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Three particles A, B and C situated at vertices of an equilateral triangle, all moving with same constant speed such that A always move towards B, B always towards C and C always towards A . Initial seperation between each of the particle is a. O is the centroid of the triangle. Distance covered by particle A when it completes one revolution around O is

A circular coil of radius R and N turns has neglible resistance. As shown in the schematic figure. Its two wnds are connected to wires and it is hanging by those wires with its plane being vertical the wires are connected to a capacitor with charge Q through a switch. The coil is a horizontal uniform magnetic field B_(o) parallel to the plane of the coil. When the switch is closed, the capacitor gets discharged through the coil in a very short time. By the time capacitor is discharged fully, magnitude of the angular momentum gained by the coil will be (assume that the discharge time is so short that the coil has hardly rotated suring this time)

Choose the correct statement regarding a system of particles. Internal forces can change the kinetic energy of the system without changing system's momentum O Impulse can be defined as a very large force that acts for a very short time and causes finite change in momentum. Internal forces can change the potential energy of the system without changing system's momentum Internal forces can change the mechanical energy of the system without changing system's momentum.

A statue 1.6m tall stands on the top of pedestal.From a point on the ground,the angle of elevation of the top of the statue is 60o and from the same point the angle of elevation of the top of the pedestal is 45o . Find the height of the pedestal.

A person standin on the top of a cliff 171 ft high has to throuw a packet to his friend standing on the ground 228 ft horizontally away. If he throws the packet directly aiming at the friend wilth a speed o 15.0 ft/s, how short will the packet fall?

The first round of the competition was hosted by The Ministry of Magic. The Ministry recently got hold of some possessions of a death eater. However, they had to find the decrypting charm to find information about the whereabouts of the other death eaters from a talking hat. The Hat gave out 3 hints to deduce the charm. If one could not guess the right charm in 3 attempts, the hat will destroy itself. The first hint given by the hat was, “BFplmNVNbACLAMlrBgmDSllV iSTjfJsehRTgsRtM" Harry is clueless and hence takes Hermonie’s help. Hermione figures out some tricks and gives Harry a charm which read as, “ NEw loGYGnPULPOliNs oF AllY HaD be Back I D saId O “. However, it turned out to be wrong. The hat then gave out the second hint, “ A failed attempt means you've either forgotten the password-protected, or you're trying to hack it. Luckily, I've decid- ed to play fair. Remember that it would be wise to pay close attention to the capitals. Capitals! Of course! Hermione instantaneously thinks of something, and gives Harry a new charm “NG TO THE CHINKS OF PURPRI”. However, this also turned out to be wrong. This time instead of a hint, a warning message is read aloud. “WARNING: You have one attempt remaining before the data corrupts. Remember, this data is a matter of life and death! Use your last guess wisely…” it says. Viktor and Fleur give up, however, Harry has one more chance to find the information. The Ministry of Magic also got hold of this document along with the hat. Do you think this document is useful? Can you help Harry find the charm? What will be the sum of the alphabets of the words if values to the alphabets are A=1, B=2, C=3, … ?