Three small villages with nearly equal population are situated at the position (1,2),(5,4) and (3,8), The block development officer wants to set up a community centre at a place which is at the same distance from the three villgaes.
Comment on the behaviour of the block development officer.

Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants to award Rs. X and Rs y each and Rs Z each of the three respective values to 3,2 and 1 students respectively with a total award money of Rs 1600. School B wants to spend Rs 2300 to award its 4,1 and 3 students on respective values (b giving the same award money for the three values as before). If the total amount of award for one prize on each value is Rs 900 , using matrices find the award money for each value. Apart from these three values, suggest one more value which should be considered for award.

Shown in the figure a spring fixed at the bottomm end of all incline of inclination 37^@ . A small block of mass 2 kg starts slipping down the incline form a point 4.8 m aaway from the spring. The block compresses the spring by 20 cm, stops momentarily and then rebounds through a distance of 1 m up the incline. Find the spring constant of the spring Take g = 10 ms^-2

A rectangular glass block of thickness 10 cm and refractive index 1.5 is placed over a small coin.A beaker is filled with water of refractive index 4//3 to a height of 10 cm and is placed over a small block. If the eye is slowly moved away from the normal at a certain position,the coin is found to diappear due to total internal reflection.At what surface does it happen and why? .

Shown in the figure a spring fixed at the bottomm end of all incline of inclination 37^@ . A small block of mass 2 kg starts slipping down the incline form a point 4.8 m aaway from the spring. The block compresses the spring by 20 cm, stops momentarily and then rebounds through a distance of 1 m up the incline. Find the friction coefficient between the palne

Given the sets A = {1, 3, 5), B = {2, 4, 6} and C = {0, 2, 4, 6, 8), which of the following may be considered as universal set (s) for all the three sets A, B and C (i) {0,1, 2, 3, 4, 5, 6} (ii) ϕ (iii) {0,1,2,3,4,5,6,7,8,9,10} (iv) {1,2,3,4,5,6,7,8}