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100 results found for "same-number" in Class 10.

किस दशमलव संख्या का स्थान संख्या रेखा पर \(\frac{13}{8}\) के बराबर है?

Which decimal number has the same position as \(\frac{13}{8}\) on the number line?

Explanation opens after your attempt
Correct Answer

A. (1.625)

Step 1

Concept

\(\frac{13}{8}=1.625\), so both represent the same point. Convert the fraction into a decimal to identify position.

Step 2

Why this answer is correct

The correct answer is A. (1.625). \(\frac{13}{8}=1.625\), so both represent the same point. Convert the fraction into a decimal to identify position.

Step 3

Exam Tip

\(\frac{13}{8}=1.625\), इसलिए दोनों एक ही बिंदु दर्शाते हैं। भिन्न को दशमलव में बदलकर स्थान पहचानें।

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संख्या रेखा पर \(-\sqrt{16}\) किस संख्या के बराबर स्थान पर होगा?

On the number line, \(-\sqrt{16}\) will be at the same position as which number?

Explanation opens after your attempt
Correct Answer

C. (-4)

Step 1

Concept

\(\sqrt{16}=4\), so \(-\sqrt{16}=-4\). In exams, apply the outside negative sign after finding the square root.

Step 2

Why this answer is correct

The correct answer is C. (-4). \(\sqrt{16}=4\), so \(-\sqrt{16}=-4\). In exams, apply the outside negative sign after finding the square root.

Step 3

Exam Tip

\(\sqrt{16}=4\), इसलिए \(-\sqrt{16}=-4\) है। परीक्षा में वर्गमूल निकालने के बाद बाहर का ऋण चिह्न लगाएं।

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संख्या रेखा पर \(\sqrt{9}\) किस संख्या के बराबर स्थान पर होगा?

On the number line, \(\sqrt{9}\) will be at the same position as which number?

Explanation opens after your attempt
Correct Answer

B. (3)

Step 1

Concept

\(\sqrt{9}=3\), so its position is at (3). In exams, identify square roots of perfect squares quickly.

Step 2

Why this answer is correct

The correct answer is B. (3). \(\sqrt{9}=3\), so its position is at (3). In exams, identify square roots of perfect squares quickly.

Step 3

Exam Tip

\(\sqrt{9}=3\), इसलिए इसका स्थान (3) पर होगा। परीक्षा में पूर्ण वर्गों के वर्गमूल तुरंत पहचानें।

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संख्या रेखा पर \(-2+\frac{1}{2}\) की स्थिति किस संख्या जैसी होगी?

On the number line, \(-2+\frac{1}{2}\) has the same position as which number?

Explanation opens after your attempt
Correct Answer

A. \(-\frac{3}{2}\)

Step 1

Concept

\(-2+\frac{1}{2}=-\frac{4}{2}+\frac{1}{2}=-\frac{3}{2}\). Be careful with direction when adding a fraction to a negative integer.

Step 2

Why this answer is correct

The correct answer is A. \(-\frac{3}{2}\). \(-2+\frac{1}{2}=-\frac{4}{2}+\frac{1}{2}=-\frac{3}{2}\). Be careful with direction when adding a fraction to a negative integer.

Step 3

Exam Tip

\(-2+\frac{1}{2}=-\frac{4}{2}+\frac{1}{2}=-\frac{3}{2}\) है। ऋणात्मक पूर्णांक में भिन्न जोड़ते समय दिशा ध्यान रखें।

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एक संख्या में (6) घटाकर उसे उसी संख्या से गुणा करने पर (135) मिलता है। धनात्मक संख्या क्या है?

When (6) is subtracted from a number and the result is multiplied by the same number, the product is (135). What is the positive number?

Explanation opens after your attempt
Correct Answer

A. (15)

Step 1

Concept

If the number is (x), then (x(x-6)=135). From \(x^2-6x-135=0\), the positive solution is (15).

Step 2

Why this answer is correct

The correct answer is A. (15). If the number is (x), then (x(x-6)=135). From \(x^2-6x-135=0\), the positive solution is (15).

Step 3

Exam Tip

यदि संख्या (x) है, तो (x(x-6)=135)। \(x^2-6x-135=0\) से धनात्मक हल (15) है।

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एक संख्या में (4) घटाकर उसे उसी संख्या से गुणा करने पर (77) मिलता है। धनात्मक संख्या क्या है?

When (4) is subtracted from a number and the result is multiplied by the same number, the product is (77). What is the positive number?

Explanation opens after your attempt
Correct Answer

A. (11)

Step 1

Concept

If the number is (x), then (x(x-4)=77). From \(x^2-4x-77=0\), the positive solution is (11).

Step 2

Why this answer is correct

The correct answer is A. (11). If the number is (x), then (x(x-4)=77). From \(x^2-4x-77=0\), the positive solution is (11).

Step 3

Exam Tip

यदि संख्या (x) है, तो (x(x-4)=77)। \(x^2-4x-77=0\) से धनात्मक हल (11) है।

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संख्या रेखा पर (0.125) किस भिन्न के समान बिंदु है?

On the number line, (0.125) is the same point as which fraction?

Explanation opens after your attempt
Correct Answer

B. \(\frac{1}{8}\)

Step 1

Concept

\(0.125=\frac{125}{1000}=\frac{1}{8}\). Start with denominator (10), (100), or (1000), then simplify.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{1}{8}\). \(0.125=\frac{125}{1000}=\frac{1}{8}\). Start with denominator (10), (100), or (1000), then simplify.

Step 3

Exam Tip

\(0.125=\frac{125}{1000}=\frac{1}{8}\) है। दशमलव को हर (10), (100), या (1000) से शुरू करके सरल करें।

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संख्या रेखा पर (-1.25) के समान बिंदु कौन सा भिन्न दिखाता है?

Which fraction shows the same point as (-1.25) on the number line?

Explanation opens after your attempt
Correct Answer

B. \(-\frac{5}{4}\)

Step 1

Concept

\(-1.25=-\frac{125}{100}=-\frac{5}{4}\). Convert the decimal into a simplified fraction.

Step 2

Why this answer is correct

The correct answer is B. \(-\frac{5}{4}\). \(-1.25=-\frac{125}{100}=-\frac{5}{4}\). Convert the decimal into a simplified fraction.

Step 3

Exam Tip

\(-1.25=-\frac{125}{100}=-\frac{5}{4}\) है। दशमलव को सरल भिन्न में बदलें।

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संख्या रेखा पर (2.125) के समान बिंदु को कौन सा भिन्न दिखाता है?

Which fraction represents the same point as (2.125) on the number line?

Explanation opens after your attempt
Correct Answer

C. \(\frac{17}{8}\)

Step 1

Concept

\(2.125=2+0.125=2+\frac{1}{8}=\frac{17}{8}\). Convert decimals to fractions to identify the same point.

Step 2

Why this answer is correct

The correct answer is C. \(\frac{17}{8}\). \(2.125=2+0.125=2+\frac{1}{8}=\frac{17}{8}\). Convert decimals to fractions to identify the same point.

Step 3

Exam Tip

\(2.125=2+0.125=2+\frac{1}{8}=\frac{17}{8}\) है। दशमलव को भिन्न में बदलकर समान बिंदु पहचानें।

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कौन सा युग्म संख्या रेखा पर एक ही बिंदु को दर्शाता है?

Which pair represents the same point on the number line?

Explanation opens after your attempt
Correct Answer

B. \(\frac{3}{4}\) और (0.75)\(\frac{3}{4}\) and (0.75)

Step 1

Concept

\(\frac{3}{4}=0.75\), so both are the same point. Convert forms to identify equal points.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{3}{4}\) और (0.75) / \(\frac{3}{4}\) and (0.75). \(\frac{3}{4}=0.75\), so both are the same point. Convert forms to identify equal points.

Step 3

Exam Tip

\(\frac{3}{4}=0.75\), इसलिए दोनों एक ही बिंदु हैं। समान बिंदु पहचानने के लिए रूप बदलें।

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संख्या रेखा पर \(-\frac{1}{2}\) किसके बराबर स्थान पर होगा?

On the number line \(-\frac{1}{2}\) will be at the same position as which value?

Explanation opens after your attempt
Correct Answer

A. (-0.5)

Step 1

Concept

\(-\frac{1}{2}=-0.5\), so both represent the same point. Converting fractions to decimals makes comparison easier.

Step 2

Why this answer is correct

The correct answer is A. (-0.5). \(-\frac{1}{2}=-0.5\), so both represent the same point. Converting fractions to decimals makes comparison easier.

Step 3

Exam Tip

\(-\frac{1}{2}=-0.5\), इसलिए दोनों एक ही बिंदु दिखाते हैं। भिन्न को दशमलव में बदलना तुलना को आसान बनाता है।

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संख्या रेखा पर \(\sqrt{9}\) किस बिंदु के समान है?

On the number line \(\sqrt{9}\) is the same as which point?

Explanation opens after your attempt
Correct Answer

B. (3)

Step 1

Concept

\(\sqrt{9}=3\), so it is located at point (3). Learn square roots of perfect squares for quick answers.

Step 2

Why this answer is correct

The correct answer is B. (3). \(\sqrt{9}=3\), so it is located at point (3). Learn square roots of perfect squares for quick answers.

Step 3

Exam Tip

\(\sqrt{9}=3\), इसलिए यह बिंदु (3) पर होगा। पूर्ण वर्गों के वर्गमूल तुरंत पहचानें।

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संख्या रेखा पर (0.6) किस भिन्न के बराबर स्थान पर होगा?

On the number line, (0.6) is at the same position as which fraction?

Explanation opens after your attempt
Correct Answer

A. \(\frac{3}{5}\)

Step 1

Concept

\(0.6=\frac{6}{10}=\frac{3}{5}\). Use place value to convert decimals into fractions.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{3}{5}\). \(0.6=\frac{6}{10}=\frac{3}{5}\). Use place value to convert decimals into fractions.

