Concept-wise Practice

reciprocal-zeroes MCQ Questions for Class 10

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Practice Questions

4 questions tagged with reciprocal-zeroes.

यदि (p(x)=x-2+bx+16) के शून्यक परस्पर व्युत्क्रम हैं, तो (b) के बारे में क्या कहा जा सकता है?

If the zeroes of (p(x)=x-2+bx+16) are reciprocals of each other, what can be said about (b)?

Explanation opens after your attempt
Correct Answer

A. ऐसा संभव नहीं हैIt is not possible

Step 1

Concept

Reciprocal zeroes must have product (1). Here the product is (16), so it is not possible.

Step 2

Why this answer is correct

The correct answer is A. ऐसा संभव नहीं है / It is not possible. Reciprocal zeroes must have product (1). Here the product is (16), so it is not possible.

Step 3

Exam Tip

परस्पर व्युत्क्रम शून्यकों का गुणनफल (1) होना चाहिए। यहाँ गुणनफल (16) है, इसलिए यह संभव नहीं है।

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यदि (p(x)=x-2-4x+1), तो शून्यकों के व्युत्क्रमों का योग क्या है?

If (p(x)=x-2-4x+1), what is the sum of reciprocals of its zeroes?

Explanation opens after your attempt
Correct Answer

A. (4)

Step 1

Concept

The sum of reciprocals is \(\frac{\alpha+\beta}{\alpha\beta}\). Here \(\alpha+\beta=4\) and \(\alpha\beta=1\), so the answer is (4).

Step 2

Why this answer is correct

The correct answer is A. (4). The sum of reciprocals is \(\frac{\alpha+\beta}{\alpha\beta}\). Here \(\alpha+\beta=4\) and \(\alpha\beta=1\), so the answer is (4).

Step 3

Exam Tip

शून्यकों के व्युत्क्रमों का योग \(\frac{\alpha+\beta}{\alpha\beta}\) होता है। यहाँ \(\alpha+\beta=4\) और \(\alpha\beta=1\), इसलिए उत्तर (4) है।

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यदि (p(x)=2x-2-9x+4), तो \(\frac{1}{\alpha}+\frac{1}{\beta}\) क्या है, जहाँ \(\alpha,\beta\) शून्यक हैं?

If (p(x)=2x-2-9x+4), what is \(\frac{1}{\alpha}+\frac{1}{\beta}\), where \(\alpha,\beta\) are zeroes?

Explanation opens after your attempt
Correct Answer

A. \(\frac{9}{4}\)

Step 1

Concept

\(\alpha+\beta=\frac{9}{2}\) and \(\alpha\beta=2\). Hence \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}=\frac{9}{4}\).

Step 2

Why this answer is correct

The correct answer is A. \(\frac{9}{4}\). \(\alpha+\beta=\frac{9}{2}\) and \(\alpha\beta=2\). Hence \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}=\frac{9}{4}\).

Step 3

Exam Tip

\(\alpha+\beta=\frac{9}{2}\) और \(\alpha\beta=2\) हैं। इसलिए \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}=\frac{9}{4}\)।

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यदि (p(x)=x-2-10x+19), तो \(\frac{1}{\alpha}+\frac{1}{\beta}\) का मान क्या है, जहाँ \(\alpha,\beta\) इसके शून्यक हैं?

If (p(x)=x-2-10x+19), what is \(\frac{1}{\alpha}+\frac{1}{\beta}\), where \(\alpha,\beta\) are its zeroes?

Explanation opens after your attempt
Correct Answer

A. \(\frac{10}{19}\)

Step 1

Concept

The sum of zeroes is (10) and the product is (19). Hence \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{10}{19}\).

Step 2

Why this answer is correct

The correct answer is A. \(\frac{10}{19}\). The sum of zeroes is (10) and the product is (19). Hence \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{10}{19}\).

Step 3

Exam Tip

शून्यकों का योग (10) और गुणनफल (19) है। अतः \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{10}{19}\)।

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