A man running around a race course notes that the sum of the distances of two flagposts from him a always 10m and the distance between the flag posts is 8m. Then the area of the path he encloses in square meters is (a)15`pi` (b) `20pi` (c) `27pi` (d) `30pi`

A man running a racecourse notes that the sum of the distances from the two flag posts from him is always 10 m and the distance between the flag posts is 8 m. Find the equation of the posts traced by the man.

A kho - kho player in a practice sesssion while running realises that the sum of the distances from the two kho-kho poles from him is always 8m. Find the equation of the path traced by him of the distances between the poles is 6m.

Concentric circles of radii 1,2,3,. . . . ,100 c m are drawn. The interior of the smallest circle is colored red and the angular regions are colored alternately green and red, so that no two adjacent regions are of the same color. Then, the total area of the green regions in sq. cm is equal to 1000pi b. 5050pi c. 4950pi d. 5151pi

The acute angle between two straight lines passing through the point M(-6,-8) and the points in which the line segment 2x+y+10=0 enclosed between the co-ordinate axes is divided in the ratio 1:2:2 in the direction from the point of its intersection with the x-axis to the point of intersection with the y-axis is: (a) pi/3 (b) pi/4 (c) pi/6 (d) pi/(12)

As mosquito is sitting on an L.P. record disc rotating on a trun tabel at 33 1/3 revolutions per minute. The distance of the mosquito from the centre of the turn table is 10 cm. Show that the friction coefficient between the record and the mosquito is greater than pi^2/81 . Take g=10m/s^2

The energy from the sun reaches just outside the earth's atmoshphere at a rate of 1400 W m^(-2) . The distance between the sun and the earth is 1.5 xx 10^(11) m . (a) Calculate the rate at which the sum is losing its mass. (b) How long will the sun last assuming a constant decay at this rate? The present mass of the sun is 2 xx 10^(30) kg

Let P_i and P_i ' be the feet of the perpendiculars drawn from the foci Sa n dS ' on a tangent T_i to an ellipse whose length of semi-major axis is 20. If sum_(i=0)^(10)(S P_i)(S^(prime)P_i ')=2560 , then the value of eccentricity is (a) 1/5 (b) 2/5 (c) 3/5 (d) 4/5

A tangent drawn to hyperbola x^2/a^2-y^2/b^2 = 1 at P(pi/6) froms a triangle of area 3a^2 square units, with the coordinate axes, then the square of its eccentricity is (A) 15 (B) 24 (C) 17 (D) 14

A tangent drawn to hyperbola x^2/a^2-y^2/b^2 = 1 at P(pi/6) froms a triangle of area 3a^2 square units, with the coordinate axes, then the square of its eccentricity is (A) 15 (B) 24 (C) 17 (D) 14

a. The top of the atmosphere is at about 400 kV with respectto the surface of the earth, corresponding to an electric field that decreases with altitude. Near the surface of the earth, the field is about 100 Vm^(-1). Why then do we not get a electric shock as we step out of our house into the openy (Assume the house to be a steel cage so there is no field inside!) b. A man fixes outside his house one evening a two metre high insulating slab carrying on its top a large aluminium sheet of area 1m^(2) . Will he get an electric shock if he touches the metal sheet next morning? c. The discharging current in the atmosphere due to the small conductivity of air is known to be 1800A on an average over the globe. Why then does the atmosphere not discharge itself completely in due course and become electrically neutral? In other words, what keeps the atmosphere charged? d. What are the forms of energy into which the electrical energy of the atmosphere is dissipated during a lightning? (Hint: The earth has an electric field of about 100 Vm^(-1) at its surface in the downward direction, corresponding to a surface charge density =-10^(-9) Cm^(-2) ?.