If $x = \sqrt 3 { \text{ + }}\sqrt 2 { \text{,}}$ then the value of ${x^3} - \frac{1}{{{x^3}}}$  is?

• 1]

  $10\sqrt 2$

• 2]

  $14\sqrt 2$

• 3]

  $22\sqrt 2$

• 4]

  $8\sqrt 2$

If $\left( {x + \frac{1}{x}} \right){ \text{ = 2,}}$    then $\left( {x - \frac{1}{x}} \right)$   is equal to = ?

• 1] 0
• 2] 1
• 3] 2
• 4] 5

Simplify : $1 - \left[ {1 - \left\{ {1 - \left( {1 - \overline {1 - 1} } \right)} \right\}} \right]$

• 1] 0
• 2] 1
• 3] 2
• 4] 3
• 5] None of these

David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?

• 1] 19th floor
• 2] 28th floor
• 3] 30th floor
• 4] 37th floor

Simplify : $1 + {1 \over {1 + {2 \over {2 + {3 \over {1 + {4 \over 5}}}}}}}$

• 1]

  $1\frac{{11}}{{17}}$

• 2]

  $1\frac{{5}}{{7}}$

• 3]

  $1\frac{{6}}{{17}}$

• 4]

  $1\frac{{21}}{{17}}$