Solve the following system of inequalities graphically:

x + 2y ≤ 10
x + y ≥ 1
x - y ≤ 0
x ≥ 0
y ≥ 0

Verify if the numbers given alongside the cubic polynomial below are its zeroes. Also, verify the relationship between the zeroes and the coefficients.

f(x) = 2x^3 + x^2 - 5x + 2; 1/2, 1, -2

A four digit number plate of a car is said to be lucky if the sum of the first two digits is equal to the sum of the last two digit. Then find the total number of lucky plates. (Assume 0000, 0011, 0111 … all are four digit numbers)

A metallic right circular cone 20 cm high and whose vertical angle is 60° is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum obtained is drawn into a wire of diameter 1/16 cm, find the length of the wire.

In a geometric progression, if the ratio of the sum of 5 terms to the sum of their reciprocals is 49 and the sum of the first and the third terms is 35. Then the first term of this geometric progression is:A.21B.7C.42D.28