The graphs of the linear equations 3x-2y=8 and 4x+3y=5 interest at the point P(α, β). What is the value of (2 α - β)?

If x²+4y²=17 and xy=2, where x>0,y>0, then what is the value of x³+8y³?

Direction: Study the following information carefully and answer the given questions.
Eight persons A, B, C, D, E, F, G, and H are seated in a linear row, some of them are facing North while others are facing South. H sits second to the left of E, who sits at an end of the row. D sits to the immediate right of A, who faces the South. C sits second to the left of D, who faces the same direction as E. H, who is not an immediate neigh bour of A, faces the opposite direction of E. F, who is not a neigh bour of E or H, faces the opposite direction of C. B faces the South. G sits second to the right of B. E and G face the same direction. C and D do not face the same direction. E and G does not sit adjacent to each other.

 Which of the following statements are correct?

if a+b+c=7 and a³+b³+c³-3abc=175, then what is the value of (ab+bc+ca)?

$$ secA(secA+tanA)(1-sinA)\over (cosec^2A-1)sin^2A$$ is equal to:

Direction: Study the following information carefully and answer the given questions.
Eight persons A, B, C, D, E, F, G, and H are seated in a linear row, some of them are facing North while others are facing South. H sits second to the left of E, who sits at an end of the row. D sits to the immediate right of A, who faces the South. C sits second to the left of D, who faces the same direction as E. H, who is not an immediate neigh bour of A, faces the opposite direction of E. F, who is not a neigh bour of E or H, faces the opposite direction of C. B faces the South. G sits second to the right of B. E and G face the same direction. C and D do not face the same direction. E and G does not sit adjacent to each other.

Four of the following five are alike in a certain way and thus form a group. Find the one that does not belong to the group.

Direction: Study the following information carefully and answer the given questions.
Eight persons A, B, C, D, E, F, G, and H are seated in a linear row, some of them are facing North while others are facing South. H sits second to the left of E, who sits at an end of the row. D sits to the immediate right of A, who faces the South. C sits second to the left of D, who faces the same direction as E. H, who is not an immediate neigh bour of A, faces the opposite direction of E. F, who is not a neigh bour of E or H, faces the opposite direction of C. B faces the South. G sits second to the right of B. E and G face the same direction. C and D do not face the same direction. E and G does not sit adjacent to each other.

Who among the following sits third to the right of B?

Direction: Study the following information carefully and answer the given questions.
Eight persons A, B, C, D, E, F, G, and H are seated in a linear row, some of them are facing North while others are facing South. H sits second to the left of E, who sits at an end of the row. D sits to the immediate right of A, who faces the South. C sits second to the left of D, who faces the same direction as E. H, who is not an immediate neigh bour of A, faces the opposite direction of E. F, who is not a neigh bour of E or H, faces the opposite direction of C. B faces the South. G sits second to the right of B. E and G face the same direction. C and D do not face the same direction. E and G does not sit adjacent to each other.

How many people are facing North?