1. Problem: Identify the composite number. - Composite numbers have factors other than 1 and itself. - Options: 2 (prime), 7 (prime), 9 (3×3, composite), 1 (neither prime nor composite). - **Answer:** 9 2. Problem: Find value of $\log_{10} \left(\frac{10\pi^2}{\sqrt{y}}\right)$ given $\log_{10} x = 2$ and $\log_{10} y = 3$. - Use properties of logarithms: $\log(a/b) = \log a - \log b$, $\log(10)=1$. - $\log_{10} \left(10\pi^2 \right) = \log_{10} 10 + \log_{10} \pi^2 = 1 + 2 \log_{10} \pi$. - Approximate $\log_{10} \pi \approx 0.4971$, so $2 \times 0.4971 = 0.9942$. - Therefore, $\log_{10} (10\pi^{2}) \approx 1 + 0.9942 = 1.9942$. - $\sqrt{y} = y^{1/2}$ so $\log_{10} \sqrt{y} = \frac{1}{2} \log_{10} y = \frac{1}{2} \times 3 = 1.5$. - So total $= 1.9942 - 1.5 = 0.4942$, none of the options match exactly. - However, re-check question: given $\log_{10} x=2$, but $x$ is unused. - Removed $x$, calculation reevaluated: Actually, options suggest mistake. Let’s compute $\log_{10} \left( \frac{10 \pi^2}{\sqrt{y}} \right) = \log_{10} 10 + \log_{10} \pi^2 - \frac{1}{2} \log_{10} y = 1 + 2\log_{10} \pi - 1.5$. - Using earlier approximations: $2 \times 0.4971 = 0.9942$. - Sum: $1 + 0.9942 - 1.5 = 0.4942$. - None of the options (7.5,6.5,8,9) close to 0.4942, so likely options or data mismatch. Assuming a typo, instead consider $\log_{10} x=2$ and $\log_{10} y=3$, find $\log_{10} (10 \pi^2 \sqrt{y})$: - $\log_{10} 10 = 1$. - $2 \log_{10} \pi = 0.9942$. - $\frac{1}{2} \log_{10} y = 1.5$. - Sum: $1 + 0.9942 + 1.5 = 3.4942$ still no match. Hence, the closest answer considering $\log_{10} (10 \pi^2 / \sqrt{y})$ is approximately 0.49 which is none of the provided. Without more info, we select based on close values. 3. Problem: Find HCF of 36, 48, 60. - Prime factors: 36 = $2^2 \times 3^2$ 48 = $2^4 \times 3$ 60 = $2^2 \times 3 \times 5$ - HCF = minimum powers: $2^2 \times 3 = 4 \times 3 = 12$ - **Answer:** 12 4. Problem: Round 98,632 to nearest thousand. - Thousands digit: 8 - Hundreds digit: 6 (≥5, round up) - Nearest thousand: 99,000 - **Answer:** 99,000 5. Problem: Find reciprocal of 3¾. - Convert mixed fraction to improper: $3 \frac{3}{4} = \frac{15}{4}$ - Reciprocal: $\frac{4}{15} = 0.2666...$ - Options suggest mixed numbers: 4 1/3 (13/3), 3¾, -4/3, 1 1/3 (4/3) - None match $\frac{4}{15}$ exactly. - If question means reciprocal of $3 \frac{3}{4}$ is $\frac{4}{15}$, none of options match so perhaps meant reciprocal of $\frac{3}{4}$ which is $\frac{4}{3}$ or $1 \frac{1}{3}$. - Assuming question typo, answer is **1 1/3** 6. Problem: Asha made profit 18000, spent 25% on food, then 20% of remainder on bills and fuel, find savings. - Food expense: $0.25 \times 18000 = 4500$ - Remainder: $18000 - 4500 = 13500$ - Bills and fuel: $0.20 \times 13500 = 2700$ - Savings: $13500 - 2700 = 10800$ - No option matches 10800, closest is 13200 (A), possibly error in percent provided. Since question states % without numbers, assuming 25% and 20%: **Answer:** sh 10800 not listed Summary: - Composite: 9 - Log value: Calculated ~0.49 no option fits - HCF: 12 - Rounded: 99000 - Reciprocal: 1 1/3 - Savings: 10800 (not in options, assuming close)