Question : Find the HCF of $\left(4^{315}-1\right)$ and $\left(4^{25}-1\right)$.
Option 1: $1$
Option 2: $\left(4^{25}-1\right)$
Option 3: $1024$
Option 4: $1023$
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Correct Answer: $1023$
Solution : Given numbers: $\left(4^{315}-1\right)$ and $\left(4^{25}-1\right)$ Now, HCF (315, 25) = 5 So, HCF of {(4315– 1) and (425 – 1)} = ( 45 – 1) = 1024 – 1 = 1023 Hence, the correct answer is $1023$.
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Question : If the sum of the diagonals of a rhombus is $L$ and the perimeter is $4P$, find the area of the rhombus.
Option 1: $\frac{1}{4}\left(\mathrm{~L}^2-\mathrm{P}^2\right)$
Option 2: $\frac{1}{2}\left(\mathrm{~L}^2-4 \mathrm{P}^2\right)$
Option 3: $\frac{1}{4}\left(\mathrm{~L}^2+3 \mathrm{P}^2\right)$
Option 4: $\frac{1}{4}\left(\mathrm{~L}^2-4 \mathrm{P}^2\right)$
Question : Find the value of $\sqrt{\left[\left(13^2-8^2\right) \times 5+4\right]}$ :
Option 1: 22
Option 2: 24
Option 3: 26
Option 4: 23
Question : What is the value of $\left[\frac{1}{5}+\left\{\frac{1}{6}\right.\right.$ of $\left.\left.\left(\frac{42}{35} \div \frac{6}{25}\right)–\left(\frac{2}{7} \times \frac{6}{5} \div \frac{18}{42}\right)\right\}+\frac{19}{30}\right]$?
Option 1: $\frac{17}{15}$
Option 2: $\frac{13}{15}$
Option 3: $\frac{14}{15}$
Option 4: $\frac{11}{15}$
Question : The value of $\frac{1}{8} × \left[\frac{1}{5}\right.$ of $\left.\frac{11}{2} ÷\left\{\left(\frac{15}{3}-\frac{18}{6}\right)\right\}\right]$ is:
Option 1: $\frac{11}{160}$
Option 2: $\frac{11}{20}$
Option 3: $\frac{8}{11}$
Option 4: $\frac{11}{8}$
Question : What is the HCF of 225 and 425?
Option 1: 5
Option 2: 17
Option 3: 25
Option 4: 9
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