Search: positive-outlook

Question Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

यदि दो वास्तविक मूलों का गुणनफल धनात्मक और योग धनात्मक है तो दोनों मूल कैसे होंगे?

If the product of two real roots is positive and their sum is positive, how will both roots be?

Explanation opens after your attempt

Correct Answer

A. दोनों धनात्मकBoth positive

Step 1

Concept

A positive product means both signs are same. A positive sum means both roots are positive.

Step 2

Why this answer is correct

The correct answer is A. दोनों धनात्मक / Both positive. A positive product means both signs are same. A positive sum means both roots are positive.

Step 3

Exam Tip

गुणनफल धनात्मक होने पर दोनों चिन्ह समान होते हैं। योग धनात्मक होने से दोनों मूल धनात्मक होंगे।

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Question Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

किस विकल्प में मूलों का योग धनात्मक और गुणनफल धनात्मक होगा?

In which option will the sum of roots be positive and the product of roots be positive?

Explanation opens after your attempt

Correct Answer

A. $x^2-9x+20=0$

Step 1

Concept

In the first option, the sum is $-\frac{b}{a}=9$ and the product is $\frac{c}{a}=20$. So both are positive.

Step 2

Why this answer is correct

The correct answer is A. $x^2-9x+20=0$. In the first option, the sum is $-\frac{b}{a}=9$ and the product is $\frac{c}{a}=20$. So both are positive.

Step 3

Exam Tip

पहले विकल्प में योग $-\frac{b}{a}=9$ और गुणनफल $\frac{c}{a}=20$ है। इसलिए दोनों धनात्मक हैं।

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Question Medium Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 5

किस स्थिति में सकारात्मक आकार सबसे स्पष्ट होगा?

In which situation will positive shape be clearest?

Explanation opens after your attempt

Correct Answer

B. जब उसका पृष्ठभूमि से अच्छा विरोध होWhen it contrasts well with background

Step 1

Concept

Contrast separates positive shape from background. Exam tip: connect figure clarity with contrast.

Step 2

Why this answer is correct

The correct answer is B. जब उसका पृष्ठभूमि से अच्छा विरोध हो / When it contrasts well with background. Contrast separates positive shape from background. Exam tip: connect figure clarity with contrast.

Step 3

Exam Tip

विरोध सकारात्मक आकार को पृष्ठभूमि से अलग करता है। परीक्षा में figure clarity को contrast से जोड़ें।

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Question Medium Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 4

सकारात्मक और ऋणात्मक स्थान का संतुलन किसमें सबसे अधिक मदद करता है?

Balance of positive and negative space helps most in what?

Explanation opens after your attempt

Correct Answer

A. स्पष्ट रचना बनाने मेंMaking clear composition

Step 1

Concept

Balance of both spaces makes composition clear and organized. Exam tip: connect space balance with composition.

Step 2

Why this answer is correct

The correct answer is A. स्पष्ट रचना बनाने में / Making clear composition. Balance of both spaces makes composition clear and organized. Exam tip: connect space balance with composition.

Step 3

Exam Tip

दोनों स्थानों का संतुलन रचना को स्पष्ट और व्यवस्थित बनाता है। परीक्षा में space balance को composition से जोड़ें।

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Question Medium Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 2

किस विकल्प में सकारात्मक और ऋणात्मक आकार का संबंध दिखता है?

Which option shows the relation of positive and negative shapes?

Explanation opens after your attempt

Correct Answer

B. काली आकृति और उसके चारों ओर सफेद खाली क्षेत्रA black figure and white empty area around it

Step 1

Concept

Main figure becomes positive and surrounding empty area becomes negative shape. Exam tip: remember figure-ground relation.

Step 2

Why this answer is correct

The correct answer is B. काली आकृति और उसके चारों ओर सफेद खाली क्षेत्र / A black figure and white empty area around it. Main figure becomes positive and surrounding empty area becomes negative shape. Exam tip: remember figure-ground relation.

Step 3

Exam Tip

मुख्य आकृति सकारात्मक और आसपास खाली क्षेत्र ऋणात्मक आकार बनाता है। परीक्षा में figure ground relation याद रखें।

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Question Easy Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 2

सकारात्मक स्थान किस भाग को कहते हैं?

Which part is called positive space?

Explanation opens after your attempt

Correct Answer

A. मुख्य वस्तु वाला भागThe area occupied by the main object

Step 1

Concept

Positive space is the area where the main subject is placed. Exam tip: write subject area as positive space.

