Class 9 Mathematics - Sequences and Progressions - Geometric Progression Medium Quiz

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वर्गमूल सर्पिल में यदि किसी चरण पर पिछला कर्ण \(\sqrt{11}\) है, तो नया कर्ण ज्ञात करने के लिए सही पाइथागोरस रूप कौन-सा होगा?

If the previous hypotenuse at a step in a square root spiral is \(\sqrt{11}\), which Pythagoras form is correct to find the new hypotenuse?

Explanation opens after your attempt
Correct Answer

B. (\sqrt{\(\sqrt{11}\)2+12})

Step 1

Concept

The previous hypotenuse is \(\sqrt{11}\) and the new perpendicular is (1) unit. So the new hypotenuse will be \(\sqrt{12}\).

Step 2

Why this answer is correct

The correct answer is B. (\sqrt{\(\sqrt{11}\)2+12}). The previous hypotenuse is \(\sqrt{11}\) and the new perpendicular is (1) unit. So the new hypotenuse will be \(\sqrt{12}\).

Step 3

Exam Tip

पिछला कर्ण \(\sqrt{11}\) और नई लंब (1) इकाई होती है। इसलिए नया कर्ण \(\sqrt{12}\) बनेगा।

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वर्गमूल सर्पिल में \(\sqrt{17}\) बनाने के लिए पिछले चरण के कर्ण और नई लंब भुजा की लंबाइयाँ कौन-सी होंगी?

To construct \(\sqrt{17}\) in a square root spiral, what will be the lengths of the previous hypotenuse and the new perpendicular side?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{16}\) और (1)\(\sqrt{16}\) and (1)

Step 1

Concept

Adding a (1) unit perpendicular to \(\sqrt{16}\) forms the new hypotenuse \(\sqrt{17}\). The previous hypotenuse has one less number.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{16}\) और (1) / \(\sqrt{16}\) and (1). Adding a (1) unit perpendicular to \(\sqrt{16}\) forms the new hypotenuse \(\sqrt{17}\). The previous hypotenuse has one less number.

Step 3

Exam Tip

\(\sqrt{16}\) के साथ (1) इकाई लंब जोड़ने पर नया कर्ण \(\sqrt{17}\) बनता है। पिछले कर्ण की संख्या एक कम होती है।

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यदि वर्गमूल सर्पिल में \(\sqrt{24}\) कर्ण बन चुका है, तो अगला कर्ण किस गणना से मिलेगा?

If the hypotenuse \(\sqrt{24}\) has been constructed in a square root spiral, by which calculation will the next hypotenuse be obtained?

Explanation opens after your attempt
Correct Answer

C. \(\sqrt{24+1}\)

Step 1

Concept

At every new step \(1^2\) is added. Therefore \(\sqrt{25}\) comes after \(\sqrt{24}\).

Step 2

Why this answer is correct

The correct answer is C. \(\sqrt{24+1}\). At every new step \(1^2\) is added. Therefore \(\sqrt{25}\) comes after \(\sqrt{24}\).

Step 3

Exam Tip

हर नए चरण में \(1^2\) जुड़ता है। इसलिए \(\sqrt{24}\) के बाद \(\sqrt{25}\) मिलता है।

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वर्गमूल सर्पिल में \(\sqrt{5}\) की लंबाई संख्या रेखा पर किस अंतराल में अंकित होगी?

In a square root spiral, in which interval will the length \(\sqrt{5}\) be marked on the number line?

Explanation opens after your attempt
Correct Answer

B. (2) और (3) के बीचBetween (2) and (3)

Step 1

Concept

Because \(2^2<5<3^2\). Therefore \(\sqrt{5}\) lies between (2) and (3).

Step 2

Why this answer is correct

The correct answer is B. (2) और (3) के बीच / Between (2) and (3). Because \(2^2<5<3^2\). Therefore \(\sqrt{5}\) lies between (2) and (3).

Step 3

Exam Tip

क्योंकि \(2^2<5<3^2\) है। इसलिए \(\sqrt{5}\) (2) और (3) के बीच होगा।

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वर्गमूल सर्पिल में \(\sqrt{10}\) बनाने के लिए कौन-सा समकोण त्रिभुज सही है?

Which right triangle is correct for constructing \(\sqrt{10}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. भुजाएँ \(\sqrt{9}\) और (1)Sides \(\sqrt{9}\) and (1)

Step 1

Concept

(\(\sqrt{9}\)2+12=10). Hence the hypotenuse will be \(\sqrt{10}\).

Step 2

Why this answer is correct

The correct answer is A. भुजाएँ \(\sqrt{9}\) और (1) / Sides \(\sqrt{9}\) and (1). (\(\sqrt{9}\)2+12=10). Hence the hypotenuse will be \(\sqrt{10}\).

Step 3

Exam Tip

(\(\sqrt{9}\)2+12=10) होता है। इसलिए कर्ण \(\sqrt{10}\) बनेगा।

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वर्गमूल सर्पिल में \(\sqrt{3}\) से \(\sqrt{4}\) बनाते समय कौन-सी सामान्य गलती से बचना चाहिए?

While making \(\sqrt{4}\) from \(\sqrt{3}\) in a square root spiral, which common mistake should be avoided?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{3}+1=\sqrt{4}\) माननाAssuming \(\sqrt{3}+1=\sqrt{4}\)

Step 1

Concept

The new hypotenuse is not formed by direct addition. In Pythagoras theorem the squares of sides are added.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{3}+1=\sqrt{4}\) मानना / Assuming \(\sqrt{3}+1=\sqrt{4}\). The new hypotenuse is not formed by direct addition. In Pythagoras theorem the squares of sides are added.

Step 3

Exam Tip

नया कर्ण सीधे जोड़ से नहीं बनता। पाइथागोरस में भुजाओं के वर्गों का योग लिया जाता है।

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यदि वर्गमूल सर्पिल में किसी चरण पर नया कर्ण \(\sqrt{31}\) है, तो उससे ठीक पहले वाला कर्ण कौन-सा था?