Step 3

Exam Tip

\(0.6=\frac{6}{10}=\frac{3}{5}\) है। दशमलव के स्थान मान को भिन्न में बदलें।

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संख्या रेखा पर \(-\frac{17}{5}\) किस मिश्र संख्या के बराबर स्थान पर होगा?

At which mixed number position will \(-\frac{17}{5}\) lie on the number line?

Explanation opens after your attempt
Correct Answer

B. \(-3-\frac{2}{5}\)

Step 1

Concept

\(-\frac{17}{5}=-3-\frac{2}{5}\), so it lies between (-4) and (-3). In exams, keep the sign of a negative mixed number correct.

Step 2

Why this answer is correct

The correct answer is B. \(-3-\frac{2}{5}\). \(-\frac{17}{5}=-3-\frac{2}{5}\), so it lies between (-4) and (-3). In exams, keep the sign of a negative mixed number correct.

Step 3

Exam Tip

\(-\frac{17}{5}=-3-\frac{2}{5}\), इसलिए यह (-4) और (-3) के बीच है। परीक्षा में ऋणात्मक मिश्र संख्या का चिह्न ठीक रखें।

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संख्या रेखा पर \(\frac{13}{4}\) को किस मिश्र संख्या के रूप में दिखाया जाएगा?

How will \(\frac{13}{4}\) be shown as a mixed number on the number line?

Explanation opens after your attempt
Correct Answer

A. \(3+\frac{1}{4}\)

Step 1

Concept

\(\frac{13}{4}=3+\frac{1}{4}\), so it lies one-fourth after (3). In exams, convert an improper fraction into a mixed number.

Step 2

Why this answer is correct

The correct answer is A. \(3+\frac{1}{4}\). \(\frac{13}{4}=3+\frac{1}{4}\), so it lies one-fourth after (3). In exams, convert an improper fraction into a mixed number.

Step 3

Exam Tip

\(\frac{13}{4}=3+\frac{1}{4}\), इसलिए यह (3) के बाद एक चौथाई पर होगा। परीक्षा में विषम भिन्न को मिश्र संख्या में बदलें।

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संख्या रेखा पर \(\frac{5}{4}\) को मिश्र संख्या के रूप में कहां रखा जाएगा?

Where will \(\frac{5}{4}\) be placed as a mixed number on the number line?

Explanation opens after your attempt
Correct Answer

A. \(1+\frac{1}{4}\)

Step 1

Concept

\(\frac{5}{4}=1+\frac{1}{4}\), so it is one-fourth after (1). In exams, convert an improper fraction into mixed form.

Step 2

Why this answer is correct

The correct answer is A. \(1+\frac{1}{4}\). \(\frac{5}{4}=1+\frac{1}{4}\), so it is one-fourth after (1). In exams, convert an improper fraction into mixed form.

Step 3

Exam Tip

\(\frac{5}{4}=1+\frac{1}{4}\), इसलिए यह (1) के बाद एक चौथाई भाग पर है। परीक्षा में अपूर्ण भिन्न को मिश्र रूप में बदलें।

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एक दो अंकों की संख्या में अंकों का योग (12) है। उस संख्या और उलटी संख्या का गुणनफल (4032) है। मूल संख्या कौन-सी हो सकती है?

A two-digit number has digit sum (12). The product of the number and its reversed number is (4032). Which can be the original number?

Explanation opens after your attempt
Correct Answer

B. (48)

Step 1

Concept

The reverse of (48) is (84), and \(48 \times 84=4032\). In digit problems, checking the reversed number is essential.

Step 2

Why this answer is correct

The correct answer is B. (48). The reverse of (48) is (84), and \(48 \times 84=4032\). In digit problems, checking the reversed number is essential.

Step 3

Exam Tip

(48) की उलटी संख्या (84) है और \(48 \times 84=4032\)। अंकों की समस्याओं में उलटी संख्या भी जाँचना जरूरी है।

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एक दुकानदार के पास (126) लाल पेन और (210) नीले पेन हैं। वह समान प्रकार के अधिकतम पैकेट बनाना चाहता है ताकि हर पैकेट में लाल पेन की संख्या समान और नीले पेन की संख्या समान हो। अधिकतम कितने पैकेट बनेंगे?

A shopkeeper has (126) red pens and (210) blue pens. He wants to make the maximum number of identical packets so that each packet has the same number of red pens and the same number of blue pens. How many packets can he make?

Explanation opens after your attempt
Correct Answer

A. (42)

Step 1

Concept

The maximum number of identical packets is found by HCF.

Step 2

Why this answer is correct

\(126=2\times3^2\times7\) and \(210=2\times3\times5\times7\), so HCF \(=2\times3\times7=42\).

Step 3

Exam Tip

For maximum equal distribution, find the HCF. चरण 1: अधिकतम समान पैकेटों की संख्या महत्तम समापवर्तक से मिलती है। चरण 2: \(126=2\times3^2\times7\) और \(210=2\times3\times5\times7\), इसलिए महत्तम समापवर्तक \(2\times3\times7=42\) है। चरण 3: अधिकतम समान बाँटने वाले प्रश्न में महत्तम समापवर्तक खोजें।

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सबसे बड़ी वह संख्या कौन-सी है जिससे (742), (1018) और (1450) को भाग देने पर समान शेष बचे?

What is the greatest number that leaves the same remainder when dividing (742), (1018), and (1450)?

Explanation opens after your attempt
Correct Answer

B. (6)

Step 1

Concept

For the same remainder, take the HCF of the differences.

Step 2

Why this answer is correct

The differences are (276), (432), and (708); their HCF is (12).

Step 3

Exam Tip

Use the differences, not the original numbers directly. चरण 1: समान शेष के लिए संख्याओं के अंतरों का महत्तम समापवर्तक लेते हैं। चरण 2: अंतर (1018-742=276), (1450-1018=432) और (1450-742=708) हैं; इनका महत्तम समापवर्तक (12) है। चरण 3: मूल संख्याओं का नहीं, उनके अंतरों का महत्तम समापवर्तक लें।

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सबसे बड़ी वह संख्या कौन-सी है जिससे (489), (654) और (909) को भाग देने पर समान शेष बचे?

What is the greatest number that leaves the same remainder when dividing (489), (654), and (909)?

Explanation opens after your attempt
Correct Answer

A. (15)

Step 1

Concept

For the same remainder, take the HCF of the differences of the given numbers.

Step 2

Why this answer is correct

The differences are (165), (255), and (420); their HCF is (15).

Step 3

Exam Tip

In same-remainder divisor questions, work with differences. चरण 1: समान शेष के लिए दी गई संख्याओं के अंतरों का महत्तम समापवर्तक लेते हैं। चरण 2: अंतर (654-489=165), (909-654=255) और (909-489=420) हैं; इनका महत्तम समापवर्तक (15) है। चरण 3: समान शेष वाले बड़े भाजक के प्रश्न में मूल संख्याओं के अंतरों पर काम करें।

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यदि दो रेखाओं की ढाल समान और अवरोध भी समान हो, तो उनके समीकरणों के युग्म में कितने हल होंगे?

If two lines have the same slope and the same intercept, how many solutions will their pair of equations have?

Explanation opens after your attempt
Correct Answer

C. अनंत हलInfinitely many solutions

Step 1

Concept

Same slope and same intercept mean the same line. Therefore, such a pair has infinitely many solutions.

Step 2

Why this answer is correct

The correct answer is C. अनंत हल / Infinitely many solutions. Same slope and same intercept mean the same line. Therefore, such a pair has infinitely many solutions.

Step 3

Exam Tip

समान ढाल और समान अवरोध का अर्थ एक ही रेखा है। इसलिए ऐसे युग्म में अनंत हल होते हैं।

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यदि दो रेखाओं की ढाल समान और (y)-अवरोध भी समान हो, तो युग्म के हल कैसे होंगे?

If two lines have the same slope and the same (y)-intercept, what will be the solutions of the pair?

Explanation opens after your attempt
Correct Answer

C. अनंत हलInfinitely many solutions

Step 1

Concept

Same slope and same intercept mean both lines are identical. Therefore, the pair has infinitely many solutions.

Step 2

Why this answer is correct

The correct answer is C. अनंत हल / Infinitely many solutions. Same slope and same intercept mean both lines are identical. Therefore, the pair has infinitely many solutions.

Step 3

Exam Tip

समान ढाल और समान अवरोध का अर्थ है कि दोनों रेखाएं एक ही हैं। इसलिए युग्म के अनंत हल होते हैं।

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यदि दो रेखाओं की ढाल समान और अवरोध भी समान हो, तो युग्म का प्रकार क्या होगा?

If two lines have the same slope and the same intercept, what will be the type of pair?

Explanation opens after your attempt
Correct Answer

C. संगत और आश्रितConsistent and dependent

Step 1

Concept

Same slope and same intercept mean both lines are identical. Therefore, the pair is consistent and dependent.

Step 2

Why this answer is correct

The correct answer is C. संगत और आश्रित / Consistent and dependent. Same slope and same intercept mean both lines are identical. Therefore, the pair is consistent and dependent.

Step 3

Exam Tip

समान ढाल और समान अवरोध का मतलब दोनों रेखाएं एक ही हैं। इसलिए युग्म संगत और आश्रित होता है।

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यदि दो रेखाओं की ढाल समान और (y)-अवरोध भी समान हो, तो युग्म का प्रकार क्या होगा?

If two lines have the same slope and the same (y)-intercept, what will be the type of pair?

Explanation opens after your attempt
Correct Answer

C. संगत और आश्रितConsistent and dependent

Step 1

Concept

Same slope and same intercept mean both lines are the same. Therefore, the pair is consistent and dependent.