Step 2

Why this answer is correct

The correct answer is A. मुख्य वस्तु वाला भाग / The area occupied by the main object. Positive space is the area where the main subject is placed. Exam tip: write subject area as positive space.

Step 3

Exam Tip

सकारात्मक स्थान वह क्षेत्र है जहां मुख्य विषय होता है। परीक्षा में subject area को positive space लिखें।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

किसी समांतर श्रेढ़ी में $S_{16}=816$ और (a=6) है। यदि (d) धनात्मक है, तो (d) ज्ञात कीजिए।

In an AP, $S_{16}=816$ and (a=6). If (d) is positive, find (d).

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

From (816=8[12+15d]), (d=6). Divide the given sum by $\frac{n}{2}$ to solve faster.

Step 2

Why this answer is correct

The correct answer is A. (6). From (816=8[12+15d]), (d=6). Divide the given sum by $\frac{n}{2}$ to solve faster.

Step 3

Exam Tip

(816=8[12+15d]) से (d=6) मिलता है। दिए गए योग को $\frac{n}{2}$ से बाँटकर जल्दी हल करें।

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Question Medium Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 62

यदि (d>0) है और प्रथम पद धनात्मक है, तो समांतर श्रेढ़ी के पद सामान्यतः कैसे बदलेंगे?

If (d>0) and the first term is positive, how will the terms of an arithmetic progression generally change?

Explanation opens after your attempt

Correct Answer

C. बढ़ेंगेThey will increase

Step 1

Concept

Positive (d) means adding each time. Therefore, the terms generally keep increasing.

Step 2

Why this answer is correct

The correct answer is C. बढ़ेंगे / They will increase. Positive (d) means adding each time. Therefore, the terms generally keep increasing.

Step 3

Exam Tip

धनात्मक (d) का अर्थ हर बार जोड़ना है। इसलिए पद सामान्यतः बढ़ते जाते हैं।

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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

यदि $x^2+px+64=0$ की जड़ें समान और धनात्मक हैं, तो (p) का मान क्या है?

If $x^2+px+64=0$ has equal and positive roots, what is the value of (p)?

Explanation opens after your attempt

Correct Answer

A. (-16)

Step 1

Concept

For equal roots, $p^2-256=0$, so $p=\pm16$. The equal root $-\frac{p}{2}$ must be positive, hence (p=-16).

Step 2

Why this answer is correct

The correct answer is A. (-16). For equal roots, $p^2-256=0$, so $p=\pm16$. The equal root $-\frac{p}{2}$ must be positive, hence (p=-16).

Step 3

Exam Tip

समान जड़ों के लिए $p^2-256=0$, इसलिए $p=\pm16$। समान जड़ $-\frac{p}{2}$ धनात्मक होनी चाहिए, अतः (p=-16)।

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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

यदि $x^2-6x+c=0$ की दोनों जड़ें वास्तविक और धनात्मक हैं, तो (c) पर सही शर्त क्या है?

If both roots of $x^2-6x+c=0$ are real and positive, what is the correct condition on (c)?

Explanation opens after your attempt

Correct Answer

A. $0<c\le9$

Step 1

Concept

The sum (6) is positive and (c>0) is needed for both positive roots. For real roots, $36-4c\ge0$, so $0<c\le9$.

Step 2

Why this answer is correct

The correct answer is A. $0<c\le9$. The sum (6) is positive and (c>0) is needed for both positive roots. For real roots, $36-4c\ge0$, so $0<c\le9$.

Step 3

Exam Tip

योग (6) धनात्मक है और दोनों धनात्मक जड़ों के लिए (c>0) चाहिए। वास्तविक जड़ों के लिए $36-4c\ge0$, इसलिए $0<c\le9$।

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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि $x^2+px+36=0$ की जड़ें समान और धनात्मक हैं, तो (p) का मान क्या है?

If $x^2+px+36=0$ has equal and positive roots, what is the value of (p)?

Explanation opens after your attempt

Correct Answer

A. (-12)

Step 1

Concept

For equal roots, $p^2-144=0$, so $p=\pm12$. The equal root $-\frac{p}{2}$ must be positive, hence (p=-12).

Step 2

Why this answer is correct

The correct answer is A. (-12). For equal roots, $p^2-144=0$, so $p=\pm12$. The equal root $-\frac{p}{2}$ must be positive, hence (p=-12).

