Q. 1 \( 4^{3}-0^{2}+\left(\frac{22}{2}\right)^{2}-8+7 \times 6 \) का मान ज्ञात कीजिए। Ans 1. 219 2. 218 3. 229 4. 224 Q. 2 Using empirical formula, calculate the mode for the following data. 17, 20, 21, 18, 25, 28, 24, 22, 16, 24, 25, 24 Ans 1. 25 2. 25.8 3. 32 4. 30.6

Find the characteristics of these numbers by following steps: - step0: Find the mean: \(17,20,21,18,25,28,24,22,16,24,25,24\) - step1: Write the expression of mean: \(\textrm{mean}=\frac{17+20+21+18+25+28+24+22+16+24+25+24}{12}\) - step2: Calculate: \(\textrm{mean}=\frac{264}{12}\) - step3: Calculate: \(\textrm{mean}=22\) Calculate or simplify the expression \( 4^3-0^2+(22/2)^2-8+7*6 \). Calculate the value by following steps: - step0: Calculate: \(4^{3}-0^{2}+\left(\frac{22}{2}\right)^{2}-8+7\times 6\) - step1: Divide the terms: \(4^{3}-0^{2}+11^{2}-8+7\times 6\) - step2: Calculate: \(4^{3}-0+11^{2}-8+7\times 6\) - step3: Multiply the numbers: \(4^{3}-0+11^{2}-8+42\) - step4: Remove 0: \(4^{3}+11^{2}-8+42\) - step5: Evaluate the power: \(64+11^{2}-8+42\) - step6: Evaluate the power: \(64+121-8+42\) - step7: Calculate: \(219\) Find the least common multiple of \( 17,20,21,18,25,28,24,22,16,24,25,24 \) Find the least common multiple by following steps: - step0: Find the least common multiple by factorization: \(17,20,21,18,25,28,24,22,16,24,25,24\) - step1: Rewrite: \(\begin{align}&17\\&20\\&21\\&18\\&25\\&28\\&24\\&22\\&16\\&24\\&25\\&24\end{align}\) - step2: Factorization the number: \(\begin{align}&17=17\\&20=2\times 2\times 5\\&21=3\times 7\\&18=2\times 3\times 3\\&25=5\times 5\\&28=2\times 2\times 7\\&24=2\times 2\times 2\times 3\\&22=2\times 11\\&16=2\times 2\times 2\times 2\\&24=2\times 2\times 2\times 3\\&25=5\times 5\\&24=2\times 2\times 2\times 3\end{align}\) - step3: Find the least common multiple: \(11\times 17\times 2\times 2\times 2\times 2\times 3\times 3\times 5\times 5\times 7\) - step4: Rewrite the expression: \(11\times 17\times 2^{4}\times 3\times 3\times 5\times 5\times 7\) - step5: Multiply the terms: \(294525\times 2^{4}\) - step6: Evaluate the power: \(294525\times 16\) - step7: Multiply: \(4712400\) Let's solve the problems step by step. ### Q. 1 We need to calculate the expression: \[ 4^{3}-0^{2}+\left(\frac{22}{2}\right)^{2}-8+7 \times 6 \] 1. Calculate \(4^3\): \[ 4^3 = 64 \] 2. Calculate \(0^2\): \[ 0^2 = 0 \] 3. Calculate \(\frac{22}{2}\): \[ \frac{22}{2} = 11 \] 4. Calculate \(11^2\): \[ 11^2 = 121 \] 5. Calculate \(7 \times 6\): \[ 7 \times 6 = 42 \] Now, substitute these values back into the expression: \[ 64 - 0 + 121 - 8 + 42 \] Now, perform the calculations step by step: - \(64 + 121 = 185\) - \(185 - 8 = 177\) - \(177 + 42 = 219\) Thus, the answer for Q. 1 is **219**. ### Q. 2 To calculate the mode using the empirical formula for the given data: \[ 17, 20, 21, 18, 25, 28, 24, 22, 16, 24, 25, 24 \] 1. First, we need to find the frequency of each number: - 16: 1 - 17: 1 - 18: 1 - 20: 1 - 21: 1 - 22: 1 - 24: 3 - 25: 2 - 28: 1 From the frequency count, the number **24** appears the most frequently (3 times). Thus, the mode is **24**. However, since the options provided do not include 24, we can calculate the mean to see if it aligns with any of the options. The mean was calculated as: \[ \text{mean} = 22 \] Since the mode is not directly provided in the options, we can conclude that the mode is **24** based on the frequency analysis. ### Final Answers: - **Q. 1:** 219 - **Q. 2:** Mode is 24 (not listed in options).