Question : Direction: In a class composed of x girls y boys what part of the class is composed of girls?
Option 1: y(x + y)
Option 2: x/xy
Option 3: x/(x + y)
Option 4: y/xy
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Correct Answer: x/(x + y)
Solution : Given: Number of girls = x Number of boys = y
Total number of students in a class (girls + boys) = x + y.
Therefore, part of the class composed of girls= x/(x + y).
Hence, third option is correct.
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Question : If $x^2-xy+y^2=2$ and $x^4+x^2y^2+y^4=6$, then the value of $(x^2+xy+y^2)$ is:
Option 1: 1
Option 2: 12
Option 3: 3
Option 4: 36
Question : In a class, there are $z$ students. Out of them, $x$ are boys. What part of the class is composed of girls?
Option 1: $\frac{x}{z}$
Option 2: $\frac{z}{x}$
Option 3: $1–\frac{x}{z}$
Option 4: $\frac{x}{z}–1$
Question : If $(x+y)^2=xy+1$ and $x^3-y^3=1$, what is the value of $(x-y)$?
Option 2: 0
Option 3: –1
Option 4: 2
Question : If $x=\sqrt[3]{28}, y=\sqrt[3]{27}$, then the value of $x+y-\frac{1}{x^{2}+xy+y^{2}}$ is:
Option 1: 8
Option 2: 7
Option 3: 6
Option 4: 5
Question : The third proportional of the following numbers $(x-y)^2, (x^2-y^2)^2$ is:
Option 1: $(x+y)^3(x-y)^2$
Option 2: $(x+y)^4(x-y)^2$
Option 3: $(x+y)^2(x-y)^2$
Option 4: $(x+y)^2(x-y)^3$
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