Quantitative Aptitude - Arithmetic Ability Questions

What is the length of the side of a regular hexagon, if its area is 54√3 sq cm?

The ratio of three numbers is 2 : 3 : 5. If the sum of the three numbers is 275, then what is the largest among the three numbers?

If (1/x) + (1/y) + (1/z) = 0 and x + y + z = 9, then what is the value of x3 + y3 + z3 – 3xyz?

If the expression px3 – 2x2 – qx + 18 is completely divisible by (x2 – 9), then what is the ratio between p and q respectively?

What is the value of 1xp-q+1+1xq-p+1?

What is the value of cosec -7π/6?

If Sec θ = 25/24 , then what is the value of Sin θ?

Consider  the  multiplication  999  ×  abc  =  def132  in  decimal  notation, where  a,  b,  c,  d,  e  and  f  are digits. What are the values of a, b, c, d, e and f respectively?