Concept-wise Practice

reciprocal-squares MCQ Questions for Class 10

reciprocal-squares se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

Practice Questions

3 questions tagged with reciprocal-squares.

यदि \(x^2-8x+2=0\) की जड़ें \(\alpha,\beta\) हैं, तो \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}\) का मान क्या है?

If \(\alpha,\beta\) are the roots of \(x^2-8x+2=0\), what is \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}\)?

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Correct Answer

A. (15)

Explanation

Simple Explanation

\(\alpha^2+\beta^2=64-4=60\) और (\(\alpha\beta\)2=4) है। इसलिए \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}=\frac{60}{4}=15\)। / Here \(\alpha^2+\beta^2=64-4=60\) and (\(\alpha\beta\)2=4). Thus \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}=\frac{60}{4}=15\).

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यदि \(x^2-6x+3=0\) की जड़ें \(\alpha,\beta\) हैं, तो \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}\) का मान क्या है?

If \(\alpha,\beta\) are the roots of \(x^2-6x+3=0\), what is \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}\)?

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Correct Answer

B. \(\frac{10}{3}\)

Explanation

Simple Explanation

(\frac{1}{\alpha-2}+\frac{1}{\beta-2}=\frac{\alpha-2+\beta-2}{\(\alpha\beta\)2}) होता है। \(\alpha^2+\beta^2=30\) और (\(\alpha\beta\)2=9), इसलिए मान \(\frac{10}{3}\) है। / We use (\frac{1}{\alpha-2}+\frac{1}{\beta-2}=\frac{\alpha-2+\beta-2}{\(\alpha\beta\)2}). Since \(\alpha^2+\beta^2=30\) and (\(\alpha\beta\)2=9), the value is \(\frac{10}{3}\).

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यदि \(x^2-5x+2=0\) की जड़ें \(\alpha,\beta\) हैं, तो \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}\) का मान क्या है?

If \(\alpha,\beta\) are the roots of \(x^2-5x+2=0\), what is \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}\)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{21}{4}\)

Explanation

Simple Explanation

(\frac{1}{\alpha-2}+\frac{1}{\beta-2}=\frac{\alpha-2+\beta-2}{\(\alpha\beta\)2}) होता है। \(\alpha^2+\beta^2=21\) और (\(\alpha\beta\)2=4), इसलिए मान \(\frac{21}{4}\) है। / We use (\frac{1}{\alpha-2}+\frac{1}{\beta-2}=\frac{\alpha-2+\beta-2}{\(\alpha\beta\)2}). Since \(\alpha^2+\beta^2=21\) and (\(\alpha\beta\)2=4), the value is \(\frac{21}{4}\).

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