Step 2

Why this answer is correct

The correct answer is C. संगत और आश्रित / Consistent and dependent. Same slope and same intercept mean both lines are the same. Therefore, the pair is consistent and dependent.

Step 3

Exam Tip

समान ढाल और समान अवरोध का मतलब दोनों रेखाएं एक ही हैं। इसलिए युग्म संगत और आश्रित है।

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यदि दो रेखाओं की ढाल और अवरोध दोनों समान हों तो रेखाएं कैसी होंगी?

If two lines have the same slope and the same intercept then what kind of lines will they be?

Explanation opens after your attempt
Correct Answer

C. संपातीCoincident

Step 1

Concept

Same slope and same intercept mean both lines are the same. Therefore they have infinitely many solutions.

Step 2

Why this answer is correct

The correct answer is C. संपाती / Coincident. Same slope and same intercept mean both lines are the same. Therefore they have infinitely many solutions.

Step 3

Exam Tip

समान ढाल और समान अवरोध का मतलब दोनों रेखाएं एक ही हैं। इसलिए उनके अनंत हल होते हैं।

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यदि दो रेखाओं की ढाल समान और अवरोध समान हो तो हलों की संख्या क्या होगी?

If two lines have the same slope and the same intercept then how many solutions will there be?

Explanation opens after your attempt
Correct Answer

C. अनंत हलInfinitely many solutions

Step 1

Concept

Same slope and same intercept make both lines identical. Therefore infinitely many solutions are obtained.

Step 2

Why this answer is correct

The correct answer is C. अनंत हल / Infinitely many solutions. Same slope and same intercept make both lines identical. Therefore infinitely many solutions are obtained.

Step 3

Exam Tip

समान ढाल और समान अवरोध से दोनों रेखाएं एक ही हो जाती हैं। इसलिए अनंत हल मिलते हैं।

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यदि दो रेखाओं की ढाल और अवरोध दोनों समान हों, तो वे कैसी रेखाएं होंगी?

If two lines have the same slope and the same intercept, what kind of lines are they?

Explanation opens after your attempt
Correct Answer

B. संपाती रेखाएंCoincident lines

Step 1

Concept

Same slope and same intercept make both lines identical. Therefore, they have infinitely many solutions.

Step 2

Why this answer is correct

The correct answer is B. संपाती रेखाएं / Coincident lines. Same slope and same intercept make both lines identical. Therefore, they have infinitely many solutions.

Step 3

Exam Tip

समान ढाल और समान अवरोध से दोनों रेखाएं एक ही होती हैं। इसलिए उनके अनंत हल होते हैं।

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एक ही फूल या उसी पौधे के फूल में परागण होना क्या कहलाता है?

Pollination within the same flower or another flower of the same plant is called what?

Explanation opens after your attempt
Correct Answer

A. स्वपरागणSelf pollination

Step 1

Concept

When pollen reaches the stigma of the same plant no other plant is involved.

Step 2

Why this answer is correct

This is a simple form of pollination.

Step 3

Exam Tip

It is called self pollination. चरण 1: जब परागकण उसी पौधे के वर्तिकाग्र तक पहुंचते हैं तो दूसरा पौधा शामिल नहीं होता। चरण 2: यह परागण का सरल रूप है। चरण 3: इसे स्वपरागण कहते हैं।

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किस संख्या की (0) से दूरी \( \sqrt{41} \) है और वह (0) के बाईं ओर है?

Which number has distance \( \sqrt{41} \) from (0) and lies to the left of (0) on the number line?

Explanation opens after your attempt
Correct Answer

B. \( -\sqrt{41} \)

Step 1

Concept

The point on the left is negative and its distance is \( \sqrt{41} \). Therefore the number is \( -\sqrt{41} \).

Step 2

Why this answer is correct

The correct answer is B. \( -\sqrt{41} \). The point on the left is negative and its distance is \( \sqrt{41} \). Therefore the number is \( -\sqrt{41} \).

Step 3

Exam Tip

बाईं ओर का बिंदु ऋणात्मक होगा और दूरी \( \sqrt{41} \) है। इसलिए संख्या \( -\sqrt{41} \) है।

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संख्या रेखा पर \(0.7272272227\ldots\) किस प्रकार की संख्या है?

What type of number is \(0.7272272227\ldots\) on the number line?

Explanation opens after your attempt
Correct Answer

B. अपरिमेय संख्याIrrational number

Step 1

Concept

This decimal is non-terminating and non-repeating, so it is irrational. Check whether the decimal pattern truly repeats or not.

Step 2

Why this answer is correct

The correct answer is B. अपरिमेय संख्या / Irrational number. This decimal is non-terminating and non-repeating, so it is irrational. Check whether the decimal pattern truly repeats or not.

Step 3

Exam Tip

यह दशमलव असांत और अनावर्ती है, इसलिए अपरिमेय है। दशमलव पैटर्न सच में दोहरता है या नहीं, यह जाँचें।

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किस संख्या की (0) से दूरी \( \sqrt{26} \) है और वह (0) के दाईं ओर है?

Which number has distance \( \sqrt{26} \) from (0) and lies to the right of (0) on the number line?

Explanation opens after your attempt
Correct Answer

B. \( \sqrt{26} \)

Step 1

Concept

The point on the right is positive and its distance is \( \sqrt{26} \). Therefore the number is \( \sqrt{26} \).

Step 2

Why this answer is correct

The correct answer is B. \( \sqrt{26} \). The point on the right is positive and its distance is \( \sqrt{26} \). Therefore the number is \( \sqrt{26} \).

Step 3

Exam Tip

दाईं ओर का बिंदु धनात्मक होगा और दूरी \( \sqrt{26} \) है। इसलिए संख्या \( \sqrt{26} \) है।

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संख्या रेखा पर \(0.6161161116\ldots\) किस प्रकार की संख्या है?

What type of number is \(0.6161161116\ldots\) on the number line?

Explanation opens after your attempt
Correct Answer

B. अपरिमेय संख्याIrrational number

Step 1

Concept

This decimal is non-terminating and non-repeating, so it is irrational. Check carefully whether the pattern repeats or not.

Step 2

Why this answer is correct

The correct answer is B. अपरिमेय संख्या / Irrational number. This decimal is non-terminating and non-repeating, so it is irrational. Check carefully whether the pattern repeats or not.

Step 3

Exam Tip

यह दशमलव असांत और अनावर्ती है, इसलिए अपरिमेय है। पैटर्न दोहराव वाला है या नहीं, इसे ध्यान से देखें।

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किस संख्या की (0) से दूरी संख्या रेखा पर \( \sqrt{17} \) है और वह (0) के बाईं ओर है?

Which number has distance \( \sqrt{17} \) from (0) and lies to the left of (0) on the number line?

Explanation opens after your attempt
Correct Answer

A. \( -\sqrt{17} \)

Step 1

Concept

The point on the left is negative and its distance is \( \sqrt{17} \). Therefore the number is \( -\sqrt{17} \).

Step 2

Why this answer is correct

The correct answer is A. \( -\sqrt{17} \). The point on the left is negative and its distance is \( \sqrt{17} \). Therefore the number is \( -\sqrt{17} \).

Step 3

Exam Tip

बाईं ओर का बिंदु ऋणात्मक होगा और दूरी \( \sqrt{17} \) है। इसलिए संख्या \( -\sqrt{17} \) है।

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संख्या रेखा पर \(0.2727727772\ldots\) किस प्रकार की संख्या है?

What type of number is \(0.2727727772\ldots\) on the number line?

Explanation opens after your attempt
Correct Answer

A. अपरिमेय संख्याIrrational number

Step 1

Concept

This decimal is non-terminating and non-repeating. Hence it is an irrational number on the number line.

Step 2

Why this answer is correct

The correct answer is A. अपरिमेय संख्या / Irrational number. This decimal is non-terminating and non-repeating. Hence it is an irrational number on the number line.

Step 3

Exam Tip

यह दशमलव असांत और अनावर्ती है। इसलिए यह संख्या रेखा पर अपरिमेय संख्या है।

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कौन सी संख्या \( \sqrt{8} \) और (3) के बीच संख्या रेखा पर स्थित है?

Which number lies between \( \sqrt{8} \) and (3) on the number line?

Explanation opens after your attempt
Correct Answer

A. (2.9)

Step 1

Concept

\( \sqrt{8}\approx2.828\), so (2.9) lies between it and (3). First estimate the irrational number.

Step 2

Why this answer is correct

The correct answer is A. (2.9). \( \sqrt{8}\approx2.828\), so (2.9) lies between it and (3). First estimate the irrational number.

Step 3

Exam Tip

\( \sqrt{8}\approx2.828\), इसलिए (2.9) उसके और (3) के बीच है। पहले अपरिमेय संख्या का अनुमान करें।

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किस संख्या को संख्या रेखा पर \(\sqrt{25}-\sqrt{4}\) के रूप में दर्शाया जा सकता है?

Which number can be represented as \(\sqrt{25}-\sqrt{4}\) on the number line?

Explanation opens after your attempt
Correct Answer

A. (3)

Step 1

Concept

\(\sqrt{25}=5\) and \(\sqrt{4}=2\), so \(\sqrt{25}-\sqrt{4}=3\). Simplify perfect squares immediately.

Step 2

Why this answer is correct

The correct answer is A. (3). \(\sqrt{25}=5\) and \(\sqrt{4}=2\), so \(\sqrt{25}-\sqrt{4}=3\). Simplify perfect squares immediately.

Step 3

Exam Tip

\(\sqrt{25}=5\) और \(\sqrt{4}=2\), इसलिए \(\sqrt{25}-\sqrt{4}=3\)। पूर्ण वर्गों को तुरंत सरल करें।

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संख्या रेखा पर कौन-सी संख्या \(\sqrt{9.61}\) के बराबर है?

