Master gave a traiangular plate with vertices `A(5,8),B(2,4) C(8,3)` and a stick to a student. He wants to balance the plate on the stick. Can you help the boy to locate theat point which can balance the plate.

Show that the points A(7, 3), B(6, 1), C(8, 2) and D(9, 4) taken in that order are vertices of a parallelogram.

Consider a triangle PQR with coordinates of its vertices as P(-8,5), Q(-15, -19), and R (1, -7). The bisector of the interior angle of P has the equation which can be written in the form ax+2y+c=0. The distance between the orthocenter and the circumcenter of triangle PQR is

In a T20 match, Chennai Super Kings needed just 6 runs to win with 1 ball left to go in the last over. The last ball was bowled and the batsman at the crease hit it high up. The ball traversed along a path in a vertical plane and the equation of the path is y=ax^(2)+bx+c with respect to a xy-coordinate system in the vertical plane and the ball traversed through the points (10,8),(20,16), (30,18) can you conclude that Chennai Super Kings won the match? Justify your answer. (All distances are measured in metres and the meeting point of the plane of the path with the farthest boundary line is (70,0).

A parallel plate capacitor has square plate of side 5 cm and separated by a distance of 1 mm . (a) Calculate the capacitance of this capacitor . (b) If a 10 V battery is connected to the capacitor what is the charge stored in any one of the plates? ( The value of epsilon_(0)= 8.85 xx10^(-12)Nm^(2)C^(-2)).

If the points A(6, 1), B(8, 2), C(9, 4) and D(P, 3) are the vertices of a parallelogram, taken in order. Find the value of P.

If A(3,2,-4),B(5,4,-6)a n dC(9,8,-10) are three collinear points, then find the ratio in which point C divides A Bdot

Vertices of a parallelogram taken in order are A, ( 2,-1,4) , B (1,0,-1) , C ( 1,2,3) and D. Distance of the point P ( 8, 2,-12) from the plane of the parallelogram is

Vertices of a parallelogram taken in order are A, ( 2,-1,4) , B (1,0,-1) , C ( 1,2,3) and D. Distance of the point P ( 8, 2,-12) from the plane of the parallelogram is

In a T20 match, Chennai Super Kings needed just 6 runs to win with 1 ball left to go in the last over. The last ball was bowled and the batsman at the crease hit it high up. The ball traversed along a path in a vertical plane and the equation of the path is y=ax^(2)+bx+c with respect to a xy -coordinate system in the vertical plane and the ball traversed through the points (10,8),(20,16),(40,22), can you conclude that Chennai Super Kings won the match? Justify your answer. (All distances are measured in metres and the meeting point of the plane of the path with the farthest boundary line is (70,0).)

a. A closed loop is held stationary int eh magnetic field between the north and south poles of two permanent magnets held fixed. Can we hope to generate current in the loop by using very strong magnets? b. A closed loop move normal to the constant electric field between the plates of a large capacitor. Is a current induced in the loop (i) when it is wholly inside the region between the capacitor plates (ii) when it is partially outside the plates of the capacitor? The electric field is normal to the plane of the loop. c. A rectangular loop and a circular loop are moving out of a uniform magnetic field (region). (see fig.) to field-free region with a constant velocity v. In which loop do you expect the induced emf to be constant during the passage out of the field region? The field is normal to the loops. d. Predict the polarity of the capacitor in the situation described by the figure below.