If the new hypotenuse at a step in a square root spiral is \(\sqrt{31}\), which was the immediately previous hypotenuse?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{30}\)

Step 1

Concept

If the new hypotenuse is \(\sqrt{n+1}\), the previous one is \(\sqrt{n}\). Therefore before \(\sqrt{31}\), it was \(\sqrt{30}\).

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{30}\). If the new hypotenuse is \(\sqrt{n+1}\), the previous one is \(\sqrt{n}\). Therefore before \(\sqrt{31}\), it was \(\sqrt{30}\).

Step 3

Exam Tip

नया कर्ण \(\sqrt{n+1}\) हो तो पिछला कर्ण \(\sqrt{n}\) होता है। इसलिए \(\sqrt{31}\) से पहले \(\sqrt{30}\) था।

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वर्गमूल सर्पिल में \(\sqrt{49}\) और \(\sqrt{50}\) के बारे में कौन-सा कथन सही है?

Which statement about \(\sqrt{49}\) and \(\sqrt{50}\) in a square root spiral is correct?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{49}\) पूर्ण संख्या और \(\sqrt{50}\) अपरिमेय है\(\sqrt{49}\) is a whole number and \(\sqrt{50}\) is irrational

Step 1

Concept

\(\sqrt{49}=7\), but (50) is not a perfect square. Therefore \(\sqrt{50}\) is irrational.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{49}\) पूर्ण संख्या और \(\sqrt{50}\) अपरिमेय है / \(\sqrt{49}\) is a whole number and \(\sqrt{50}\) is irrational. \(\sqrt{49}=7\), but (50) is not a perfect square. Therefore \(\sqrt{50}\) is irrational.

Step 3

Exam Tip

\(\sqrt{49}=7\) है, लेकिन (50) पूर्ण वर्ग नहीं है। इसलिए \(\sqrt{50}\) अपरिमेय है।

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वर्गमूल सर्पिल में (1) इकाई लंब को \(90^\circ\) पर बनाने की आवश्यकता किस कारण से है?

Why is it necessary to draw the (1) unit perpendicular at \(90^\circ\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. ताकि समकोण त्रिभुज बने और पाइथागोरस प्रमेय लागू हो सकेSo that a right triangle is formed and Pythagoras theorem can be applied

Step 1

Concept

Pythagoras theorem applies only to a right triangle. Therefore a \(90^\circ\) angle is necessary.

Step 2

Why this answer is correct

The correct answer is A. ताकि समकोण त्रिभुज बने और पाइथागोरस प्रमेय लागू हो सके / So that a right triangle is formed and Pythagoras theorem can be applied. Pythagoras theorem applies only to a right triangle. Therefore a \(90^\circ\) angle is necessary.

Step 3

Exam Tip

पाइथागोरस प्रमेय केवल समकोण त्रिभुज में लागू होता है। इसलिए \(90^\circ\) कोण जरूरी है।

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वर्गमूल सर्पिल में \(\sqrt{65}\) की लंबाई संख्या रेखा पर किन पूर्ण संख्याओं के बीच होगी?

In a square root spiral, between which whole numbers will the length \(\sqrt{65}\) lie on the number line?

Explanation opens after your attempt
Correct Answer

B. (8) और (9)(8) and (9)

Step 1

Concept

Because \(8^2<65<9^2\). Therefore \(8<\sqrt{65}<9\).

Step 2

Why this answer is correct

The correct answer is B. (8) और (9) / (8) and (9). Because \(8^2<65<9^2\). Therefore \(8<\sqrt{65}<9\).

Step 3

Exam Tip

क्योंकि \(8^2<65<9^2\) है। इसलिए \(8<\sqrt{65}<9\) होगा।

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वर्गमूल सर्पिल में यदि \(\sqrt{n}\) के बाद \(\sqrt{n+1}\) बनता है, तो इसका मुख्य गणितीय कारण क्या है?

If \(\sqrt{n+1}\) is formed after \(\sqrt{n}\) in a square root spiral, what is the main mathematical reason?

Explanation opens after your attempt
Correct Answer

C. पिछले कर्ण के वर्ग में \(1^2\) जुड़ता है\(1^2\) is added to the square of the previous hypotenuse

Step 1

Concept

By Pythagoras theorem (\(\sqrt{n}\)2+12=n+1). Therefore the new hypotenuse becomes \(\sqrt{n+1}\).

Step 2

Why this answer is correct

The correct answer is C. पिछले कर्ण के वर्ग में \(1^2\) जुड़ता है / \(1^2\) is added to the square of the previous hypotenuse. By Pythagoras theorem (\(\sqrt{n}\)2+12=n+1). Therefore the new hypotenuse becomes \(\sqrt{n+1}\).

Step 3

Exam Tip

पाइथागोरस प्रमेय से (\(\sqrt{n}\)2+12=n+1) होता है। इसलिए नया कर्ण \(\sqrt{n+1}\) बनता है।

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वर्गमूल सर्पिल में \(\sqrt{2}\) को संख्या रेखा पर अंकित करते समय कंपास का केंद्र सामान्यतः कहाँ रखा जाता है?

While marking \(\sqrt{2}\) on the number line from a square root spiral, where is the compass center usually placed?

Explanation opens after your attempt
Correct Answer

A. मूल बिंदु परAt the origin

Step 1

Concept

Taking the hypotenuse length in the compass, an arc is drawn from the origin. This gives the correct point on the number line.

Step 2

Why this answer is correct

The correct answer is A. मूल बिंदु पर / At the origin. Taking the hypotenuse length in the compass, an arc is drawn from the origin. This gives the correct point on the number line.

Step 3

Exam Tip

कर्ण की लंबाई कंपास में लेकर मूल बिंदु से चाप खींचते हैं। इससे संख्या रेखा पर सही स्थान मिलता है।

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वर्गमूल सर्पिल में \(\sqrt{80}\) बनाने के लिए कौन-सा पिछला कर्ण और नई लंब सही है?

