Question : The quotient when $10^{100}$ is divided by $5^{75}$ is:
Option 1: $2^{25}×10^{75}$
Option 2: $10^{25}$
Option 3: $2^{75}$
Option 4: $2^{75}×10^{25}$
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Correct Answer: $2^{75}×10^{25}$
Solution : Given: $10^{100}$ is divided by $5^{75}$. = $\frac{10^{100}}{5^{75}}$ = $\frac{(2×5)^{100}}{5^{75}}$ = $\frac{2^{100}×5^{100}}{5^{75}}$ = $2^{100}×\frac{5^{100}}{5^{75}}$ By using, $\frac{a^{m}}{a^{n}}=a^{(m–n)}$ = $2^{100}×5^{(100-75)}$ = $2^{100}×5^{25}$ = $2^{75}×2^{25}×5^{25}$ = $2^{75}×10^{25}$ Hence, the correct answer is $2^{75}×10^{25}$.
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Question : A number when divided by 78 gives the quotient 280 and the remainder 0. If the same number is divided by 65, what will be the value of the remainder?
Option 1: 1
Option 2: 3
Option 3: 0
Option 4: 2
Question : What is the value of $\frac{\frac{5}{6} \text { of } \frac{1}{3} \times \frac{12}{25}-\frac{1}{3} \text { of } \frac{5}{6} \times \frac{18}{25}}{\frac{25}{12} \text { of } \frac{1}{6} \times \frac{2}{5}+\frac{3}{8} \text { of } \frac{12}{25} \times \frac{5}{6}}$?
Option 1: $-\frac{3}{13}$
Option 2: $-\frac{5}{13}$
Option 3: $-\frac{8}{25}$
Option 4: $-\frac{3}{25}$
Question : Directions: In the following question you have to identify the correct response from the given premises stated according to the following symbols. If × means addition, – means division, / means subtraction, and + means multiplication, then which of the equations is correct?
Option 1: 25 + 10 – 5 / 10 × 3 = 43
Option 2: 25 – 10 × 5 + 10 / 3 = 72
Option 3: 25 × 10 / 5 + 10 – 3 = 12
Option 4: 25 / 10 + 5 × 10 / 3 = 18
Question : What is the remainder when $3^8$ is divided by 7?
Option 1: 5
Option 2: 4
Option 3: 6
Question : The divisor is 10 times the quotient and 5 times the remainder in a division sum. What is the dividend if the remainder is 46?
Option 1: 5972
Option 2: 4286
Option 3: 4874
Option 4: 5336
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