Find the sum of the product of 1,2,3….20 taken two at a time.

A factory uses three different respurce for the manufacture of two different products, 20 units of the resource A, 12 units of B and 16 unit of C being available. One unit of the first product requires 2,2 and 4 units of the resources and one unit of the second product requires 4,2 and 0 units of the resources taken in order. It is known that the first product gives a profit of ₹20 per unit and the second ₹ 30 prt uniy. Formulate the LPP so as to earn maximum profit.

During flight there are two instants of time when the projectile is at same height from the ground. Show that the sum of the two instants is equal to total time of flight.

Find two positive numbers whose product is 256 and whose sum is least.

Find the sum of the following 1.2 C_(2) + 2.3 C_(3) + ... + (n-1)nCn

Find the sum of the following C_1 + 2^2 C_2 + 3^2 C_3 + ... + n^2C_n

Find the sum of the following C_1 - 2C_2 + 3C_3 - ..... + n(-1)^(n-1) C_n

The sum of two numbers is 24. Find the numbers, so that their product is maximum.