Question : Directions: Study the following graph and answer the question.

In 2005, the exports of company X were double that of company Y in that year. If the imports of company X during the year were Rs. 180 crores, what was the amount (in crores) of imports of company Y during the year?

Option 1: 212

Option 2: 210

Option 3: 315

Option 4: 282

Question : Directions: Study the following graph and answer the question.
If the imports of company X in 2007 were increased by 40%, what would be the ratio of exports to the increased imports?

Option 1: 1.25

Option 2: 1.75

Option 3: 0.25

Option 4: 0.75

Question : Simplify the given expression $\frac{(x^3-y^3)(x+y)}{x^2+x y+y^2}$.

Option 1: $x - y$

Option 2: $x^2-y^2$

Option 3: $x + y$

Option 4: $x^2+y^2$

Question : Directions: In a certain code language,
X + Y means X is the sister of Y,
X # Y means X is the husband of Y,
X & Y means X is the daughter of Y,
X % Y means X is the mother of Y,
X @ Y means X is the brother of Y.
Based on the above, which of the following expressions denotes that D is the wife of F?

Option 1: D % P # K + R % F

Option 2: F @ R + K + P % D

Option 3: P & D % R + K % F

Option 4: D % P + K @ R & F

Question : Simplify the given expression. $\frac{x^3+y^3+z^3-3 x y z}{(x-y)^2+(y-z)^2+(z-x)^2}$

Option 1: $\frac{1}{3}(x+y+z)$

Option 2: $(x+y+z)$

Option 3: $\frac{1}{4}(x+y+z)$

Option 4: $\frac{1}{2}(x+y+z)$

Question : If $\tan (x + y)=1$ and $\cos (x-y)={\frac{\sqrt3}{2}}$, then what is the value of $x$ and $y$?

Option 1: $x = 3^\circ, y = 4.5^\circ$

Option 2: $x = 37.5^\circ, y = 7.5^\circ$

Option 3: $x = 7.5^\circ, y = 37.5^\circ$

Option 4: $x = 4.5^\circ, y = 3^\circ$