Question : The frequency distribution data is given below. If the average age is 17 years, the value of m is: Age (in years): 8, 20, 26, 29 Number of people: 3, 2, m, 1
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
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Correct Answer: 1
Solution : Using frequency distribution table: Given: The average age = 17 years According to the question, $\frac{8 × 3+20×2+26×m+29×1}{3+2+m+1} = 17$ ⇒ $\frac{24+40+26m+29}{6+m} = 17$ ⇒ $93+26m = 102+17m$ ⇒ $9m=9$ $\therefore m=1$ Hence, the correct answer is 1.
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Question : The ratio of A's age to B's age is $4:3$. A will be 26 years old after 6 years. The age of B now is:
Option 1: $19\frac{1}{2}$ years
Option 2: $12$ years
Option 3: $21$ years
Option 4: $15$ years
Question : There are 3 members in a family. The average age of the father and mother is 40 years. The average age of the father, mother, and daughter is 30 years. Find the age (in years) of the daughter.
Option 1: 6
Option 2: 12
Option 3: 10
Option 4: 8
Question : If $2x-\frac{2}{x}=1(x \neq 0)$, then the the value of $(x^3-\frac{1}{x^3})$ is:
Option 1: $\frac{13}{4}$
Option 2: $\frac{13}{8}$
Option 3: $\frac {17}{4}$
Option 4: $\frac{17}{8}$
Question : Direction: Joan's age is 42, and Kelvin's age is 26. How many years ago was Kelvin's age half of Joan's age?
Option 1: 6 years
Option 2: 4 years
Option 3: 10 years
Option 4: 8 years
Question : If $\sin \theta=\frac{8}{17}$, then find the value of $\tan \theta$.
Option 1: $\frac{15}{17}$
Option 2: $\frac{8}{15}$
Option 3: $\frac{15}{8}$
Option 4: $\frac{17}{15}$
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