To construct \(\sqrt{80}\) in a square root spiral, which previous hypotenuse and new perpendicular are correct?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{79}\) और (1)\(\sqrt{79}\) and (1)

Step 1

Concept

(\(\sqrt{79}\)2+12=80). Therefore the new hypotenuse will be \(\sqrt{80}\).

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{79}\) और (1) / \(\sqrt{79}\) and (1). (\(\sqrt{79}\)2+12=80). Therefore the new hypotenuse will be \(\sqrt{80}\).

Step 3

Exam Tip

(\(\sqrt{79}\)2+12=80) होता है। इसलिए नया कर्ण \(\sqrt{80}\) बनेगा।

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वर्गमूल सर्पिल में \(\sqrt{36}\) और \(\sqrt{37}\) में कौन-सा कथन सही है?

Which statement about \(\sqrt{36}\) and \(\sqrt{37}\) in a square root spiral is correct?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{36}\) पूर्ण संख्या है और \(\sqrt{37}\) अपरिमेय है\(\sqrt{36}\) is a whole number and \(\sqrt{37}\) is irrational

Step 1

Concept

\(\sqrt{36}=6\), but (37) is not a perfect square. Therefore \(\sqrt{37}\) is irrational.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{36}\) पूर्ण संख्या है और \(\sqrt{37}\) अपरिमेय है / \(\sqrt{36}\) is a whole number and \(\sqrt{37}\) is irrational. \(\sqrt{36}=6\), but (37) is not a perfect square. Therefore \(\sqrt{37}\) is irrational.

Step 3

Exam Tip

\(\sqrt{36}=6\) है, लेकिन (37) पूर्ण वर्ग नहीं है। इसलिए \(\sqrt{37}\) अपरिमेय है।

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वर्गमूल सर्पिल में \(\sqrt{18}\) की लंबाई संख्या रेखा पर किस अंतराल में होगी?

In a square root spiral, in which interval will the length \(\sqrt{18}\) lie on the number line?

Explanation opens after your attempt
Correct Answer

B. (4) और (5) के बीचBetween (4) and (5)

Step 1

Concept

Because \(4^2<18<5^2\). Therefore \(\sqrt{18}\) lies between (4) and (5).

Step 2

Why this answer is correct

The correct answer is B. (4) और (5) के बीच / Between (4) and (5). Because \(4^2<18<5^2\). Therefore \(\sqrt{18}\) lies between (4) and (5).

Step 3

Exam Tip

क्योंकि \(4^2<18<5^2\) है। इसलिए \(\sqrt{18}\) (4) और (5) के बीच है।

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वर्गमूल सर्पिल बनाते समय यदि नई लंब भुजा (1) की जगह (2) इकाई रखी जाए, तो सामान्य क्रम क्यों बदल जाएगा?

If the new perpendicular side is taken as (2) units instead of (1) unit while making a square root spiral, why will the usual sequence change?

Explanation opens after your attempt
Correct Answer

A. क्योंकि \(1^2\) की जगह \(2^2\) जुड़ जाएगाBecause \(2^2\) will be added instead of \(1^2\)

Step 1

Concept

In the usual spiral \(1^2\) is added each time to give the next square root. Taking (2) units will add (4).

Step 2

Why this answer is correct

The correct answer is A. क्योंकि \(1^2\) की जगह \(2^2\) जुड़ जाएगा / Because \(2^2\) will be added instead of \(1^2\). In the usual spiral \(1^2\) is added each time to give the next square root. Taking (2) units will add (4).

Step 3

Exam Tip

सामान्य सर्पिल में हर बार \(1^2\) जुड़कर अगला वर्गमूल देता है। (2) इकाई लेने पर वृद्धि (4) की होगी।

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वर्गमूल सर्पिल में \(\sqrt{99}\) के बाद अगला कर्ण कौन-सा होगा?

In a square root spiral, which hypotenuse will come after \(\sqrt{99}\)?

Explanation opens after your attempt
Correct Answer

C. \(\sqrt{100}\)

Step 1

Concept

The number increases by (1) at each step. Therefore \(\sqrt{100}\) comes after \(\sqrt{99}\).

Step 2

Why this answer is correct

The correct answer is C. \(\sqrt{100}\). The number increases by (1) at each step. Therefore \(\sqrt{100}\) comes after \(\sqrt{99}\).

Step 3

Exam Tip

हर चरण में संख्या (1) बढ़ती है। इसलिए \(\sqrt{99}\) के बाद \(\sqrt{100}\) आएगा।

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वर्गमूल सर्पिल में कौन-सा कथन निर्माण के लिए सबसे सही है?

Which statement is most correct for the construction of a square root spiral?

Explanation opens after your attempt
Correct Answer

A. हर नया त्रिभुज पिछले कर्ण और (1) इकाई लंब से बनता हैEach new triangle is made from the previous hypotenuse and a (1) unit perpendicular

Step 1

Concept

A square root spiral is a chain of right triangles. The previous hypotenuse and a (1) unit perpendicular form the new triangle.

Step 2

Why this answer is correct

The correct answer is A. हर नया त्रिभुज पिछले कर्ण और (1) इकाई लंब से बनता है / Each new triangle is made from the previous hypotenuse and a (1) unit perpendicular. A square root spiral is a chain of right triangles. The previous hypotenuse and a (1) unit perpendicular form the new triangle.

Step 3

Exam Tip

वर्गमूल सर्पिल समकोण त्रिभुजों की श्रृंखला है। पिछला कर्ण और (1) इकाई लंब नया त्रिभुज बनाते हैं।

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वर्गमूल सर्पिल में \(\sqrt{121}\) और \(\sqrt{122}\) के बारे में कौन-सा कथन सही है?

