Question : If $a:b=5:7$, then $\left(6a^2-2b^2\right):\left(b^2-a^2\right)$ will be:
Option 1: 12 : 5
Option 2: 21 : 5
Option 3: 13 : 6
Option 4: 17 : 8
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Correct Answer: 13 : 6
Solution : $a: b=5: 7$ Assume $a$ as 5 and $b$ as 7. $(6a^2-2b^2):(b^2-a^2)$ $= (6×5^2-2×7^2):(7^2-5^2)$ $= (6×25-2×49):(49-25)$ $= (150-98):(49-25)$ $= 52:24$ $= 13:6$ Hence, the correct answer is 13 : 6.
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Question : If $\left (a+b \right):\left (b+c \right):\left (c+a \right)= 6:7:8$ and $\left (a+b+c \right) = 14,$ then value of $c$ is:
Question : Solve: $\left(1+\frac{5}{6}+\frac{7}{8}+\frac{11}{12}\right) \div\left(\frac{3}{4}-\frac{5}{8}\right)$
Question : If $\left(3 y+\frac{3}{y}\right)=8$, then find the value of $\left(y^2+\frac{1}{y^2}\right)$.
Question : If A : B = 2 : 3, B : C = 6 : 7, C : D = 14 : 3, then find A : B : C : D.
Question : If $\left(z+\frac{1}{z}\right)=4$, then what will be the value of $\frac{1}{2}\left(z^2+\frac{1}{z^2}\right)$?
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