Step 3

Exam Tip

समान जड़ों के लिए $p^2-144=0$, इसलिए $p=\pm12$। समान जड़ $-\frac{p}{2}$ धनात्मक होनी चाहिए, अतः (p=-12)।

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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि $x^2-5x+c=0$ की दोनों जड़ें वास्तविक और धनात्मक हैं, तो (c) पर सही शर्त क्या है?

If both roots of $x^2-5x+c=0$ are real and positive, what is the correct condition on (c)?

Explanation opens after your attempt

Correct Answer

B. $0<c\le\frac{25}{4}$

Step 1

Concept

The sum (5) is positive and product (c>0) is needed for both roots. For real roots, $25-4c\ge0$, so $0<c\le\frac{25}{4}$.

Step 2

Why this answer is correct

The correct answer is B. $0<c\le\frac{25}{4}$. The sum (5) is positive and product (c>0) is needed for both roots. For real roots, $25-4c\ge0$, so $0<c\le\frac{25}{4}$.

Step 3

Exam Tip

योग (5) धनात्मक है और दोनों जड़ों के लिए गुणनफल (c>0) चाहिए। वास्तविक जड़ों के लिए $25-4c\ge0$, इसलिए $0<c\le\frac{25}{4}$।

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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

यदि $x^2+px+16=0$ की जड़ें समान और धनात्मक हैं, तो (p) का मान क्या है?

If $x^2+px+16=0$ has equal and positive roots, what is the value of (p)?

Explanation opens after your attempt

Correct Answer

A. (-8)

Step 1

Concept

For equal roots, $p^2-64=0$, so $p=\pm8$. The root $-\frac{p}{2}$ must be positive, hence (p=-8).

Step 2

Why this answer is correct

The correct answer is A. (-8). For equal roots, $p^2-64=0$, so $p=\pm8$. The root $-\frac{p}{2}$ must be positive, hence (p=-8).

Step 3

Exam Tip

समान जड़ों के लिए $p^2-64=0$, इसलिए $p=\pm8$। जड़ $-\frac{p}{2}$ धनात्मक होनी चाहिए, अतः (p=-8)।

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Question Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

$x^2-sx+9=0$ की जड़ें समान और धनात्मक हों, तो (s) का मान क्या होगा?

If $x^2-sx+9=0$ has equal and positive roots, what is (s)?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

For equal roots, $s^2-36=0$, so $s=\pm6$. The equal root is $\frac{s}{2}$, which is positive when (s=6).

Step 2

Why this answer is correct

The correct answer is A. (6). For equal roots, $s^2-36=0$, so $s=\pm6$. The equal root is $\frac{s}{2}$, which is positive when (s=6).

Step 3

Exam Tip

समान जड़ों के लिए $s^2-36=0$, इसलिए $s=\pm6$। समान जड़ $\frac{s}{2}$ है, जो धनात्मक होने पर (s=6) देता है।

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Question Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

समीकरण $x^2+px+36=0$ के मूल समान और धनात्मक हैं। (p) का मान क्या होगा?

The roots of $x^2+px+36=0$ are equal and positive. What is the value of (p)?

Explanation opens after your attempt

Correct Answer

A. (-12)

Step 1

Concept

For equal roots, $p^2-144=0$ gives $p=\pm12$. For equal positive roots, $-\frac{p}{2}>0$, so (p=-12).

Step 2

Why this answer is correct

The correct answer is A. (-12). For equal roots, $p^2-144=0$ gives $p=\pm12$. For equal positive roots, $-\frac{p}{2}>0$, so (p=-12).

Step 3

Exam Tip

समान मूलों के लिए $p^2-144=0$ से $p=\pm12$ मिलता है। धनात्मक समान मूल के लिए $-\frac{p}{2}>0$, इसलिए (p=-12)।

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Question Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

समीकरण $x^2+px+25=0$ के मूल समान और धनात्मक हैं। (p) का मान क्या होगा?

The roots of $x^2+px+25=0$ are equal and positive. What is the value of (p)?

Explanation opens after your attempt

Correct Answer

A. (-10)

Step 1

Concept

For equal roots, $p^2-100=0$ gives $p=\pm10$. For equal positive roots, $-\frac{p}{2}>0$, so (p=-10).

Step 2

Why this answer is correct

The correct answer is A. (-10). For equal roots, $p^2-100=0$ gives $p=\pm10$. For equal positive roots, $-\frac{p}{2}>0$, so (p=-10).

