Correlation and RegressionMCQPYQ July 21Question 3643 of 188
All Questions

The sum of square of any real positive quantities and its reciprocal is never less than:

Options

A4
B2
C3
D4
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Correct Answer

✅ Option b — 2

All Options:

  • A4
  • B2
  • C3
  • D4

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Detailed Solution & Explanation

**Mathematical inequality — AM-GM application:** Let t>0\displaystyle t > 0 be any real positive quantity. We need to find the minimum value of t+frac1t\displaystyle t + \\frac{1}{t}. **Using AM-GM inequality:** fract+frac1t2geqsqrttcdotfrac1t=sqrt1=1\\frac{t + \\frac{1}{t}}{2} \\geq \\sqrt{t \\cdot \\frac{1}{t}} = \\sqrt{1} = 1 t+frac1tgeq2t + \\frac{1}{t} \\geq 2 Equality holds when t=frac1tRightarrowt2=1Rightarrowt=1\displaystyle t = \\frac{1}{t} \\Rightarrow t^2 = 1 \\Rightarrow t = 1 (since t>0\displaystyle t > 0). **Verification at t=1\displaystyle t = 1:** 1+frac11=2checkmark1 + \\frac{1}{1} = 2 \\checkmark Therefore, the sum of any positive quantity and its reciprocal is **never less than 2**. This result is used in proving that −1leqrleq1\displaystyle -1 \\leq r \\leq 1 for the correlation coefficient. Hence, **Option B** is the correct answer.

About This Chapter: Correlation and Regression

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Correlation Coefficient, Regression Equations

This chapter covers Correlation Coefficient, Regression Equations and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

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Correlation vs Regression: Statistics for CA Foundation

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