Which statement about \(\sqrt{121}\) and \(\sqrt{122}\) in a square root spiral is correct?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{121}=11\) और \(\sqrt{122}\) अपरिमेय है\(\sqrt{121}=11\) and \(\sqrt{122}\) is irrational

Step 1

Concept

(121) is a perfect square, but (122) is not. Therefore \(\sqrt{122}\) is irrational.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{121}=11\) और \(\sqrt{122}\) अपरिमेय है / \(\sqrt{121}=11\) and \(\sqrt{122}\) is irrational. (121) is a perfect square, but (122) is not. Therefore \(\sqrt{122}\) is irrational.

Step 3

Exam Tip

(121) पूर्ण वर्ग है, लेकिन (122) पूर्ण वर्ग नहीं है। इसलिए \(\sqrt{122}\) अपरिमेय है।

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वर्गमूल सर्पिल में \(\sqrt{3}\) को \(\sqrt{2}\) से बनाते समय कौन-सी भुजाएँ समकोण बनाती हैं?

While making \(\sqrt{3}\) from \(\sqrt{2}\) in a square root spiral, which sides form the right angle?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{2}\) और (1)\(\sqrt{2}\) and (1)

Step 1

Concept

The previous hypotenuse \(\sqrt{2}\) becomes one side and a (1) unit perpendicular is added. The new hypotenuse is \(\sqrt{3}\).

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{2}\) और (1) / \(\sqrt{2}\) and (1). The previous hypotenuse \(\sqrt{2}\) becomes one side and a (1) unit perpendicular is added. The new hypotenuse is \(\sqrt{3}\).

Step 3

Exam Tip

पिछला कर्ण \(\sqrt{2}\) नई भुजा बनता है और (1) इकाई लंब जोड़ी जाती है। नया कर्ण \(\sqrt{3}\) होता है।

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वर्गमूल सर्पिल में \(\sqrt{32}\) को संख्या रेखा पर रखने के लिए कौन-सा अंतराल सही है?

Which interval is correct for placing \(\sqrt{32}\) on the number line using a square root spiral?

Explanation opens after your attempt
Correct Answer

B. (5) और (6) के बीचBetween (5) and (6)

Step 1

Concept

Because \(5^2<32<6^2\). Therefore \(\sqrt{32}\) lies between (5) and (6).

Step 2

Why this answer is correct

The correct answer is B. (5) और (6) के बीच / Between (5) and (6). Because \(5^2<32<6^2\). Therefore \(\sqrt{32}\) lies between (5) and (6).

Step 3

Exam Tip

क्योंकि \(5^2<32<6^2\) है। इसलिए \(\sqrt{32}\) (5) और (6) के बीच है।

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वर्गमूल सर्पिल में \(\sqrt{48}\) बनाने के लिए कौन-सा पिछला कर्ण सही है?

Which previous hypotenuse is correct for constructing \(\sqrt{48}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{47}\)

Step 1

Concept

Adding a (1) unit perpendicular to \(\sqrt{47}\) forms \(\sqrt{48}\). In the previous step the number is (1) less.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{47}\). Adding a (1) unit perpendicular to \(\sqrt{47}\) forms \(\sqrt{48}\). In the previous step the number is (1) less.

Step 3

Exam Tip

\(\sqrt{47}\) में (1) इकाई लंब जोड़ने पर \(\sqrt{48}\) बनता है। पिछले चरण में संख्या (1) कम होती है।

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वर्गमूल सर्पिल में \(\sqrt{8}\) के लिए कौन-सा कथन सही है?

Which statement is correct for \(\sqrt{8}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. यह \(\sqrt{7}\) और (1) इकाई लंब से बनता हैIt is formed from \(\sqrt{7}\) and a (1) unit perpendicular

Step 1

Concept

In the usual sequence of the square root spiral, \(\sqrt{8}\) comes after \(\sqrt{7}\). The new perpendicular is always (1) unit.

Step 2

Why this answer is correct

The correct answer is A. यह \(\sqrt{7}\) और (1) इकाई लंब से बनता है / It is formed from \(\sqrt{7}\) and a (1) unit perpendicular. In the usual sequence of the square root spiral, \(\sqrt{8}\) comes after \(\sqrt{7}\). The new perpendicular is always (1) unit.

Step 3

Exam Tip

वर्गमूल सर्पिल के सामान्य क्रम में \(\sqrt{7}\) के बाद \(\sqrt{8}\) आता है। नई लंब हमेशा (1) इकाई होती है।

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वर्गमूल सर्पिल में \(\sqrt{20}\) किस प्रकार की संख्या है और क्यों?

What type of number is \(\sqrt{20}\) in a square root spiral and why?

Explanation opens after your attempt
Correct Answer

B. अपरिमेय संख्या, क्योंकि (20) पूर्ण वर्ग नहीं हैIrrational number because (20) is not a perfect square

Step 1

Concept

(20) is not a perfect square. Therefore \(\sqrt{20}\) gives an irrational length.

Step 2

Why this answer is correct

The correct answer is B. अपरिमेय संख्या, क्योंकि (20) पूर्ण वर्ग नहीं है / Irrational number because (20) is not a perfect square. (20) is not a perfect square. Therefore \(\sqrt{20}\) gives an irrational length.

Step 3

Exam Tip

(20) पूर्ण वर्ग नहीं है। इसलिए \(\sqrt{20}\) अपरिमेय लंबाई देता है।

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यदि वर्गमूल सर्पिल में किसी कर्ण की लंबाई \(\sqrt{m}\) है और (m) पूर्ण वर्ग है, तो उस लंबाई के बारे में क्या कहा जा सकता है?

If a hypotenuse in a square root spiral has length \(\sqrt{m}\) and (m) is a perfect square, what can be said about that length?

Explanation opens after your attempt
Correct Answer

A. वह पूर्ण संख्या होगीIt will be a whole number

Step 1

Concept

The square root of a perfect square is a whole number. For example, \(\sqrt{25}=5\).

