Question : if $a-b=3$ and $a^3-b^3=117$, then $|a+b|$ is equal to:
Option 1: 3
Option 2: 5
Option 3: 7
Option 4: 9
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Correct Answer: 7
Solution : Given: a – b = 3 a3 – b3 = 117 We know, a3 – b3 = (a – b)3 + 3ab(a – b) ⇒ 117 = 27 + 3ab(3) ⇒ 9ab = 117 – 27 ⇒ 9ab = 90 So, ab = 10 Now, (a + b)2 = (a – b)2 + 4ab = 9 + 40 = 49 ∴ |a + b| = 7 Hence, the correct answer is 7.
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Question : If $A:B=7:9$ and $B:C =3:5$, then $A:B:C$ is equal to:
Option 1: $7:9:5$
Option 2: $21:35:45$
Option 3: $7:9:15$
Option 4: $7:3:15$
Question : If $\left(3 y+\frac{3}{y}\right)=8$, then find the value of $\left(y^2+\frac{1}{y^2}\right)$.
Option 1: $5\frac{1}{9}$
Option 2: $4\frac{5}{6}$
Option 3: $7\frac{1}{9}$
Option 4: $9\frac{1}{9}$
Question : If $\sqrt{a}=3b$, then $\frac{a}{b^2}$ is equal to:
Option 1: $\frac{1}{6}$
Option 2: $6$
Option 3: $\frac{1}{9}$
Option 4: $9$
Question : If 45% of a certain number is equal to $\frac{6}{5}$th of another number, what is the ratio between the numbers?
Option 1: 9 : 11
Option 2: 8 : 3
Option 3: 1 : 7
Option 4: 7 : 4
Question : If $\operatorname{cosec} A+\cot A=7$, then $\operatorname{cosec} A$ is equal to:
Option 1: $\frac{11}{7}$
Option 2: $\frac{16}{7}$
Option 3: $\frac{25}{7}$
Option 4: $\frac{19}{7}$
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