Question : There is a number consisting of two digits, the digit in the unit place is twice that in the tens place and if 2 is subtracted from the sum of the digits, the difference is equal to $\frac{1}{6}$th of the number. The number is:
Option 1: 26
Option 2: 25
Option 3: 24
Option 4: 23
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Correct Answer: 24
Solution : Let the tens digit be $x$. Then, the unit digit is $2x$. The number is given as $10x + 2x = 12x$. According to the question, ⇒ $\frac{1}{6}\times 12x = x + 2x -2$ ⇒ $2x=3x-2$ ⇒ $3x-2x = 2$ $\therefore x=2$ The number is $12x=2 \times12 = 24$ Hence, the correct answer is 24.
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Question : If $\tan \theta+\sec \theta=7, \theta$ being acute, then the value of $5 \sin \theta$ is:
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