Step 2

Why this answer is correct

The correct answer is A. वह पूर्ण संख्या होगी / It will be a whole number. The square root of a perfect square is a whole number. For example, \(\sqrt{25}=5\).

Step 3

Exam Tip

पूर्ण वर्ग का वर्गमूल पूर्ण संख्या होता है। जैसे \(\sqrt{25}=5\)।

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वर्गमूल सर्पिल में \(\sqrt{3}\) बनाने के बाद \(\sqrt{4}\) का कर्ण बनने पर लंबाई किस पूर्ण संख्या के बराबर हो जाती है?

After constructing \(\sqrt{3}\) in a square root spiral, when \(\sqrt{4}\) is formed, the length becomes equal to which whole number?

Explanation opens after your attempt
Correct Answer

B. (2)

Step 1

Concept

\(\sqrt{4}=2\). At some steps the square root can also be a whole number.

Step 2

Why this answer is correct

The correct answer is B. (2). \(\sqrt{4}=2\). At some steps the square root can also be a whole number.

Step 3

Exam Tip

\(\sqrt{4}=2\) होता है। कुछ चरणों पर वर्गमूल पूर्ण संख्या भी हो सकता है।

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वर्गमूल सर्पिल में \(\sqrt{72}\) के लिए सही संख्या-रेखा स्थान कौन-सा है?

Which number-line location is correct for \(\sqrt{72}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

B. \(8<\sqrt{72}<9\)

Step 1

Concept

Because \(8^2=64\) and \(9^2=81\). The number (72) lies between them.

Step 2

Why this answer is correct

The correct answer is B. \(8<\sqrt{72}<9\). Because \(8^2=64\) and \(9^2=81\). The number (72) lies between them.

Step 3

Exam Tip

क्योंकि \(8^2=64\) और \(9^2=81\) हैं। (72) इनके बीच है।

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वर्गमूल सर्पिल में \(\sqrt{2}\) से \(\sqrt{3}\) बनने का सही कारण कौन-सा है?

What is the correct reason for \(\sqrt{3}\) being formed from \(\sqrt{2}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. (\(\sqrt{2}\)2+12=3)

Step 1

Concept

By Pythagoras theorem, the squares of the sides are added. Therefore the new hypotenuse becomes \(\sqrt{3}\).

Step 2

Why this answer is correct

The correct answer is A. (\(\sqrt{2}\)2+12=3). By Pythagoras theorem, the squares of the sides are added. Therefore the new hypotenuse becomes \(\sqrt{3}\).

Step 3

Exam Tip

पाइथागोरस प्रमेय से भुजाओं के वर्ग जुड़ते हैं। इसलिए नया कर्ण \(\sqrt{3}\) बनता है।

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वर्गमूल सर्पिल में \(\sqrt{100}\) से अगला कर्ण कौन-सा होगा और \(\sqrt{100}\) की लंबाई क्या है?

In a square root spiral, which hypotenuse comes after \(\sqrt{100}\) and what is the length of \(\sqrt{100}\)?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{101}\) और (10)\(\sqrt{101}\) and (10)

Step 1

Concept

\(\sqrt{100}=10\) and the next hypotenuse is \(\sqrt{101}\). The number increases by one in the sequence.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{101}\) और (10) / \(\sqrt{101}\) and (10). \(\sqrt{100}=10\) and the next hypotenuse is \(\sqrt{101}\). The number increases by one in the sequence.

Step 3

Exam Tip

\(\sqrt{100}=10\) और अगला कर्ण \(\sqrt{101}\) होगा। क्रम में संख्या एक बढ़ती है।

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वर्गमूल सर्पिल में \(\sqrt{27}\) को संख्या रेखा पर रखने से पहले कौन-सा अंतराल पहचानना चाहिए?

Before placing \(\sqrt{27}\) on the number line using a square root spiral, which interval should be identified?

Explanation opens after your attempt
Correct Answer

B. (5) और (6)(5) and (6)

Step 1

Concept

Because \(5^2<27<6^2\). Therefore \(\sqrt{27}\) lies between (5) and (6).

Step 2

Why this answer is correct

The correct answer is B. (5) और (6) / (5) and (6). Because \(5^2<27<6^2\). Therefore \(\sqrt{27}\) lies between (5) and (6).

Step 3

Exam Tip

क्योंकि \(5^2<27<6^2\) है। इसलिए \(\sqrt{27}\) (5) और (6) के बीच होगा।

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वर्गमूल सर्पिल में किस स्थिति में कर्ण पूर्ण संख्या नहीं होगा?

In a square root spiral, in which situation will the hypotenuse not be a whole number?

Explanation opens after your attempt
Correct Answer

D. जब कर्ण \(\sqrt{38}\) होWhen the hypotenuse is \(\sqrt{38}\)

Step 1

Concept

The number (38) is not a perfect square. Therefore \(\sqrt{38}\) will not be a whole number.

Step 2

Why this answer is correct

The correct answer is D. जब कर्ण \(\sqrt{38}\) हो / When the hypotenuse is \(\sqrt{38}\). The number (38) is not a perfect square. Therefore \(\sqrt{38}\) will not be a whole number.

Step 3

Exam Tip

(38) पूर्ण वर्ग नहीं है। इसलिए \(\sqrt{38}\) पूर्ण संख्या नहीं होगा।

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वर्गमूल सर्पिल में यदि \(\sqrt{14}\) कर्ण पर (1) इकाई लंब बनती है, तो नया कर्ण किस अंतराल में आएगा?

If a (1) unit perpendicular is drawn on hypotenuse \(\sqrt{14}\) in a square root spiral, in which interval will the new hypotenuse lie?

Explanation opens after your attempt
Correct Answer

B. (3) और (4) के बीचBetween (3) and (4)

Step 1

Concept

The new hypotenuse will be \(\sqrt{15}\). Since \(3^2<15<4^2\), it lies between (3) and (4).