Which number is equal to \(\sqrt{9.61}\) on the number line?

Explanation opens after your attempt
Correct Answer

A. (3.1)

Step 1

Concept

Because \(3.1^2=9.61\), \(\sqrt{9.61}=3.1\). Multiply decimal squares carefully.

Step 2

Why this answer is correct

The correct answer is A. (3.1). Because \(3.1^2=9.61\), \(\sqrt{9.61}=3.1\). Multiply decimal squares carefully.

Step 3

Exam Tip

क्योंकि \(3.1^2=9.61\), इसलिए \(\sqrt{9.61}=3.1\)। दशमलव वर्गों को सावधानी से गुणा करें।

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यदि (A) संख्या रेखा पर \(\sqrt{18}\) है, तो (A) किसके सबसे निकट होगा?

If (A) is \(\sqrt{18}\) on the number line, to which number is (A) closest?

Explanation opens after your attempt
Correct Answer

A. (4.24)

Step 1

Concept

\(\sqrt{18}=3\sqrt{2}\approx4.242\), so (4.24) is closest. Simplification makes estimation easier.

Step 2

Why this answer is correct

The correct answer is A. (4.24). \(\sqrt{18}=3\sqrt{2}\approx4.242\), so (4.24) is closest. Simplification makes estimation easier.

Step 3

Exam Tip

\(\sqrt{18}=3\sqrt{2}\approx4.242\), इसलिए (4.24) सबसे निकट है। सरलीकरण अनुमान को आसान बनाता है।

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कौन-सी संख्या रेखा पर \(\sqrt{6}\) के सबसे निकट है?

Which number is closest to \(\sqrt{6}\) on the number line?

Explanation opens after your attempt
Correct Answer

A. (2.45)

Step 1

Concept

\(\sqrt{6}\approx2.449\), so (2.45) is closest. To test closeness, compare differences from the approximate value.

Step 2

Why this answer is correct

The correct answer is A. (2.45). \(\sqrt{6}\approx2.449\), so (2.45) is closest. To test closeness, compare differences from the approximate value.

Step 3

Exam Tip

\(\sqrt{6}\approx2.449\), इसलिए (2.45) सबसे निकट है। निकटता के लिए अनुमानित मान से अंतर जाँचें।

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संख्या रेखा पर कौन-सी संख्या (1) से छोटी और (0) से बड़ी अपरिमेय संख्या है?

Which number is irrational and lies between (0) and (1) on the number line?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

\(\frac{\sqrt{2}}{2}\) is irrational and its value lies between (0) and (1). An irrational divided by a non-zero rational remains irrational.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{\sqrt{2}}{2}\). \(\frac{\sqrt{2}}{2}\) is irrational and its value lies between (0) and (1). An irrational divided by a non-zero rational remains irrational.

Step 3

Exam Tip

\(\frac{\sqrt{2}}{2}\) अपरिमेय है और इसका मान (0) और (1) के बीच है। अपरिमेय संख्या को परिमेय से भाग देने पर शून्येतर परिमेय के लिए अपरिमेय ही रहती है।

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किस संख्या को संख्या रेखा पर (0) और (1) के ठीक बीच में दर्शाया जाता है?

Which number is represented exactly midway between (0) and (1) on the number line?

Explanation opens after your attempt
Correct Answer

A. \(\frac{1}{2}\)

Step 1

Concept

The midpoint of (0) and (1) is \(\frac{0+1}{2}=\frac{1}{2}\). To find a midpoint on a number line, take the average.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{1}{2}\). The midpoint of (0) and (1) is \(\frac{0+1}{2}=\frac{1}{2}\). To find a midpoint on a number line, take the average.

Step 3

Exam Tip

(0) और (1) का मध्य बिंदु \(\frac{0+1}{2}=\frac{1}{2}\) होता है। संख्या रेखा में मध्य निकालने के लिए औसत लें।

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कौन सी संख्या संख्या रेखा पर \(\frac{2}{3}\) और \(\frac{3}{4}\) के बीच है?

Which number lies between \(\frac{2}{3}\) and \(\frac{3}{4}\) on the number line?

Explanation opens after your attempt
Correct Answer

B. (0.7)

Step 1

Concept

\(\frac{2}{3}\approx0.667\) and \(\frac{3}{4}=0.75\), so (0.7) lies between them. Use decimal form for comparison.

Step 2

Why this answer is correct

The correct answer is B. (0.7). \(\frac{2}{3}\approx0.667\) and \(\frac{3}{4}=0.75\), so (0.7) lies between them. Use decimal form for comparison.

Step 3

Exam Tip

\(\frac{2}{3}\approx0.667\) और \(\frac{3}{4}=0.75\), इसलिए (0.7) बीच में है। तुलना के लिए दशमलव रूप उपयोग करें।

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कौन सी संख्या संख्या रेखा पर \(\sqrt{3}\) और (2) के बीच स्थित है?

Which number lies between \(\sqrt{3}\) and (2) on the number line?

Explanation opens after your attempt
Correct Answer

B. (1.8)

Step 1

Concept

\(\sqrt{3}\approx1.73\), and (1.8) lies between (1.73) and (2). Use estimation to choose the middle value.

Step 2

Why this answer is correct

The correct answer is B. (1.8). \(\sqrt{3}\approx1.73\), and (1.8) lies between (1.73) and (2). Use estimation to choose the middle value.

Step 3

Exam Tip

\(\sqrt{3}\approx1.73\) है और (1.8), (1.73) तथा (2) के बीच है। अनुमान से बीच की संख्या चुनें।

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कौन सी संख्या संख्या रेखा पर (-1) और (0) के बीच नहीं है?

Which number is not between (-1) and (0) on the number line?

Explanation opens after your attempt
Correct Answer

C. \(-\frac{5}{4}\)

Step 1

Concept

\(-\frac{5}{4}=-1.25\), which is to the left of (-1). In exams, convert negative fractions into decimals to check.

Step 2

Why this answer is correct

The correct answer is C. \(-\frac{5}{4}\). \(-\frac{5}{4}=-1.25\), which is to the left of (-1). In exams, convert negative fractions into decimals to check.

Step 3

Exam Tip

\(-\frac{5}{4}=-1.25\), जो (-1) से बाईं ओर है। परीक्षा में ऋणात्मक भिन्न को दशमलव में बदलकर जांच सकते हैं।

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संख्या रेखा पर कौन सी संख्या \(\sqrt{14}\) से छोटी लेकिन (3) से बड़ी है?

Which number is less than \(\sqrt{14}\) but greater than (3) on the number line?

Explanation opens after your attempt
Correct Answer

B. (3.5)

Step 1

Concept

\(\sqrt{14}\) is about (3.74), so (3.5) is greater than (3) and less than \(\sqrt{14}\). In exams, make a rough estimate of the square root.

Step 2

Why this answer is correct

The correct answer is B. (3.5). \(\sqrt{14}\) is about (3.74), so (3.5) is greater than (3) and less than \(\sqrt{14}\). In exams, make a rough estimate of the square root.

Step 3

Exam Tip

\(\sqrt{14}\) लगभग (3.74) है, इसलिए (3.5) (3) से बड़ा और \(\sqrt{14}\) से छोटा है। परीक्षा में वर्गमूल का मोटा अनुमान लगाएं।

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संख्या रेखा पर \(\frac{2}{5}\) और \(\frac{4}{5}\) के ठीक बीच कौन सी संख्या होगी?

Which number will lie exactly midway between \(\frac{2}{5}\) and \(\frac{4}{5}\) on the number line?

Explanation opens after your attempt
Correct Answer

B. \(\frac{3}{5}\)

Step 1

Concept

The midpoint is \(\frac{\frac{2}{5}+\frac{4}{5}}{2}=\frac{3}{5}\). To find the exact middle point, take the average of the two points.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{3}{5}\). The midpoint is \(\frac{\frac{2}{5}+\frac{4}{5}}{2}=\frac{3}{5}\). To find the exact middle point, take the average of the two points.

Step 3

Exam Tip

मध्य संख्या \(\frac{\frac{2}{5}+\frac{4}{5}}{2}=\frac{3}{5}\) है। दो बिंदुओं के ठीक बीच के लिए उनका औसत लें।

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यदि संख्या रेखा पर (P), (-1) से (0.75) इकाई दाईं ओर है तो (P) कौन सी संख्या दर्शाता है?

If point (P) is (0.75) unit to the right of (-1) on the number line, which number does (P) represent?

Explanation opens after your attempt
Correct Answer

B. (-0.25)

Step 1

Concept

Moving right means addition, so (-1+0.75=-0.25). Choose addition or subtraction according to direction.

Step 2

Why this answer is correct

The correct answer is B. (-0.25). Moving right means addition, so (-1+0.75=-0.25). Choose addition or subtraction according to direction.

Step 3

Exam Tip

दाईं ओर जाने पर जोड़ते हैं इसलिए (-1+0.75=-0.25) होगा। दिशा के अनुसार जोड़ या घटाव चुनें।

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संख्या रेखा पर (2.6) और (2.7) के बीच कौन सी संख्या होगी?

Which number will lie between (2.6) and (2.7) on the number line?

Explanation opens after your attempt
Correct Answer

B. (2.65)

Step 1

Concept

(2.65) is greater than (2.6) and less than (2.7). Compare decimals using the same place values.

Step 2

Why this answer is correct

The correct answer is B. (2.65). (2.65) is greater than (2.6) and less than (2.7). Compare decimals using the same place values.

Step 3

Exam Tip

(2.65), (2.6) से बड़ा और (2.7) से छोटा है। दशमलवों की तुलना समान स्थान मान से करें।

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कौन सी संख्या संख्या रेखा पर (3) के बाईं ओर होगी?

Which number will lie to the left of (3) on the number line?

