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Mathematics

Assertion (A) : If in a pie chart representing the number of students of opting for different streams in college admission out of a total admissions of 3300, the central angle for the sector representing mathematics is 48°, then the number of students who opt for mathematics is 440.

Reason (R) : Central angle for sector (Component) = (Value of the componentTotal value×360°)\Big(\dfrac{\text{Value of the component}}{\text{Total value}} \times 360°\Big)

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. A is false, but R is true.

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Answer

Given, total admissions = 3300

The central angle for the sector representing mathematics = 48°

By formula,

Central angle for sector (Component) = (Value of the componentTotal value×360°)\Big(\dfrac{\text{Value of the component}}{\text{Total value}} \times 360°\Big)

Substituting the values,

48°=(Value of the component3300×360°)Value of the component=(48°×3300360°)Value of the component=(158400°360°)Value of the component=440.\Rightarrow 48° = \Big(\dfrac{\text{Value of the component}}{3300} \times 360°\Big) \\[1em] \Rightarrow \text{Value of the component} = \Big(\dfrac{48° \times 3300}{360°}\Big) \\[1em] \Rightarrow \text{Value of the component} = \Big(\dfrac{158400°}{360°}\Big) \\[1em] \Rightarrow \text{Value of the component} = 440.

So, assertion (A) is true.

∴ Both A and R are correct, and R is the correct explanation for A.

Hence, option 1 is the correct option.

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