Step 2

Why this answer is correct

The correct answer is B. (3) और (4) के बीच / Between (3) and (4). The new hypotenuse will be \(\sqrt{15}\). Since \(3^2<15<4^2\), it lies between (3) and (4).

Step 3

Exam Tip

नया कर्ण \(\sqrt{15}\) होगा। क्योंकि \(3^2<15<4^2\), यह (3) और (4) के बीच है।

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वर्गमूल सर्पिल में \(\sqrt{121}\) बनाने से ठीक पहले कौन-सा कर्ण होना चाहिए?

Just before constructing \(\sqrt{121}\) in a square root spiral, which hypotenuse should be present?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{120}\)

Step 1

Concept

Adding a (1) unit perpendicular to \(\sqrt{120}\) forms \(\sqrt{121}\). This is the rule of stepwise construction.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{120}\). Adding a (1) unit perpendicular to \(\sqrt{120}\) forms \(\sqrt{121}\). This is the rule of stepwise construction.

Step 3

Exam Tip

\(\sqrt{120}\) में (1) इकाई लंब जोड़ने पर \(\sqrt{121}\) बनता है। यह क्रमिक निर्माण का नियम है।

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वर्गमूल सर्पिल में \(\sqrt{2}\) और \(\sqrt{3}\) दोनों संख्या रेखा पर (1) और (2) के बीच क्यों आते हैं?

Why do both \(\sqrt{2}\) and \(\sqrt{3}\) lie between (1) and (2) on the number line in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. क्योंकि \(1^2<2,3<2^2\)Because \(1^2<2,3<2^2\)

Step 1

Concept

Both (2) and (3) are between (1) and (4). Therefore their square roots lie between (1) and (2).

Step 2

Why this answer is correct

The correct answer is A. क्योंकि \(1^2<2,3<2^2\) / Because \(1^2<2,3<2^2\). Both (2) and (3) are between (1) and (4). Therefore their square roots lie between (1) and (2).

Step 3

Exam Tip

(2) और (3) दोनों (1) और (4) के बीच हैं। इसलिए उनके वर्गमूल (1) और (2) के बीच आते हैं।

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वर्गमूल सर्पिल में \(\sqrt{50}\) किस अंतराल में होगा?

In a square root spiral, in which interval will \(\sqrt{50}\) lie?

Explanation opens after your attempt
Correct Answer

C. (7) और (8) के बीचBetween (7) and (8)

Step 1

Concept

Because \(7^2<50<8^2\). Therefore \(\sqrt{50}\) lies between (7) and (8).

Step 2

Why this answer is correct

The correct answer is C. (7) और (8) के बीच / Between (7) and (8). Because \(7^2<50<8^2\). Therefore \(\sqrt{50}\) lies between (7) and (8).

Step 3

Exam Tip

क्योंकि \(7^2<50<8^2\) है। इसलिए \(\sqrt{50}\) (7) और (8) के बीच है।

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वर्गमूल सर्पिल में \(\sqrt{1}\) से \(\sqrt{2}\) बनने में कौन-सा संबंध सही है?

Which relation is correct in forming \(\sqrt{2}\) from \(\sqrt{1}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

In the first step the sides are (1) and (1) units. The hypotenuse \(\sqrt{2}\) is obtained by Pythagoras theorem.

Step 2

Why this answer is correct

The correct answer is A. (\(\sqrt{1}\)2+12=2). In the first step the sides are (1) and (1) units. The hypotenuse \(\sqrt{2}\) is obtained by Pythagoras theorem.

Step 3

Exam Tip

पहले चरण में (1) और (1) इकाई भुजाएँ होती हैं। कर्ण \(\sqrt{2}\) पाइथागोरस से मिलता है।

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वर्गमूल सर्पिल में \(\sqrt{75}\) बनाने के लिए पिछले कर्ण पर क्या करना होगा?

What must be done on the previous hypotenuse to construct \(\sqrt{75}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{74}\) पर (1) इकाई लंब बनानी होगीDraw a (1) unit perpendicular on \(\sqrt{74}\)

Step 1

Concept

\(\sqrt{75}\) is formed from \(\sqrt{74}\) and a (1) unit perpendicular. The previous hypotenuse always has one less number.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{74}\) पर (1) इकाई लंब बनानी होगी / Draw a (1) unit perpendicular on \(\sqrt{74}\). \(\sqrt{75}\) is formed from \(\sqrt{74}\) and a (1) unit perpendicular. The previous hypotenuse always has one less number.

Step 3

Exam Tip

\(\sqrt{74}\) और (1) इकाई लंब से \(\sqrt{75}\) बनता है। पिछला कर्ण हमेशा एक कम संख्या वाला होता है।

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वर्गमूल सर्पिल में \(\sqrt{90}\) को संख्या रेखा पर अंकित करने से पहले सही अंतराल कौन-सा है?

Before marking \(\sqrt{90}\) on the number line using a square root spiral, which interval is correct?

Explanation opens after your attempt
Correct Answer

B. (9) और (10)(9) and (10)

Step 1

Concept

Because \(9^2<90<10^2\). Therefore \(9<\sqrt{90}<10\).

Step 2

Why this answer is correct

The correct answer is B. (9) और (10) / (9) and (10). Because \(9^2<90<10^2\). Therefore \(9<\sqrt{90}<10\).

Step 3

Exam Tip

क्योंकि \(9^2<90<10^2\) है। इसलिए \(9<\sqrt{90}<10\) होता है।

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वर्गमूल सर्पिल में \(\sqrt{64}\) से \(\sqrt{65}\) बनने पर कौन-सा कथन सही है?

When \(\sqrt{65}\) is formed from \(\sqrt{64}\) in a square root spiral, which statement is correct?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{64}=8\) और नया कर्ण \(\sqrt{65}\) है\(\sqrt{64}=8\) and the new hypotenuse is \(\sqrt{65}\)

Step 1

Concept

\(\sqrt{64}=8\) is a whole number. Adding a (1) unit perpendicular forms the next hypotenuse \(\sqrt{65}\).