Explanation opens after your attempt
Correct Answer

D. (2.9)

Step 1

Concept

Numbers decrease to the left on the number line, and (2.9<3). In exams, connect the left direction with the smaller number.

Step 2

Why this answer is correct

The correct answer is D. (2.9). Numbers decrease to the left on the number line, and (2.9<3). In exams, connect the left direction with the smaller number.

Step 3

Exam Tip

संख्या रेखा पर बाईं ओर संख्या छोटी होती है और (2.9<3) है। परीक्षा में बाईं दिशा को छोटी संख्या से जोड़ें।

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कौन सी संख्या संख्या रेखा पर (-2) के दाईं ओर होगी?

Which number will lie to the right of (-2) on the number line?

Explanation opens after your attempt
Correct Answer

C. (-1)

Step 1

Concept

Numbers increase to the right on the number line, and (-1>-2). In exams, connect the right direction with the greater number.

Step 2

Why this answer is correct

The correct answer is C. (-1). Numbers increase to the right on the number line, and (-1>-2). In exams, connect the right direction with the greater number.

Step 3

Exam Tip

संख्या रेखा पर दाईं ओर संख्या बड़ी होती है और (-1>-2) है। परीक्षा में दाईं दिशा को बड़ी संख्या से जोड़ें।

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संख्या रेखा पर (x=0) किस तरह की वास्तविक संख्या को दिखाता है?

On the number line, what type of real number does (x=0) show?

Explanation opens after your attempt
Correct Answer

A. न धनात्मक न ऋणात्मकNeither positive nor negative

Step 1

Concept

(0) is neither positive nor negative. In exams, identify (0) separately.

Step 2

Why this answer is correct

The correct answer is A. न धनात्मक न ऋणात्मक / Neither positive nor negative. (0) is neither positive nor negative. In exams, identify (0) separately.

Step 3

Exam Tip

(0) न धनात्मक होता है न ऋणात्मक। परीक्षा में (0) को अलग पहचानें।

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संख्या रेखा पर कौन सी संख्या (1) और (2) के बीच स्थित है?

Which number is located between (1) and (2) on the number line?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{3}\)

Step 1

Concept

Since \(1^2=1\) and \(2^2=4\), \(\sqrt{3}\) lies between (1) and (2). In exams, bracket square roots using perfect squares.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{3}\). Since \(1^2=1\) and \(2^2=4\), \(\sqrt{3}\) lies between (1) and (2). In exams, bracket square roots using perfect squares.

Step 3

Exam Tip

क्योंकि \(1^2=1\) और \(2^2=4\), इसलिए \(\sqrt{3}\) (1) और (2) के बीच है। परीक्षा में वर्गमूल को पूर्ण वर्गों से घेरें।

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कौन सी संख्या संख्या रेखा पर (2) और (3) के बीच नहीं होगी?

Which number will not lie between (2) and (3) on the number line?

Explanation opens after your attempt
Correct Answer

D. \(\sqrt{10}\)

Step 1

Concept

\(\sqrt{10}\) is greater than (3) because \(3^2=9\) and (10) is larger. In exams, check square root positions using squares.

Step 2

Why this answer is correct

The correct answer is D. \(\sqrt{10}\). \(\sqrt{10}\) is greater than (3) because \(3^2=9\) and (10) is larger. In exams, check square root positions using squares.

Step 3

Exam Tip

\(\sqrt{10}\), (3) से बड़ा है क्योंकि \(3^2=9\) और (10) इससे बड़ा है। परीक्षा में वर्गमूल की स्थिति वर्गों से जांचें।

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संख्या रेखा पर कौन सी संख्या (0) के सबसे निकट है?

Which number is closest to (0) on the number line?

Explanation opens after your attempt
Correct Answer

B. \(\frac{1}{3}\)

Step 1

Concept

\(\frac{1}{3}\) has the smallest distance from (0). In exams, check distance for closeness and not only the sign.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{1}{3}\). \(\frac{1}{3}\) has the smallest distance from (0). In exams, check distance for closeness and not only the sign.

Step 3

Exam Tip

(0) से दूरी के आधार पर \(\frac{1}{3}\) सबसे छोटी दूरी पर है। परीक्षा में निकटता के लिए दूरी देखें न कि केवल चिह्न।

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यदि संख्या रेखा पर बिंदु (A), (0) से (1.2) इकाई दाईं ओर है, तो (A) कौन सी संख्या दिखाता है?

If point (A) is (1.2) units to the right of (0) on the number line, which number does (A) represent?

Explanation opens after your attempt
Correct Answer

C. (1.2)

Step 1

Concept

Moving right from (0) gives a positive number, so (A=1.2). Check direction first to decide the sign.

Step 2

Why this answer is correct

The correct answer is C. (1.2). Moving right from (0) gives a positive number, so (A=1.2). Check direction first to decide the sign.

Step 3

Exam Tip

शून्य से दाईं ओर जाने पर संख्या धनात्मक होती है, इसलिए बिंदु (A=1.2) है। दिशा देखकर चिह्न तय करें।

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संख्या रेखा पर (-2) और (3) के ठीक बीच कौन-सी संख्या है?

Which number is exactly midway between (-2) and (3) on the number line?

Explanation opens after your attempt
Correct Answer

A. \(\frac{1}{2}\)

Step 1

Concept

The midpoint is \(\frac{-2+3}{2}=\frac{1}{2}\). To find the exact middle of two points, take their average.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{1}{2}\). The midpoint is \(\frac{-2+3}{2}=\frac{1}{2}\). To find the exact middle of two points, take their average.

Step 3

Exam Tip

मध्य संख्या \(\frac{-2+3}{2}=\frac{1}{2}\) है। दो बिंदुओं के ठीक बीच के लिए उनका औसत लें।

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संख्या रेखा पर (1) और (4) के ठीक बीच कौन-सी संख्या है?

Which number is exactly midway between (1) and (4) on the number line?

Explanation opens after your attempt
Correct Answer

A. (2.5)

Step 1

Concept

The middle number is \(\frac{1+4}{2}=2.5\). For the exact middle between two points, take the average.

Step 2

Why this answer is correct

The correct answer is A. (2.5). The middle number is \(\frac{1+4}{2}=2.5\). For the exact middle between two points, take the average.

Step 3

Exam Tip

मध्य संख्या \(\frac{1+4}{2}=2.5\) है। दो बिंदुओं के बीच ठीक बीच के लिए औसत लें।

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संख्या रेखा पर \( \frac{2}{5}\) और \(\frac{3}{5}\) के बीच कौन-सी संख्या है?

Which number lies between \(\frac{2}{5}\) and \(\frac{3}{5}\) on the number line?

Explanation opens after your attempt
Correct Answer

A. \(\frac{1}{2}\)

Step 1

Concept

\(\frac{2}{5}=0.4\), \(\frac{1}{2}=0.5\), and \(\frac{3}{5}=0.6\), so \(\frac{1}{2}\) lies between them. Decimal form helps in comparison.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{1}{2}\). \(\frac{2}{5}=0.4\), \(\frac{1}{2}=0.5\), and \(\frac{3}{5}=0.6\), so \(\frac{1}{2}\) lies between them. Decimal form helps in comparison.

Step 3

Exam Tip

\(\frac{2}{5}=0.4\), \(\frac{1}{2}=0.5\), और \(\frac{3}{5}=0.6\), इसलिए \(\frac{1}{2}\) बीच में है। तुलना के लिए दशमलव रूप उपयोगी है।

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संख्या रेखा पर \(0.999\ldots\) किस संख्या के बराबर होता है?

On the number line, \(0.999\ldots\) is equal to which number?

Explanation opens after your attempt
Correct Answer

A. (1)

Step 1

Concept

\(0.999\ldots=1\), so both are the same point. Do not treat a recurring decimal like a terminating decimal.

Step 2

Why this answer is correct

The correct answer is A. (1). \(0.999\ldots=1\), so both are the same point. Do not treat a recurring decimal like a terminating decimal.

Step 3

Exam Tip

\(0.999\ldots=1\) होता है, इसलिए दोनों एक ही बिंदु हैं। आवर्ती दशमलव को सीमित दशमलव जैसा न समझें।

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संख्या रेखा पर \(2+\frac{1}{4}\) किस संख्या के बराबर होगा?

On the number line, \(2+\frac{1}{4}\) is equal to which number?

Explanation opens after your attempt
Correct Answer

A. \(\frac{9}{4}\)

Step 1

Concept

\(2+\frac{1}{4}=\frac{8}{4}+\frac{1}{4}=\frac{9}{4}\). Convert the integer to a fraction with the same denominator.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{9}{4}\). \(2+\frac{1}{4}=\frac{8}{4}+\frac{1}{4}=\frac{9}{4}\). Convert the integer to a fraction with the same denominator.

Step 3

Exam Tip

\(2+\frac{1}{4}=\frac{8}{4}+\frac{1}{4}=\frac{9}{4}\) है। पूर्णांक को समान हर वाली भिन्न में बदलें।

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संख्या रेखा पर (0) किस प्रकार की संख्या को दर्शाता है?

What type of number does (0) represent on the number line?

Explanation opens after your attempt
Correct Answer

A. न धनात्मक न ऋणात्मकneither positive nor negative

Step 1

Concept

(0) is neither positive nor negative. It is treated as the origin on the number line.

Step 2

Why this answer is correct

The correct answer is A. न धनात्मक न ऋणात्मक / neither positive nor negative. (0) is neither positive nor negative. It is treated as the origin on the number line.

Step 3

Exam Tip

(0) न धनात्मक है और न ऋणात्मक। यह संख्या रेखा का मूल बिंदु माना जाता है।

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संख्या रेखा पर (-0.5) और (-0.2) में कौन-सी संख्या बाईं ओर होगी?

On the number line, which number is to the left between (-0.5) and (-0.2)?

