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rational sum MCQ Questions for Class 10

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4 questions tagged with rational sum.

Question 1/4 Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 27

किस बहुपद में शून्यकों का योग परिमेय है लेकिन दोनों शून्यक अपरिमेय हैं?

Which polynomial has a rational sum of zeroes but both zeroes are irrational?

Explanation opens after your attempt
Correct Answer

A. \(x^2-4x+1\)

Step 1

Concept

In \(x^2-4x+1\), the sum is (4) and (D=16-4=12), so the zeroes are irrational. A rational sum does not mean rational zeroes.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-4x+1\). In \(x^2-4x+1\), the sum is (4) and (D=16-4=12), so the zeroes are irrational. A rational sum does not mean rational zeroes.

Step 3

Exam Tip

\(x^2-4x+1\) में योग (4) है और (D=16-4=12) से शून्यक अपरिमेय हैं। परिमेय योग का अर्थ परिमेय शून्यक होना नहीं है।

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Question 2/4 Expert Mathematics Real Numbers Irrational numbers Class 10 Level 14

किस विकल्प में \(\sqrt{a}+\sqrt{b}\) परिमेय है?

In which option is \(\sqrt{a}+\sqrt{b}\) rational?

Explanation opens after your attempt
Correct Answer

B. (a=25,b=49)

Step 1

Concept

(25) and (49) are both perfect squares.

Step 2

Why this answer is correct

\(\sqrt{25}+\sqrt{49}=5+7=12\), which is rational.

Step 3

Exam Tip

For a rational sum, check both square roots separately. चरण 1: (25) और (49) दोनों पूर्ण वर्ग हैं। चरण 2: \(\sqrt{25}+\sqrt{49}=5+7=12\), जो परिमेय है। चरण 3: परिमेय योग के लिए दोनों वर्गमूलों को अलग-अलग जाँचें।

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Question 3/4 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 4/4 Hard Mathematics Real Numbers Irrational numbers Class 10 Level 14

निम्न में से कौन-सा योग परिमेय है?

Which of the following sums is rational?

Explanation opens after your attempt
Correct Answer

A. (\(2+\sqrt{3}\)+\(5-\sqrt{3}\))

Step 1

Concept

First look for like irrational terms.

Step 2

Why this answer is correct

(\(2+\sqrt{3}\)+\(5-\sqrt{3}\)=7) because \(\sqrt{3}\) and \(-\sqrt{3}\) cancel.

Step 3

Exam Tip

Opposite irrational terms can produce a rational result. चरण 1: पहले समान अपरिमेय पदों को देखें। चरण 2: (\(2+\sqrt{3}\)+\(5-\sqrt{3}\)=7), क्योंकि \(\sqrt{3}\) और \(-\sqrt{3}\) कट जाते हैं। चरण 3: विपरीत अपरिमेय पदों से परिमेय उत्तर बन सकता है।

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