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{64}=8\) और नया कर्ण \(\sqrt{65}\) है / \(\sqrt{64}=8\) and the new hypotenuse is \(\sqrt{65}\). \(\sqrt{64}=8\) is a whole number. Adding a (1) unit perpendicular forms the next hypotenuse \(\sqrt{65}\).

Step 3

Exam Tip

\(\sqrt{64}=8\) पूर्ण संख्या है। (1) इकाई लंब जोड़ने पर अगला कर्ण \(\sqrt{65}\) बनता है।

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वर्गमूल सर्पिल में \(\sqrt{n}\) को संख्या रेखा पर दिखाने के लिए कौन-सी लंबाई कंपास में ली जाती है?

To show \(\sqrt{n}\) on the number line using a square root spiral, which length is taken in the compass?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{n}\) वाले कर्ण की लंबाईThe length of the hypotenuse \(\sqrt{n}\)

Step 1

Concept

The hypotenuse length of the required square root is taken in the compass. Then an arc is drawn from the origin.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{n}\) वाले कर्ण की लंबाई / The length of the hypotenuse \(\sqrt{n}\). The hypotenuse length of the required square root is taken in the compass. Then an arc is drawn from the origin.

Step 3

Exam Tip

जिस वर्गमूल को अंकित करना है, उसी कर्ण की लंबाई कंपास में ली जाती है। फिर मूल बिंदु से चाप खींचते हैं।

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वर्गमूल सर्पिल में \(\sqrt{45}\) के बाद आने वाला कर्ण और उसका अंतराल कौन-सा है?

In a square root spiral, which hypotenuse comes after \(\sqrt{45}\) and in which interval does it lie?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{46}\), (6) और (7) के बीच\(\sqrt{46}\), between (6) and (7)

Step 1

Concept

The next hypotenuse is \(\sqrt{46}\). Since \(6^2<46<7^2\), it lies between (6) and (7).

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{46}\), (6) और (7) के बीच / \(\sqrt{46}\), between (6) and (7). The next hypotenuse is \(\sqrt{46}\). Since \(6^2<46<7^2\), it lies between (6) and (7).

Step 3

Exam Tip

अगला कर्ण \(\sqrt{46}\) है। क्योंकि \(6^2<46<7^2\), यह (6) और (7) के बीच होगा।

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वर्गमूल सर्पिल में कौन-सा उपकरण किस कार्य के लिए सही जोड़ा गया है?

Which tool is correctly matched with its work in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. कंपास, कर्ण की लंबाई संख्या रेखा पर स्थानांतरित करने के लिएCompass, to transfer hypotenuse length to the number line

Step 1

Concept

A compass is used to take the hypotenuse length and draw an arc on the number line. This is the correct way to transfer the length.

Step 2

Why this answer is correct

The correct answer is A. कंपास, कर्ण की लंबाई संख्या रेखा पर स्थानांतरित करने के लिए / Compass, to transfer hypotenuse length to the number line. A compass is used to take the hypotenuse length and draw an arc on the number line. This is the correct way to transfer the length.

Step 3

Exam Tip

कंपास से कर्ण की लंबाई लेकर संख्या रेखा पर चाप लगाया जाता है। यही लंबाई स्थानांतरित करने का सही तरीका है।

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वर्गमूल सर्पिल में \(\sqrt{125}\) का सही संख्या-रेखा अंतराल कौन-सा है?

What is the correct number-line interval for \(\sqrt{125}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

B. (11) और (12)(11) and (12)

Step 1

Concept

Because \(11^2<125<12^2\). Therefore \(11<\sqrt{125}<12\).

Step 2

Why this answer is correct

The correct answer is B. (11) और (12) / (11) and (12). Because \(11^2<125<12^2\). Therefore \(11<\sqrt{125}<12\).

Step 3

Exam Tip

क्योंकि \(11^2<125<12^2\) है। इसलिए \(11<\sqrt{125}<12\) होगा।

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वर्गमूल सर्पिल में \(\sqrt{2}\) और \(\sqrt{3}\) के निर्माण में समानता क्या है?

What is common in the construction of \(\sqrt{2}\) and \(\sqrt{3}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. दोनों में समकोण त्रिभुज और पाइथागोरस प्रमेय का प्रयोग होता हैBoth use a right triangle and Pythagoras theorem

Step 1

Concept

Both constructions are based on right triangles. The hypotenuse is found by Pythagoras theorem.

Step 2

Why this answer is correct

The correct answer is A. दोनों में समकोण त्रिभुज और पाइथागोरस प्रमेय का प्रयोग होता है / Both use a right triangle and Pythagoras theorem. Both constructions are based on right triangles. The hypotenuse is found by Pythagoras theorem.

Step 3

Exam Tip

दोनों निर्माण समकोण त्रिभुज पर आधारित हैं। कर्ण पाइथागोरस प्रमेय से मिलता है।

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वर्गमूल सर्पिल में यदि \(\sqrt{15}\) बन चुका है, तो अगले चरण में बनने वाले कर्ण की लंबाई किस पूर्ण संख्या के बराबर होगी?

If \(\sqrt{15}\) has been constructed in a square root spiral, in the next step the hypotenuse length will be equal to which whole number?

Explanation opens after your attempt
Correct Answer

B. (4)

Step 1

Concept

After \(\sqrt{15}\), \(\sqrt{16}\) is formed and \(\sqrt{16}=4\). Therefore the next hypotenuse is the whole number (4).

Step 2

Why this answer is correct

The correct answer is B. (4). After \(\sqrt{15}\), \(\sqrt{16}\) is formed and \(\sqrt{16}=4\). Therefore the next hypotenuse is the whole number (4).

