a force of 300 N up an inclined plane which makes an angle of 30° with the horizon. The coefficient of kinetic friction between the plane and the crate is 0.225. If the crates starts from rest, calculate its speed after it has been pulled 15.0 m. Draw the free body diagram.

Explain the working of p-channel JFET using a circuit diagram showing its voltage biasing with appropriate polarities. Draw its drain characteristics with Vos <OV and Vos≥ 0 V.

The intrinsic carrier concentration of a semiconductor is 3x10¹⁷ m^-³. It is doped with a trivalent impurity with dopant atom density of 8x10¹⁸ m^-³. The electron and hole mobilities are 0.5 m² V-¹s^-1 and 0.3 m² V^-1s^-1 respectively. Calculate its conductivity before and after the doping.

Describe the formation of depletion layer in a p-n junction diode. Explain the I-V characteristics of p-n junction in forward and reversed biased conditions.