Solve \(\frac {1}{3}\) (x + y - 5) = y - z = 2x - 11 = 9 - (x + 2z).

One hundred and fifty students are admitted to a school. They are distributed over three sections A, B and C. If 6 students are shifted from section A to section C, the sections will have equal number of students. If 4 times of students of section C exceeds the number of students of section A by the number of students in section B, find the number of students in the three sections.

In a three-digit number, when the tens and the hundreds digit are interchanged the new number is 54 more than three times the original number. If 198 is added to the number, the digits are reversed. The tens digit exceeds the hundreds digit by twice as that of the tens digit exceeds the unit digit. Find the original number.

Find the least common multiple of xy(k² + 1) + k(x² + y²) and xy(k² - 1) + k(x² - y²)

Find the GCD of the following by division algorithm 2x⁴ + 13x³ + 27x²+23x + 7, x³ + 3x² + 3x + 1, x² + 2x + 1

Reduce the given Rational expressions to its lowest form
\(\frac { { x }^{ 3a }-8 }{ { x }^{ 2a }+2{ x }^{ a }+4 } \)

Simplify \(\frac { \frac { 1 }{ p } +\frac { 1 }{ q+r } }{ \frac { 1 }{ p } -\frac { 1 }{ q+r } } \times \left( 1+\frac { { q }^{ 2 }+{ r }^{ 2 }-{ p }^{ 2 } }{ 2qr } \right) \)

Arul, Mohan and Ram working together can clean a store in 6 hours. Working alone, Mohan takes twice as long to clean the store as Arul does. Ram needs three times as long as Arul does. How long would it take each if they are working alone?

Find the square root of 289x⁴ - 612x³ + 970x² - 684x + 361

Solve \(\sqrt { y+1 } +\sqrt { 2y-5 } \) = 3