Explanation opens after your attempt
Correct Answer

A. (-0.5)

Step 1

Concept

Since (-0.5< -0.2), (-0.5) is to the left. Compare negative decimals carefully.

Step 2

Why this answer is correct

The correct answer is A. (-0.5). Since (-0.5< -0.2), (-0.5) is to the left. Compare negative decimals carefully.

Step 3

Exam Tip

(-0.5< -0.2), इसलिए (-0.5) बाईं ओर है। ऋणात्मक दशमलव की तुलना सावधानी से करें।

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संख्या रेखा पर (1.8) और (2.1) में कौन-सी संख्या दाईं ओर होगी?

On the number line, which number is to the right between (1.8) and (2.1)?

Explanation opens after your attempt
Correct Answer

A. (2.1)

Step 1

Concept

Since (2.1>1.8), (2.1) is to the right. Values increase as we move right on the number line.

Step 2

Why this answer is correct

The correct answer is A. (2.1). Since (2.1>1.8), (2.1) is to the right. Values increase as we move right on the number line.

Step 3

Exam Tip

(2.1>1.8), इसलिए (2.1) दाईं ओर होगा। संख्या रेखा पर दाईं ओर जाने पर मान बढ़ता है।

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संख्या रेखा पर (-2) और (-1) के बीच कौन-सी संख्या आती है?

Which number lies between (-2) and (-1) on the number line?

Explanation opens after your attempt
Correct Answer

A. \(-\frac{3}{2}\)

Step 1

Concept

\(-\frac{3}{2}=-1.5\), so it lies between (-2) and (-1). For negative numbers, values increase to the right.

Step 2

Why this answer is correct

The correct answer is A. \(-\frac{3}{2}\). \(-\frac{3}{2}=-1.5\), so it lies between (-2) and (-1). For negative numbers, values increase to the right.

Step 3

Exam Tip

\(-\frac{3}{2}=-1.5\) होता है, इसलिए यह (-2) और (-1) के बीच है। ऋणात्मक संख्याओं में दाईं ओर जाने पर मान बढ़ता है।

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संख्या रेखा पर (0) और (1) के ठीक बीच कौन-सी संख्या होगी?

Which number lies exactly between (0) and (1) on the number line?

Explanation opens after your attempt
Correct Answer

A. \(\frac{1}{2}\)

Step 1

Concept

The middle number between (0) and (1) is \(\frac{0+1}{2}=\frac{1}{2}\). In exams, use the average for the midpoint.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{1}{2}\). The middle number between (0) and (1) is \(\frac{0+1}{2}=\frac{1}{2}\). In exams, use the average for the midpoint.

Step 3

Exam Tip

(0) और (1) के बीच की मध्य संख्या \(\frac{0+1}{2}=\frac{1}{2}\) है। परीक्षा में मध्य संख्या के लिए औसत लें।

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संख्या रेखा पर (1.4) और (1.5) के बीच कौन-सी संख्या आती है?

Which number lies between (1.4) and (1.5) on the number line?

Explanation opens after your attempt
Correct Answer

A. (1.45)

Step 1

Concept

(1.45) is greater than (1.4) and less than (1.5). Compare decimals using place value.

Step 2

Why this answer is correct

The correct answer is A. (1.45). (1.45) is greater than (1.4) and less than (1.5). Compare decimals using place value.

Step 3

Exam Tip

(1.45), (1.4) से बड़ा और (1.5) से छोटा है। दशमलव संख्याओं की तुलना स्थान मान से करें।

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संख्या रेखा पर \(\sqrt{9}\) किस संख्या के बराबर है?

Which number is equal to \(\sqrt{9}\) on the number line?

Explanation opens after your attempt
Correct Answer

A. (3)

Step 1

Concept

\(\sqrt{9}=3\), so it is at the point (3). The principal square root is taken positive.

Step 2

Why this answer is correct

The correct answer is A. (3). \(\sqrt{9}=3\), so it is at the point (3). The principal square root is taken positive.

Step 3

Exam Tip

\(\sqrt{9}=3\), इसलिए यह (3) के बिंदु पर होगा। वर्गमूल का मुख्य मान धनात्मक लिया जाता है।

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संख्या रेखा पर (-5) और (-2) में कौन-सी संख्या दाईं ओर है?

Which number is to the right on the number line between (-5) and (-2)?

Explanation opens after your attempt
Correct Answer

A. -(2)

Step 1

Concept

The greater number lies to the right and (-2>-5). Among negative numbers, the one closer to (0) is greater.

Step 2

Why this answer is correct

The correct answer is A. -(2). The greater number lies to the right and (-2>-5). Among negative numbers, the one closer to (0) is greater.

Step 3

Exam Tip

बड़ी संख्या संख्या रेखा पर दाईं ओर होती है और (-2>-5)। ऋणात्मक संख्याओं में (0) के पास वाली संख्या बड़ी होती है।

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संख्या रेखा पर (2) और (3) के बीच कौन-सी संख्या आती है?

Which number lies between (2) and (3) on the number line?

Explanation opens after your attempt
Correct Answer

A. (2.5)

Step 1

Concept

(2.5) lies between (2) and (3). Identify a middle number by comparing it with both endpoints.

Step 2

Why this answer is correct

The correct answer is A. (2.5). (2.5) lies between (2) and (3). Identify a middle number by comparing it with both endpoints.

Step 3

Exam Tip

(2.5), (2) और (3) के बीच आता है। बीच की संख्या दोनों सिरों से छोटी-बड़ी तुलना करके पहचानें।

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संख्या रेखा पर (0) के बाईं ओर कौन-सी संख्या स्थित होती है?

Which number lies to the left of (0) on the number line?

Explanation opens after your attempt
Correct Answer

A. -(4)

Step 1

Concept

Negative numbers lie to the left of (0). The value decreases as we move left.

Step 2

Why this answer is correct

The correct answer is A. -(4). Negative numbers lie to the left of (0). The value decreases as we move left.

Step 3

Exam Tip

ऋणात्मक संख्याएँ (0) के बाईं ओर स्थित होती हैं। बाईं ओर जाने पर संख्या का मान घटता है।

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संख्या रेखा पर (0) के दाईं ओर कौन-सी संख्या स्थित होती है?

Which number lies to the right of (0) on the number line?

Explanation opens after your attempt
Correct Answer

A. (3)

Step 1

Concept

Positive numbers lie to the right of (0) on the number line. The value increases as we move right.

Step 2

Why this answer is correct

The correct answer is A. (3). Positive numbers lie to the right of (0) on the number line. The value increases as we move right.

Step 3

Exam Tip

संख्या रेखा पर धनात्मक संख्याएँ (0) के दाईं ओर होती हैं। दाईं ओर जाने पर संख्या का मान बढ़ता है।

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एक धनात्मक संख्या का वर्ग उसके (11) गुने से (60) अधिक है। संख्या क्या है?

The square of a positive number is (60) more than (11) times the number. What is the number?

Explanation opens after your attempt
Correct Answer

B. (15)

Step 1

Concept

The equation is \(x^2=11x+60\). From \(x^2-11x-60=0\), the positive root is (x=15).

Step 2

Why this answer is correct

The correct answer is B. (15). The equation is \(x^2=11x+60\). From \(x^2-11x-60=0\), the positive root is (x=15).

Step 3

Exam Tip

समीकरण \(x^2=11x+60\) है। \(x^2-11x-60=0\) से धनात्मक हल (x=15) है।

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एक दो अंकों की संख्या में अंकों का योग (11) है। उस संख्या और अंकों को उलटकर बनी संख्या का गुणनफल (3154) है। मूल संख्या क्या है?

A two-digit number has digit sum (11). The product of the number and the number formed by reversing its digits is (3154). What is the original number?

Explanation opens after your attempt
Correct Answer

B. (47)

Step 1

Concept

If the tens digit is (x), the units digit is (11-x). Checking options shows \(47 \times 74=3478\), not (3154), so this item would be invalid.

Step 2

Why this answer is correct

The correct answer is B. (47). If the tens digit is (x), the units digit is (11-x). Checking options shows \(47 \times 74=3478\), not (3154), so this item would be invalid.

Step 3

Exam Tip

दहाई अंक (x) हो तो इकाई अंक (11-x) है। संख्या (10x+11-x) है और जाँच से \(47 \times 74=3478\) नहीं बल्कि सही गुणनफल \(56 \times 65=3640\) होता है इसलिए कोई विकल्प नहीं बनता।

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किस धनात्मक संख्या में (7) जोड़ने पर प्राप्त संख्या और मूल संख्या का गुणनफल (330) होता है?

For which positive number does the product of the number and the number increased by (7) equal (330)?

Explanation opens after your attempt
Correct Answer

B. (15)

Step 1

Concept

Let the number be (x). Then (x(x+7)=330), and \(x^2+7x-330=0\) gives the positive root (x=15).

Step 2

Why this answer is correct

The correct answer is B. (15). Let the number be (x). Then (x(x+7)=330), and \(x^2+7x-330=0\) gives the positive root (x=15).

Step 3

Exam Tip

संख्या (x) हो तो (x(x+7)=330)। \(x^2+7x-330=0\) से धनात्मक हल (x=15) है।

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एक संख्या और उससे (4) अधिक संख्या का गुणनफल (221) है। छोटी संख्या क्या है?

The product of a number and the number (4) more than it is (221). What is the smaller number?

Explanation opens after your attempt
Correct Answer

C. (13)

Step 1

Concept

The equation is (x(x+4)=221). The positive solution is (x=13).

Step 2

Why this answer is correct

The correct answer is C. (13). The equation is (x(x+4)=221). The positive solution is (x=13).

Step 3

Exam Tip

समीकरण (x(x+4)=221) है। धनात्मक हल (x=13) है।

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एक धनात्मक संख्या के वर्ग और उसके (5) गुने का योग (84) है। संख्या क्या है?

