Concept-wise Practice

conjugate sum MCQ Questions for Class 9

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

Practice Questions

6 questions tagged with conjugate sum.

\( \frac{1}{3+\sqrt{8}}+\frac{1}{3-\sqrt{8}} \) का मान क्या है?

What is the value of \( \frac{1}{3+\sqrt{8}}+\frac{1}{3-\sqrt{8}} \)?

Explanation opens after your attempt
Correct Answer

A. (6)

Step 1

Concept

The common denominator is (9-8=1), and the numerator is \(3-\sqrt{8}+3+\sqrt{8}=6\). Therefore the value is (6).

Step 2

Why this answer is correct

The correct answer is A. (6). The common denominator is (9-8=1), and the numerator is \(3-\sqrt{8}+3+\sqrt{8}=6\). Therefore the value is (6).

Step 3

Exam Tip

समान हर (9-8=1) और अंश \(3-\sqrt{8}+3+\sqrt{8}=6\) है। इसलिए मान (6) है।

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\( \frac{1}{\sqrt{13}+2}+\frac{1}{\sqrt{13}-2} \) का मान क्या है?

What is the value of \( \frac{1}{\sqrt{13}+2}+\frac{1}{\sqrt{13}-2} \)?

Explanation opens after your attempt
Correct Answer

A. \( \frac{2\sqrt{13}}{9} \)

Step 1

Concept

The common denominator is (13-4=9), and the numerator is \(2\sqrt{13}\). Therefore the value is \( \frac{2\sqrt{13}}{9} \).

Step 2

Why this answer is correct

The correct answer is A. \( \frac{2\sqrt{13}}{9} \). The common denominator is (13-4=9), and the numerator is \(2\sqrt{13}\). Therefore the value is \( \frac{2\sqrt{13}}{9} \).

Step 3

Exam Tip

समान हर (13-4=9) और अंश \(2\sqrt{13}\) है। इसलिए मान \( \frac{2\sqrt{13}}{9} \) है।

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( \left\(\frac{1}{5-\sqrt{21}}\right\)+\left\(\frac{1}{5+\sqrt{21}}\right\) ) का मान क्या है?

What is the value of ( \left\(\frac{1}{5-\sqrt{21}}\right\)+\left\(\frac{1}{5+\sqrt{21}}\right\) )?

Explanation opens after your attempt
Correct Answer

A. \( \frac{5}{2} \)

Step 1

Concept

The common denominator is (25-21=4), and the numerator is (10). So the value is \( \frac{10}{4}=\frac{5}{2} \).

Step 2

Why this answer is correct

The correct answer is A. \( \frac{5}{2} \). The common denominator is (25-21=4), and the numerator is (10). So the value is \( \frac{10}{4}=\frac{5}{2} \).

Step 3

Exam Tip

समान हर (25-21=4) और अंश (10) है। इसलिए मान \( \frac{10}{4}=\frac{5}{2} \) है।

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\( \frac{1}{2+\sqrt{3}}+\frac{1}{2-\sqrt{3}} \) का मान क्या है?

What is the value of \( \frac{1}{2+\sqrt{3}}+\frac{1}{2-\sqrt{3}} \)?

Explanation opens after your attempt
Correct Answer

A. (4)

Step 1

Concept

The common denominator is (4-3=1), and the numerator is \(2-\sqrt{3}+2+\sqrt{3}=4\). Therefore the value is (4).

Step 2

Why this answer is correct

The correct answer is A. (4). The common denominator is (4-3=1), and the numerator is \(2-\sqrt{3}+2+\sqrt{3}=4\). Therefore the value is (4).

Step 3

Exam Tip

समान हर (4-3=1) और अंश \(2-\sqrt{3}+2+\sqrt{3}=4\) है। इसलिए मान (4) है।

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\( \frac{1}{\sqrt{11}+3}+\frac{1}{\sqrt{11}-3} \) का मान क्या है?

What is the value of \( \frac{1}{\sqrt{11}+3}+\frac{1}{\sqrt{11}-3} \)?

Explanation opens after your attempt
Correct Answer

A. \( \sqrt{11} \)

Step 1

Concept

The common denominator is (11-9=2), and the numerator is \(2\sqrt{11}\). Therefore the value is \( \sqrt{11} \).

Step 2

Why this answer is correct

The correct answer is A. \( \sqrt{11} \). The common denominator is (11-9=2), and the numerator is \(2\sqrt{11}\). Therefore the value is \( \sqrt{11} \).

Step 3

Exam Tip

समान हर (11-9=2) और अंश \(2\sqrt{11}\) है। इसलिए मान \( \sqrt{11} \) है।

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( \left\(\frac{1}{3-\sqrt{7}}\right\)+\left\(\frac{1}{3+\sqrt{7}}\right\) ) का मान क्या है?

What is the value of ( \left\(\frac{1}{3-\sqrt{7}}\right\)+\left\(\frac{1}{3+\sqrt{7}}\right\) )?

Explanation opens after your attempt
Correct Answer

A. (3)

Step 1

Concept

The common denominator is (9-7=2), and the numerator is \(3+\sqrt{7}+3-\sqrt{7}=6\). So the value is \( \frac{6}{2}=3 \).

Step 2

Why this answer is correct

The correct answer is A. (3). The common denominator is (9-7=2), and the numerator is \(3+\sqrt{7}+3-\sqrt{7}=6\). So the value is \( \frac{6}{2}=3 \).

Step 3

Exam Tip

समान हर (9-7=2) और अंश \(3+\sqrt{7}+3-\sqrt{7}=6\) है। इसलिए मान \( \frac{6}{2}=3 \) है।

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