Question : Simplify the following. $\frac{3 a+b}{2}-\frac{a-3 b}{3}+2b$
Option 1: $\frac{5(a+3b)}{6}$
Option 2: $\frac{7a+3b}{6}$
Option 3: $\frac{7(a+3b)}{6}$
Option 4: $\frac{a+3b}{6}$
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Correct Answer: $\frac{7(a+3b)}{6}$
Solution : Given: $\frac{3a+b}{2}-\frac{a-3b}{3}+2b$ = $\frac{9a+3b-(2a-6b)}{6}+2b$ = $\frac{7a+9b}{6}+2b$ = $\frac{7a+9b + 12b}{6}$ = $\frac{7a+21b }{6}$ = $\frac{7(a+3b) }{6}$ Hence, the correct answer is $\frac{7(a+3b) }{6}$.
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Question : Simplify the following expression. $\frac{7}{10} \div \frac{3}{7}$ of $\left(2 \frac{3}{10}+2 \frac{3}{5}\right)+\frac{1}{5} \div 1 \frac{2}{5}-\frac{2}{7}$
Option 1: $-\frac{4}{21}$
Option 2: $\frac{5}{21}$
Option 3: $\frac{4}{21}$
Option 4: $-\frac{5}{21}$
Question : The arithmetic mean of the following numbers 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7 is:
Option 1: 4
Option 2: 5
Option 3: 14
Option 4: 20
Question : Directions: Select the option that represents the correct order of the given words as they would appear in an English dictionary. 1. Lesage 2. Laudatory 3. Laureate 4. Latitude 5. Legacy 6. Laudanum 7. Launder
Option 1: 4, 6, 7, 3, 2, 1, 5
Option 2: 4, 6, 7, 2, 3, 1, 5
Option 3: 4, 6, 2, 7, 3, 5, 1
Option 4: 4, 6, 2, 3, 7, 1, 5
Question : Directions: Select the option that represents the correct order of the given words as they would appear in an English dictionary. 1. Effluent 2. Edifice 3. Effleurage 4. Edacious 5. Effeminate 6. Eccentric 7. Effulgent
Option 1: 6, 4, 2, 5, 3, 1, 7
Option 2: 6, 4, 2, 3, 5, 1, 7
Option 3: 6, 4, 2, 5, 1, 3, 7
Option 4: 6, 4, 2, 5, 7, 3, 1
Question : Directions: Select the option that represents the correct order of the given words as they would appear in an English dictionary. 1. Fustian 2. Funerary 3. Fusion 4. Funicular 5. Fuscous 6. Fundament 7. Fuselage
Option 1: 6, 2, 5, 7, 3, 4, 1
Option 2: 6, 2, 5, 7, 4, 1, 3
Option 3: 6, 2, 4, 5, 7, 3, 1
Option 4: 6, 2, 5, 4, 7, 3, 1
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