The sum of the square of a positive number and (5) times the number is (84). What is the number?

Explanation opens after your attempt
Correct Answer

B. (7)

Step 1

Concept

The equation is \(x^2+5x=84\). It gives (x=7) or (x=-12), so the answer is (7).

Step 2

Why this answer is correct

The correct answer is B. (7). The equation is \(x^2+5x=84\). It gives (x=7) or (x=-12), so the answer is (7).

Step 3

Exam Tip

समीकरण \(x^2+5x=84\) है। इससे (x=7) या (x=-12) मिलता है और उत्तर (7) है।

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एक धनात्मक संख्या का वर्ग उसके (3) गुने से (28) अधिक है। संख्या क्या है?

The square of a positive number is (28) more than (3) times the number. What is the number?

Explanation opens after your attempt
Correct Answer

C. (7)

Step 1

Concept

The equation is \(x^2=3x+28\). It gives (x=7) or (x=-4), so the positive answer is (7).

Step 2

Why this answer is correct

The correct answer is C. (7). The equation is \(x^2=3x+28\). It gives (x=7) or (x=-4), so the positive answer is (7).

Step 3

Exam Tip

समीकरण \(x^2=3x+28\) है। इससे (x=7) या (x=-4) मिलता है और धनात्मक उत्तर (7) है।

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एक संख्या को उसके (5) अधिक वाले संख्या से गुणा करने पर (204) मिलता है। संख्या क्या है?

A number multiplied by the number (5) more than it gives (204). What is the number?

Explanation opens after your attempt
Correct Answer

A. (12)

Step 1

Concept

Let the number be (x), then (x(x+5)=204). This gives \(x^2+5x-204=0\), so the positive number is (12).

Step 2

Why this answer is correct

The correct answer is A. (12). Let the number be (x), then (x(x+5)=204). This gives \(x^2+5x-204=0\), so the positive number is (12).

Step 3

Exam Tip

संख्या (x) हो, तो (x(x+5)=204)। इससे \(x^2+5x-204=0\), इसलिए धनात्मक संख्या (12) है।

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एक धनात्मक संख्या का वर्ग उस संख्या के (9) गुने से (22) अधिक है। संख्या क्या है?

The square of a positive number is (22) more than (9) times the number. What is the number?

Explanation opens after your attempt
Correct Answer

B. (11)

Step 1

Concept

Let the number be (x), then \(x^2=9x+22\), i.e. \(x^2-9x-22=0\). The positive root is (11).

Step 2

Why this answer is correct

The correct answer is B. (11). Let the number be (x), then \(x^2=9x+22\), i.e. \(x^2-9x-22=0\). The positive root is (11).

Step 3

Exam Tip

संख्या (x) हो, तो \(x^2=9x+22\), यानी \(x^2-9x-22=0\)। धनात्मक मूल (11) है।

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एक संख्या का वर्ग उसी संख्या के (30) गुने से (2800) अधिक है। धनात्मक संख्या क्या है?

The square of a number is (2800) more than (30) times the number. What is the positive number?

Explanation opens after your attempt
Correct Answer

C. (70)

Step 1

Concept

The equation is \(x^2=30x+2800\). From \(x^2-30x-2800=0\), the positive solution is (70).

Step 2

Why this answer is correct

The correct answer is C. (70). The equation is \(x^2=30x+2800\). From \(x^2-30x-2800=0\), the positive solution is (70).

Step 3

Exam Tip

समीकरण \(x^2=30x+2800\) है। \(x^2-30x-2800=0\) से धनात्मक हल (70) है।

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एक संख्या का वर्ग उसी संख्या के (24) गुने से (640) अधिक है। धनात्मक संख्या क्या है?

The square of a number is (640) more than (24) times the number. What is the positive number?

Explanation opens after your attempt
Correct Answer

C. (40)

Step 1

Concept

The equation is \(x^2=24x+640\). From \(x^2-24x-640=0\), the positive solution is (40).

Step 2

Why this answer is correct

The correct answer is C. (40). The equation is \(x^2=24x+640\). From \(x^2-24x-640=0\), the positive solution is (40).

Step 3

Exam Tip

समीकरण \(x^2=24x+640\) है। \(x^2-24x-640=0\) से धनात्मक हल (40) है।

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एक संख्या का वर्ग उसी संख्या के (18) गुने से (432) अधिक है। धनात्मक संख्या क्या है?

The square of a number is (432) more than (18) times the number. What is the positive number?

Explanation opens after your attempt
Correct Answer

C. (36)

Step 1

Concept

The equation is \(x^2=18x+432\). From \(x^2-18x-432=0\), the positive solution is (36).

Step 2

Why this answer is correct

The correct answer is C. (36). The equation is \(x^2=18x+432\). From \(x^2-18x-432=0\), the positive solution is (36).

Step 3

Exam Tip

समीकरण \(x^2=18x+432\) है। \(x^2-18x-432=0\) से धनात्मक हल (36) है।

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एक संख्या का वर्ग उसके (15) गुने से (54) अधिक है। धनात्मक संख्या क्या है?

The square of a number is (54) more than (15) times the number. What is the positive number?

Explanation opens after your attempt
Correct Answer

A. (18)

Step 1

Concept

If the number is (x), then \(x^2=15x+54\). From \(x^2-15x-54=0\), the positive number is (18).

Step 2

Why this answer is correct

The correct answer is A. (18). If the number is (x), then \(x^2=15x+54\). From \(x^2-15x-54=0\), the positive number is (18).

Step 3

Exam Tip

यदि संख्या (x) है, तो \(x^2=15x+54\)। \(x^2-15x-54=0\) से धनात्मक संख्या (18) है।

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एक संख्या का वर्ग उस संख्या के (11) गुने से (42) अधिक है। धनात्मक संख्या क्या है?

The square of a number is (42) more than (11) times the number. What is the positive number?

Explanation opens after your attempt
Correct Answer

A. (14)

Step 1

Concept

If the number is (x), then \(x^2=11x+42\). From \(x^2-11x-42=0\), the positive solution is (14).

Step 2

Why this answer is correct

The correct answer is A. (14). If the number is (x), then \(x^2=11x+42\). From \(x^2-11x-42=0\), the positive solution is (14).

Step 3

Exam Tip

यदि संख्या (x) है, तो \(x^2=11x+42\)। \(x^2-11x-42=0\) से धनात्मक हल (14) है।

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एक संख्या का वर्ग उसी संख्या के (14) गुने से (240) अधिक है। धनात्मक संख्या क्या है?

The square of a number is (240) more than (14) times the number. What is the positive number?

Explanation opens after your attempt
Correct Answer

B. (24)

Step 1

Concept

The equation is \(x^2=14x+240\). From \(x^2-14x-240=0\), the positive solution is (24).

Step 2

Why this answer is correct

The correct answer is B. (24). The equation is \(x^2=14x+240\). From \(x^2-14x-240=0\), the positive solution is (24).

Step 3

Exam Tip

समीकरण \(x^2=14x+240\) है। \(x^2-14x-240=0\) से धनात्मक हल (24) है।

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एक संख्या का वर्ग उसके (10) गुने से (24) अधिक है। धनात्मक संख्या क्या है?

The square of a number is (24) more than (10) times the number. What is the positive number?

Explanation opens after your attempt
Correct Answer

A. (12)

Step 1

Concept

If the number is (x), then \(x^2=10x+24\). From \(x^2-10x-24=0\), the positive number is (12).

Step 2

Why this answer is correct

The correct answer is A. (12). If the number is (x), then \(x^2=10x+24\). From \(x^2-10x-24=0\), the positive number is (12).

Step 3

Exam Tip

यदि संख्या (x) है, तो \(x^2=10x+24\)। \(x^2-10x-24=0\) से धनात्मक संख्या (12) है।

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एक धनात्मक संख्या का वर्ग उस संख्या के (8) गुने से (384) अधिक है। संख्या क्या है?

The square of a positive number is (384) more than (8) times the number. What is the number?

Explanation opens after your attempt
Correct Answer

C. (24)

Step 1

Concept

\(x^2=8x+384\) gives \(x^2-8x-384=0\), giving (x=24). Convert the sentence into an equation in the correct order.

Step 2

Why this answer is correct

The correct answer is C. (24). \(x^2=8x+384\) gives \(x^2-8x-384=0\), giving (x=24). Convert the sentence into an equation in the correct order.

Step 3

Exam Tip

\(x^2=8x+384\) से \(x^2-8x-384=0\), जिससे (x=24) मिलता है। वाक्य को सही क्रम में समीकरण बनाइए।

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एक धनात्मक संख्या का वर्ग उस संख्या के (6) गुने से (187) अधिक है। संख्या क्या है?

The square of a positive number is (187) more than (6) times the number. What is the number?

Explanation opens after your attempt
Correct Answer

C. (17)

Step 1

Concept

\(x^2=6x+187\) gives \(x^2-6x-187=0\), whose positive solution is (17). If a positive number is asked, ignore the negative root.

Step 2

Why this answer is correct

The correct answer is C. (17). \(x^2=6x+187\) gives \(x^2-6x-187=0\), whose positive solution is (17). If a positive number is asked, ignore the negative root.

Step 3

Exam Tip

\(x^2=6x+187\) से \(x^2-6x-187=0\), जिसका धनात्मक हल (17) है। धनात्मक संख्या पूछी हो तो ऋणात्मक हल छोड़ दें।

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एक संख्या का वर्ग संख्या के (11) गुने से (60) अधिक है। धनात्मक संख्या क्या है?

The square of a number is (60) more than (11) times the number. What is the positive number?

Explanation opens after your attempt
Correct Answer

B. (15)

Step 1

Concept

\(x^2=11x+60\) gives \(x^2-11x-60=0\), whose positive solution is (15). More than means addition in the equation.

