Class 9 Mathematics - Number Systems - General chapter practice Easy Quiz

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\( \pi \) को सामान्यतः किस प्रकार की संख्या माना जाता है?

What type of number is \( \pi \) generally considered?

Explanation opens after your attempt
Correct Answer

B. अपरिमेय वास्तविक संख्याIrrational real number

Step 1

Concept

\( \pi \) is an irrational number and lies on the real number line. Do not treat it as exactly equal to \( \frac{22}{7} \).

Step 2

Why this answer is correct

The correct answer is B. अपरिमेय वास्तविक संख्या / Irrational real number. \( \pi \) is an irrational number and lies on the real number line. Do not treat it as exactly equal to \( \frac{22}{7} \).

Step 3

Exam Tip

\( \pi \) अपरिमेय संख्या है और वास्तविक संख्या रेखा पर स्थित है। इसे \( \frac{22}{7} \) के बिल्कुल बराबर न मानें।

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यदि (r) परिमेय है और (x) अपरिमेय है तो (r+x) सामान्यतः क्या होगा जब (r=5) और \(x=\sqrt{2}\)?

If (r) is rational and (x) is irrational then what is (r+x) generally when (r=5) and \(x=\sqrt{2}\)?

Explanation opens after your attempt
Correct Answer

B. अपरिमेयIrrational

Step 1

Concept

\(5+\sqrt{2}\) is irrational because adding a rational and an irrational gives an irrational. In such questions watch the irrational part.

Step 2

Why this answer is correct

The correct answer is B. अपरिमेय / Irrational. \(5+\sqrt{2}\) is irrational because adding a rational and an irrational gives an irrational. In such questions watch the irrational part.

Step 3

Exam Tip

\(5+\sqrt{2}\) अपरिमेय है क्योंकि परिमेय में अपरिमेय जोड़ने से अपरिमेय मिलता है। ऐसे सवाल में अपरिमेय भाग देखें।

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वर्गमूल सर्पिल में किसी चरण पर पिछला कर्ण \(\sqrt{n}\) हो, तो (1) इकाई लंब जोड़ने पर नया कर्ण क्या होगा?

If the previous hypotenuse at a step in a square root spiral is \(\sqrt{n}\), what is the new hypotenuse after adding a (1) unit perpendicular?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{n+1}\)

Step 1

Concept

The new hypotenuse is (\sqrt{\(\sqrt{n}\)2+12}=\sqrt{n+1}). This is the rule of the square root spiral.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{n+1}\). The new hypotenuse is (\sqrt{\(\sqrt{n}\)2+12}=\sqrt{n+1}). This is the rule of the square root spiral.

Step 3

Exam Tip

नया कर्ण (\sqrt{\(\sqrt{n}\)2+12}=\sqrt{n+1}) होता है। यह वर्गमूल सर्पिल का नियम है।

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वर्गमूल सर्पिल में यदि नया कर्ण \(\sqrt{n+1}\) है, तो पिछला कर्ण क्या था?

In a square root spiral, if the new hypotenuse is \(\sqrt{n+1}\), what was the previous hypotenuse?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{n}\)

Step 1

Concept

The new hypotenuse is formed from previous \(\sqrt{n}\) and a (1) unit perpendicular. Therefore the previous hypotenuse was \(\sqrt{n}\).

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{n}\). The new hypotenuse is formed from previous \(\sqrt{n}\) and a (1) unit perpendicular. Therefore the previous hypotenuse was \(\sqrt{n}\).

Step 3

Exam Tip

नया कर्ण पिछले \(\sqrt{n}\) और (1) इकाई लंब से बनता है। इसलिए पिछला कर्ण \(\sqrt{n}\) था।

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यदि किसी चरण पर कर्ण \(\sqrt{n}\) है तो अगला कर्ण किस सूत्र से मिलेगा?

If the hypotenuse at a step is \(\sqrt{n}\), by which formula will the next hypotenuse be obtained?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{n+1}\)

Step 1

Concept

The new hypotenuse is (\sqrt{\(\sqrt{n}\)2+12}=\sqrt{n+1}). This is the general rule of the spiral.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{n+1}\). The new hypotenuse is (\sqrt{\(\sqrt{n}\)2+12}=\sqrt{n+1}). This is the general rule of the spiral.

Step 3

Exam Tip

नया कर्ण (\sqrt{\(\sqrt{n}\)2+12}=\sqrt{n+1}) होता है। यही सर्पिल का सामान्य नियम है।

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वर्गमूल सर्पिल में (1) इकाई लंब जोड़ने पर \(\sqrt{n}\) से \(\sqrt{n+1}\) क्यों बनता है?

Why does \(\sqrt{n}\) become \(\sqrt{n+1}\) after adding a (1) unit perpendicular in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. क्योंकि (\(\sqrt{n}\)2+12=n+1)Because (\(\sqrt{n}\)2+12=n+1)

Step 1

Concept

In Pythagoras theorem the squares of sides are added. Therefore the new hypotenuse is \(\sqrt{n+1}\).

Step 2

Why this answer is correct

The correct answer is A. क्योंकि (\(\sqrt{n}\)2+12=n+1) / Because (\(\sqrt{n}\)2+12=n+1). In Pythagoras theorem the squares of sides are added. Therefore the new hypotenuse is \(\sqrt{n+1}\).

Step 3

Exam Tip

पाइथागोरस प्रमेय में भुजाओं के वर्ग जुड़ते हैं। इसलिए नया कर्ण \(\sqrt{n+1}\) होता है।

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\(\sqrt{n}\) कर्ण पर (1) इकाई लंब जोड़ने पर नया कर्ण सामान्यतः क्या होगा?

If a (1) unit perpendicular is added to the hypotenuse \(\sqrt{n}\), what will the new hypotenuse generally be?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{n+1}\)

Step 1

Concept

By Pythagoras the new hypotenuse is (\sqrt{\(\sqrt{n}\)2+12}=\sqrt{n+1}). This is the general rule.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{n+1}\). By Pythagoras the new hypotenuse is (\sqrt{\(\sqrt{n}\)2+12}=\sqrt{n+1}). This is the general rule.

Step 3

Exam Tip

पाइथागोरस से नया कर्ण (\sqrt{\(\sqrt{n}\)2+12}=\sqrt{n+1}) होता है। यही सामान्य नियम है।

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वर्गमूल सर्पिल में कौन-सा कथन \(\sqrt{n}\) से \(\sqrt{n+1}\) बनने को सही समझाता है?

Which statement correctly explains how \(\sqrt{n}\) becomes \(\sqrt{n+1}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. पिछले कर्ण और (1) इकाई लंब के वर्गों का योग लिया जाता हैThe sum of squares of previous hypotenuse and (1) unit perpendicular is taken

Step 1

Concept

Pythagoras theorem uses the sum of squares. Therefore the new hypotenuse becomes \(\sqrt{n+1}\).

Step 2

Why this answer is correct

The correct answer is A. पिछले कर्ण और (1) इकाई लंब के वर्गों का योग लिया जाता है / The sum of squares of previous hypotenuse and (1) unit perpendicular is taken. Pythagoras theorem uses the sum of squares. Therefore the new hypotenuse becomes \(\sqrt{n+1}\).

Step 3

Exam Tip

पाइथागोरस प्रमेय में वर्गों का योग आता है। इसलिए नया कर्ण \(\sqrt{n+1}\) बनता है।

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