Question : In a 1500 m race, Anil beats Bakul by 150 m, and in the same race, Bakul beats Charles by 75 m. By what distance does Anil beat Charles?

Option 1: 217.50 m

Option 2: 200.15 m

Option 3: 293.50 m

Option 4: 313.75 m

Question : What is the simplified value of $\frac{(x+y+z)(x y+y z+z x)–x y z}{(x+y)(y+z)(z+x)}$?

Option 1: $y$

Option 2: $z$

Option 3: $1$

Option 4: $x$

Question : The value of $\frac{(x-y)^3+(y-z)^3+(z-x)^3}{6(x-y)(y-z)(z-x)}$, where $x \neq y \neq z$, is equal to:

Option 1: $\frac{1}{4}$

Option 2: $\frac{1}{2}$

Option 3: $\frac{1}{3}$

Option 4: $\frac{1}{9}$

Question : $\text { If } x^2+y^2+z^2=x y+y z+z x \text { and } x=1 \text {, then find the value of } \frac{10 x^4+5 y^4+7 z^4}{13 x^2 y^2+6 y^2 z^2+3 z^2 x^2}$.

Option 1: 2

Option 2: 0

Option 3: –1

Option 4: 1

Question : Three fractions $x, y$ and $z$ are such that $x > y > z$. When the smallest of them is divided by the greatest, the result is $\frac{9}{16}$, which exceeds $y$ by 0.0625. If $x+y+z=2 \frac{3}{12}$, then what is the value of $x + z$?

Option 1: $\frac{5}{4}$

Option 2: $\frac{3}{4}$

Option 3: $\frac{7}{4}$

Option 4: $\frac{1}{4}$