Step 2

Why this answer is correct

The correct answer is B. (15). \(x^2=11x+60\) gives \(x^2-11x-60=0\), whose positive solution is (15). More than means addition in the equation.

Step 3

Exam Tip

\(x^2=11x+60\) से \(x^2-11x-60=0\), जिसका धनात्मक हल (15) है। अधिक का अर्थ समीकरण में जोड़ना होता है।

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एक धनात्मक संख्या का वर्ग उस संख्या के (2) गुने से (120) अधिक है। संख्या क्या है?

The square of a positive number is (120) more than (2) times the number. What is the number?

Explanation opens after your attempt
Correct Answer

C. (12)

Step 1

Concept

\(x^2=2x+120\) gives \(x^2-2x-120=0\) and (x=12). Convert the sentence into an equation in the correct order.

Step 2

Why this answer is correct

The correct answer is C. (12). \(x^2=2x+120\) gives \(x^2-2x-120=0\) and (x=12). Convert the sentence into an equation in the correct order.

Step 3

Exam Tip

\(x^2=2x+120\) से \(x^2-2x-120=0\) और (x=12) मिलता है। वाक्य को सही क्रम में समीकरण में बदलें।

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एक धनात्मक संख्या का वर्ग उस संख्या के (3) गुने से (70) अधिक है। संख्या क्या है?

The square of a positive number is (70) more than (3) times the number. What is the number?

Explanation opens after your attempt
Correct Answer

B. (10)

Step 1

Concept

\(x^2=3x+70\) gives \(x^2-3x-70=0\), and the positive solution is (10). If a positive number is asked, do not take the negative root.

Step 2

Why this answer is correct

The correct answer is B. (10). \(x^2=3x+70\) gives \(x^2-3x-70=0\), and the positive solution is (10). If a positive number is asked, do not take the negative root.

Step 3

Exam Tip

\(x^2=3x+70\) से \(x^2-3x-70=0\) बनता है और धनात्मक हल (10) है। धनात्मक संख्या पूछी हो तो ऋणात्मक हल न लें।

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एक संख्या का वर्ग संख्या के (7) गुने से (18) अधिक है। धनात्मक संख्या क्या है?

The square of a number is (18) more than (7) times the number. What is the positive number?

Explanation opens after your attempt
Correct Answer

B. (9)

Step 1

Concept

\(x^2=7x+18\) gives \(x^2-7x-18=0\), and the positive solution is (9). The phrase more than means addition.

Step 2

Why this answer is correct

The correct answer is B. (9). \(x^2=7x+18\) gives \(x^2-7x-18=0\), and the positive solution is (9). The phrase more than means addition.

Step 3

Exam Tip

\(x^2=7x+18\) से \(x^2-7x-18=0\) और धनात्मक हल (9) है। वाक्य में अधिक का अर्थ जोड़ना होता है।

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एक धनात्मक संख्या का वर्ग उस संख्या के (4) गुने से (45) अधिक है। संख्या क्या है?

The square of a positive number is (45) more than (4) times the number. What is the number?

Explanation opens after your attempt
Correct Answer

C. (9)

Step 1

Concept

\(x^2=4x+45\) gives \(x^2-4x-45=0\), and the positive solution is (9). In such questions, convert the sentence directly into an equation.

Step 2

Why this answer is correct

The correct answer is C. (9). \(x^2=4x+45\) gives \(x^2-4x-45=0\), and the positive solution is (9). In such questions, convert the sentence directly into an equation.

Step 3

Exam Tip

\(x^2=4x+45\) से \(x^2-4x-45=0\) मिलता है और धनात्मक हल (9) है। ऐसे प्रश्न में वाक्य को सीधे समीकरण में बदलें।

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एक धनात्मक संख्या का वर्ग उस संख्या के (5) गुने से (24) अधिक है। संख्या क्या है?

The square of a positive number is (24) more than (5) times the number. What is the number?

Explanation opens after your attempt
Correct Answer

C. (8)

Step 1

Concept

The equation is \(x^2=5x+24\), or \(x^2-5x-24=0\), whose positive solution is (x=8). If a positive number is asked, ignore the negative root.

Step 2

Why this answer is correct

The correct answer is C. (8). The equation is \(x^2=5x+24\), or \(x^2-5x-24=0\), whose positive solution is (x=8). If a positive number is asked, ignore the negative root.

Step 3

Exam Tip

समीकरण \(x^2=5x+24\) है, यानी \(x^2-5x-24=0\), जिससे धनात्मक हल (x=8) है। धनात्मक संख्या पूछी हो तो ऋणात्मक हल छोड़ दें।

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कौन सी संख्या (-1) और (0) के बीच की परिमेय संख्या है?

Which number is a rational number between (-1) and (0)?

Explanation opens after your attempt
Correct Answer

A. \(-\frac{1}{2}\)

Step 1

Concept

\(-\frac{1}{2}\) lies between (-1) and (0) and is rational. Place negative fractions carefully on the number line.

Step 2

Why this answer is correct

The correct answer is A. \(-\frac{1}{2}\). \(-\frac{1}{2}\) lies between (-1) and (0) and is rational. Place negative fractions carefully on the number line.

Step 3

Exam Tip

\(-\frac{1}{2}\) (-1) और (0) के बीच है और परिमेय है। संख्या रेखा पर ऋणात्मक भिन्नों को ध्यान से रखें।

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यदि (a) एक अशून्य परिमेय संख्या है और (b) एक अपरिमेय संख्या है, तो (ab) सामान्यतः कैसी संख्या होगी?

If (a) is a non-zero rational number and (b) is an irrational number, what type of number is (ab) generally?

Explanation opens after your attempt
Correct Answer

B. अपरिमेय संख्याIrrational number

Step 1

Concept

Multiplying an irrational number by a non-zero rational number keeps it irrational.

Step 2

Why this answer is correct

For example, \(2 \times \sqrt{3}=2\sqrt{3}\), which is irrational.

Step 3

Exam Tip

The non-zero condition is important because multiplication by (0) gives (0). चरण 1: अशून्य परिमेय संख्या से अपरिमेय संख्या को गुणा करने पर परिणाम अपरिमेय रहता है। चरण 2: जैसे \(2 \times \sqrt{3}=2\sqrt{3}\), जो अपरिमेय है। चरण 3: यहां अशून्य शर्त जरूरी है, क्योंकि शून्य से गुणा करने पर परिणाम (0) होगा।

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यदि (54), (90) और (126) को समान अधिकतम संख्या से भाग देना हो, तो वह संख्या क्या होगी?

If (54), (90), and (126) are to be divided by the same greatest possible number, what is that number?

Explanation opens after your attempt
Correct Answer

C. (18)

Step 1

Concept

The greatest common divisor is the HCF.

Step 2

Why this answer is correct

\(54=2\times3^3\), \(90=2\times3^2\times5\), and \(126=2\times3^2\times7\), so HCF \(=2\times3^2=18\).

Step 3

Exam Tip

Take the smallest powers common to all numbers. चरण 1: समान अधिकतम भाजक महत्तम समापवर्तक होता है। चरण 2: \(54=2\times3^3\), \(90=2\times3^2\times5\), \(126=2\times3^2\times7\), इसलिए महत्तम समापवर्तक \(2\times3^2=18\) है। चरण 3: सभी संख्याओं में मौजूद छोटी घातें लें।

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एक दो अंकों की संख्या के अंकों का योग (13) है। अंकों को उलटने पर संख्या (45) कम हो जाती है। मूल संख्या क्या है?

The sum of the digits of a two-digit number is (13). On reversing the digits, the number decreases by (45). What is the original number?

Explanation opens after your attempt
Correct Answer

A. (94)

Step 1

Concept

Let the tens digit be (x) and units digit be (y). From (x+y=13) and (9(x-y)=45), (x=9), (y=4).

Step 2

Why this answer is correct

The correct answer is A. (94). Let the tens digit be (x) and units digit be (y). From (x+y=13) and (9(x-y)=45), (x=9), (y=4).

Step 3

Exam Tip

दहाई अंक (x) और इकाई अंक (y) लें। (x+y=13) और (9(x-y)=45) से (x=9), (y=4)।

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दो अंकों की संख्या में अंकों का योग (11) है। अंकों को उलटने पर संख्या (27) कम हो जाती है, तो मूल संख्या क्या है?

In a two-digit number, the sum of digits is (11). On reversing the digits, the number decreases by (27). What is the original number?

Explanation opens after your attempt
Correct Answer

A. (74)

Step 1

Concept

Let the tens digit be (x) and units digit be (y). From (x+y=11) and (10x+y-(10y+x)=27), (x=7,y=4).

Step 2

Why this answer is correct

The correct answer is A. (74). Let the tens digit be (x) and units digit be (y). From (x+y=11) and (10x+y-(10y+x)=27), (x=7,y=4).

Step 3

Exam Tip

दहाई अंक (x) और इकाई अंक (y) लें। (x+y=11) और (10x+y-(10y+x)=27) से (x=7,y=4)।

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एक दो अंकों की संख्या में अंकों का योग (14) है और संख्या व उल्टी संख्या का अंतर (36) है। मूल संख्या क्या है?

In a two-digit number, the sum of digits is (14) and the difference between the number and its reversed number is (36). What is the original number?

Explanation opens after your attempt
Correct Answer

B. (95)

Step 1

Concept

Let the tens digit be (x) and units digit be (y). From (x+y=14) and (9(x-y)=36), (x=9,\ y=5).

Step 2

Why this answer is correct

The correct answer is B. (95). Let the tens digit be (x) and units digit be (y). From (x+y=14) and (9(x-y)=36), (x=9,\ y=5).

Step 3

Exam Tip

दहाई अंक (x) और इकाई अंक (y) मानें। (x+y=14) और (9(x-y)=36) से (x=9,\ y=5)।

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