Question : If $3^{10} × 27^{2}= 9^{2}×3^{n}$, then the value of $n$ is:
Option 1: 10
Option 2: 12
Option 3: 15
Option 4: 30
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Correct Answer: 12
Solution : Given: $3^{10} × 27^{2}= 9^{2}×3^{n}$ Simplify the given expression for the same base, $⇒3^{10} × (3^{3})^{2}= 9^{2}×3^{n}$ $⇒(3^{10+6})= (3^{2})^{2}×3^{n}$ $⇒3^{16}= 3^{4}×3^{n}$ $⇒3^{16}= 3^{4+n}$ By comparing this, $⇒16=4+n$ $\therefore n =12$ Hence, the correct answer is 12.
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Question : If $4x^{2}=15^{2}–9^{2}$, then the value of $x$ is:
Option 1: 9
Option 2: 6
Option 3: 3
Option 4: 12
Question : If $14 : 30 :: 7 : x$, then what is the value of $x$?
Option 1: 15
Option 2: 21
Option 3: 9
Question : If 10% of $x$ is 3 times of 15% of $y$, then find $x:y$.
Option 1: $7:2$
Option 2: $9:2$
Option 3: $8:3$
Option 4: $11:4$
Question : X is directly proportional to the square of Y. When X is 12, then Y is 2. Find the value of X when Y is 3.
Option 1: 30
Option 2: 9
Option 3: 27
Option 4: 18
Question : The mode of the following data is __________. 13, 15, 31, 12, 27, 13, 27, 30, 27, 28 and 16
Option 1: 28
Option 2: 27
Option 3: 30
Option 4: 31
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