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reciprocal MCQ Questions for Class 10

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35 questions tagged with reciprocal.

Question 31/35 Expert Mathematics Real Numbers Irrational numbers Class 10 Level 14

यदि \(x=5-\sqrt{24}\), तो \(\frac{1}{x}\) का सही रूप कौन-सा है?

If \(x=5-\sqrt{24}\), which is the correct form of \(\frac{1}{x}\)?

Explanation opens after your attempt
Correct Answer

A. \(5+\sqrt{24}\)

Step 1

Concept

(\(5-\sqrt{24}\)\(5+\sqrt{24}\)=25-24=1).

Step 2

Why this answer is correct

Therefore \(5+\sqrt{24}\) is the reciprocal of \(5-\sqrt{24}\).

Step 3

Exam Tip

If conjugates multiply to (1), the reciprocal is directly the conjugate. चरण 1: (\(5-\sqrt{24}\)\(5+\sqrt{24}\)=25-24=1)। चरण 2: इसलिए \(5+\sqrt{24}\), \(5-\sqrt{24}\) का व्युत्क्रम है। चरण 3: यदि संयुग्मी गुणन (1) दे, तो व्युत्क्रम सीधे संयुग्मी होता है।

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Question 32/35 Expert Mathematics Real Numbers Irrational numbers Class 10 Level 14

किस विकल्प में (x) अपरिमेय है, पर \(x+\frac{1}{x}\) परिमेय है?

In which option is (x) irrational but \(x+\frac{1}{x}\) rational?

Explanation opens after your attempt
Correct Answer

A. \(x=3+\sqrt{8}\)

Step 1

Concept

\(3+\sqrt{8}=3+2\sqrt{2}\) is irrational.

Step 2

Why this answer is correct

Its reciprocal is \(3-\sqrt{8}\), because (\(3+\sqrt{8}\)\(3-\sqrt{8}\)=1). Hence the sum is (6), which is rational.

Step 3

Exam Tip

When conjugates multiply to (1), the reciprocal is easy to identify. चरण 1: \(3+\sqrt{8}=3+2\sqrt{2}\) अपरिमेय है। चरण 2: इसका व्युत्क्रम \(3-\sqrt{8}\) है, क्योंकि (\(3+\sqrt{8}\)\(3-\sqrt{8}\)=1)। इसलिए योग (6) परिमेय है। चरण 3: जिन संयुग्मियों का गुणन (1) हो, वहाँ व्युत्क्रम तुरंत मिल सकता है।

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Question 33/35 Expert Mathematics Real Numbers Irrational numbers Class 10 Level 13

यदि \(x=2+\sqrt{3}\), तो \(x+\frac{1}{x}\) का मान क्या है?

If \(x=2+\sqrt{3}\), what is the value of \(x+\frac{1}{x}\)?

Explanation opens after your attempt
Correct Answer

A. (4)

Step 1

Concept

\(\frac{1}{2+\sqrt{3}}=2-\sqrt{3}\).

Step 2

Why this answer is correct

(x+\frac{1}{x}=\(2+\sqrt{3}\)+\(2-\sqrt{3}\)=4).

Step 3

Exam Tip

Recognizing the conjugate reciprocal saves long calculation. चरण 1: \(\frac{1}{2+\sqrt{3}}=2-\sqrt{3}\) होता है। चरण 2: (x+\frac{1}{x}=\(2+\sqrt{3}\)+\(2-\sqrt{3}\)=4)। चरण 3: संयुग्मी व्युत्क्रम को पहचानने से लंबी गणना बचती है।

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Question 34/35 Expert Mathematics Real Numbers Irrational numbers Class 10 Level 13

किस विकल्प में संख्या अपरिमेय है, लेकिन उसका व्युत्क्रम भी अपरिमेय है?

In which option is the number irrational and its reciprocal also irrational?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{12}\)

Step 1

Concept

\(\sqrt{12}=2\sqrt{3}\) is irrational.

Step 2

Why this answer is correct

Its reciprocal \(\frac{1}{2\sqrt{3}}=\frac{\sqrt{3}}{6}\) is also irrational.

Step 3

Exam Tip

Do not assume the reciprocal of a non-zero irrational surd is rational. चरण 1: \(\sqrt{12}=2\sqrt{3}\) अपरिमेय है। चरण 2: इसका व्युत्क्रम \(\frac{1}{2\sqrt{3}}=\frac{\sqrt{3}}{6}\) भी अपरिमेय है। चरण 3: अशून्य अपरिमेय मूल के व्युत्क्रम को परिमेय मानने की गलती न करें।

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Question 35/35 Hard Mathematics Real Numbers Irrational numbers Class 10 Level 15

यदि \(\frac{1}{x}\) परिमेय है और \(x\neq0\), तो (x) के अपरिमेय होने के बारे में सही निष्कर्ष क्या है?

If \(\frac{1}{x}\) is rational and \(x\neq0\), what is the correct conclusion about (x) being irrational?

Explanation opens after your attempt
Correct Answer

B. (x) अवश्य परिमेय है(x) must be rational

Step 1

Concept

If \(\frac{1}{x}\) is rational and non-zero, then its reciprocal is also rational.

Step 2

Why this answer is correct

Therefore (x) is rational, not irrational.

Step 3

Exam Tip

In reciprocal questions, always check the non-zero condition. चरण 1: यदि \(\frac{1}{x}\) परिमेय है और शून्य नहीं है, तो उसका व्युत्क्रम भी परिमेय होगा। चरण 2: इसलिए (x) परिमेय होगा, अपरिमेय नहीं। चरण 3: व्युत्क्रम वाले प्रश्नों में शून्य की शर्त जरूर देखें।

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