Step 3

Exam Tip

\(\sqrt{15}\) के बाद \(\sqrt{16}\) बनता है और \(\sqrt{16}=4\) है। इसलिए अगला कर्ण पूर्ण संख्या (4) है।

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वर्गमूल सर्पिल में \(\sqrt{7}\) बनाने की सही प्रक्रिया कौन-सी है?

What is the correct process to construct \(\sqrt{7}\) in a square root spiral?

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Correct Answer

A. \(\sqrt{6}\) के सिरे पर (1) इकाई लंब बनाकर नया कर्ण लेनाDraw a (1) unit perpendicular at the end of \(\sqrt{6}\) and take the new hypotenuse

Step 1

Concept

From \(\sqrt{6}\) and a (1) unit perpendicular, the new hypotenuse \(\sqrt{7}\) is formed. This is the step rule.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{6}\) के सिरे पर (1) इकाई लंब बनाकर नया कर्ण लेना / Draw a (1) unit perpendicular at the end of \(\sqrt{6}\) and take the new hypotenuse. From \(\sqrt{6}\) and a (1) unit perpendicular, the new hypotenuse \(\sqrt{7}\) is formed. This is the step rule.

Step 3

Exam Tip

\(\sqrt{6}\) और (1) इकाई लंब से नया कर्ण \(\sqrt{7}\) बनता है। यही क्रमिक नियम है।

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वर्गमूल सर्पिल में कौन-सा कथन गलत है और क्यों?

Which statement is wrong for a square root spiral and why?

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Correct Answer

A. सभी कर्ण पूर्ण संख्याएँ होते हैं, क्योंकि हर कर्ण वर्गमूल हैAll hypotenuses are whole numbers because every hypotenuse is a square root

Step 1

Concept

\(\sqrt{2}\) and \(\sqrt{3}\) are not whole numbers. Therefore all hypotenuses cannot be whole numbers.

Step 2

Why this answer is correct

The correct answer is A. सभी कर्ण पूर्ण संख्याएँ होते हैं, क्योंकि हर कर्ण वर्गमूल है / All hypotenuses are whole numbers because every hypotenuse is a square root. \(\sqrt{2}\) and \(\sqrt{3}\) are not whole numbers. Therefore all hypotenuses cannot be whole numbers.

Step 3

Exam Tip

\(\sqrt{2}\) और \(\sqrt{3}\) पूर्ण संख्याएँ नहीं हैं। इसलिए सभी कर्ण पूर्ण संख्याएँ नहीं हो सकते।

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वर्गमूल सर्पिल में \(\sqrt{2}\) की लंबाई को संख्या रेखा पर रखने का सही तरीका कौन-सा है?

What is the correct way to place length \(\sqrt{2}\) on the number line using a square root spiral?

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Correct Answer

A. \(\sqrt{2}\) कर्ण की लंबाई कंपास में लेकर मूल बिंदु से चाप खींचनाTake the \(\sqrt{2}\) hypotenuse length in a compass and draw an arc from the origin

Step 1

Concept

The same hypotenuse length must be taken in the compass. Drawing an arc from the origin gives the correct point.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{2}\) कर्ण की लंबाई कंपास में लेकर मूल बिंदु से चाप खींचना / Take the \(\sqrt{2}\) hypotenuse length in a compass and draw an arc from the origin. The same hypotenuse length must be taken in the compass. Drawing an arc from the origin gives the correct point.

Step 3

Exam Tip

कंपास में वही कर्ण लंबाई लेनी चाहिए जिसे अंकित करना है। मूल बिंदु से चाप खींचने पर सही बिंदु मिलता है।

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वर्गमूल सर्पिल में यदि कोई विद्यार्थी \(\sqrt{n}+1=\sqrt{n+1}\) लिखकर अगला कर्ण बताता है, तो सुधार क्या होगा?

If a student writes \(\sqrt{n}+1=\sqrt{n+1}\) to state the next hypotenuse in a square root spiral, what is the correction?

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Correct Answer

A. सही रूप (\sqrt{\(\sqrt{n}\)2+12}=\sqrt{n+1}) हैThe correct form is (\sqrt{\(\sqrt{n}\)2+12}=\sqrt{n+1})

Step 1

Concept

In a square root spiral, the hypotenuse is formed by Pythagoras theorem. Directly adding lengths is wrong.

Step 2

Why this answer is correct

The correct answer is A. सही रूप (\sqrt{\(\sqrt{n}\)2+12}=\sqrt{n+1}) है / The correct form is (\sqrt{\(\sqrt{n}\)2+12}=\sqrt{n+1}). In a square root spiral, the hypotenuse is formed by Pythagoras theorem. Directly adding lengths is wrong.

Step 3

Exam Tip

वर्गमूल सर्पिल में कर्ण पाइथागोरस से बनता है। सीधे लंबाइयों को जोड़ना गलत है।

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वर्गमूल सर्पिल की मदद से अपरिमेय संख्याओं को संख्या रेखा पर दिखाने का मुख्य विचार क्या है?

What is the main idea of showing irrational numbers on the number line using a square root spiral?

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Correct Answer

A. समकोण त्रिभुजों से वर्गमूल लंबाई बनाकर उसे कंपास से संख्या रेखा पर स्थानांतरित करनाConstruct the square root length using right triangles and transfer it to the number line with a compass

Step 1

Concept

First the exact square root length is constructed. Then the same length is marked on the number line using a compass.

Step 2

Why this answer is correct

The correct answer is A. समकोण त्रिभुजों से वर्गमूल लंबाई बनाकर उसे कंपास से संख्या रेखा पर स्थानांतरित करना / Construct the square root length using right triangles and transfer it to the number line with a compass. First the exact square root length is constructed. Then the same length is marked on the number line using a compass.

Step 3

Exam Tip

पहले सटीक वर्गमूल लंबाई बनाई जाती है। फिर कंपास से उसी लंबाई को संख्या रेखा पर अंकित किया जाता है।

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Class 9 Mathematics Quiz FAQs

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