Step 3

Exam Tip

समान मूलों के लिए $p^2-100=0$ से $p=\pm10$ मिलता है। धनात्मक समान मूल के लिए $-\frac{p}{2}>0$, इसलिए (p=-10)।

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Question Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण $x^2+px+16=0$ के मूल समान और धनात्मक हैं। (p) का मान क्या होगा?

The roots of $x^2+px+16=0$ are equal and positive. What is the value of (p)?

Explanation opens after your attempt

Correct Answer

A. (-8)

Step 1

Concept

For equal roots, $p^2-64=0$ gives $p=\pm8$. For equal positive roots, $-\frac{p}{2}>0$, so (p=-8).

Step 2

Why this answer is correct

The correct answer is A. (-8). For equal roots, $p^2-64=0$ gives $p=\pm8$. For equal positive roots, $-\frac{p}{2}>0$, so (p=-8).

Step 3

Exam Tip

समान मूलों के लिए $p^2-64=0$ से $p=\pm8$ मिलता है। धनात्मक समान मूल के लिए $-\frac{p}{2}>0$, इसलिए (p=-8)।

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Question Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

किस समीकरण में मूल बराबर और धनात्मक होंगे?

Which equation will have equal and positive roots?

Explanation opens after your attempt

Correct Answer

A. $x^2-12x+36=0$

Step 1

Concept

(x^-2-12x+36=(x-6)²), so both roots are (6). Both roots are equal and positive.

Step 2

Why this answer is correct

The correct answer is A. $x^2-12x+36=0$. (x^-2-12x+36=(x-6)²), so both roots are (6). Both roots are equal and positive.

Step 3

Exam Tip

(x^-2-12x+36=(x-6)²), इसलिए दोनों मूल (6) हैं। दोनों मूल बराबर और धनात्मक हैं।

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Question Medium Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

समीकरण $x^2+kx+49=0$ में यदि मूल समान और धनात्मक हैं, तो (k) का संभव मान कौन-सा है?

In $x^2+kx+49=0$, if the roots are equal and positive, which possible value of (k) is correct?

Explanation opens after your attempt

Correct Answer

B. (-14)

Step 1

Concept

For equal roots, $k^2=196$, and the equal root is $-\frac{k}{2}$. For a positive root, (k=-14) is correct.

Step 2

Why this answer is correct

The correct answer is B. (-14). For equal roots, $k^2=196$, and the equal root is $-\frac{k}{2}$. For a positive root, (k=-14) is correct.

Step 3

Exam Tip

समान मूलों के लिए $k^2=196$ और समान मूल $-\frac{k}{2}$ होगा। धनात्मक मूल के लिए (k=-14) सही है।

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Question Expert Social Science The Age of Industrialisation Nationalism and Imperialism Class 10 Level 2

बाल्कन के मामले में राष्ट्रवाद को सकारात्मक और नकारात्मक दोनों रूपों में क्यों देखा जा सकता है?

Why can nationalism be seen in both positive and negative forms in the case of the Balkans?

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Correct Answer

A. इसने स्वतंत्रता की चेतना जगाई लेकिन आपसी संघर्ष भी बढ़ायाIt awakened freedom consciousness but also increased mutual conflict

Step 1

Concept

Nationalism inspires people toward freedom.

Step 2

Why this answer is correct

But when many claims clash, conflict increases.

Step 3

Exam Tip

The Balkans is a balanced example of this. चरण 1: राष्ट्रवाद लोगों को स्वतंत्रता के लिए प्रेरित करता है। चरण 2: लेकिन जब कई दावे टकराते हैं तो संघर्ष बढ़ता है। चरण 3: बाल्कन इसका संतुलित उदाहरण है।

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Question Medium Social Science The Age of Industrialisation Nationalism and Imperialism Class 10 Level 3

निम्नलिखित में से कौन सा कथन राष्ट्रवाद के सकारात्मक और नकारात्मक दोनों रूपों को समझाता है?

Which statement explains both positive and negative forms of nationalism?

Explanation opens after your attempt

Correct Answer

B. राष्ट्रवाद एकता दे सकता है, पर संकीर्ण रूप में संघर्ष भी पैदा कर सकता हैNationalism can create unity, but in a narrow form it can also create conflict

Step 1

Concept

Nationalism can give people shared identity and unity.

Step 2

Why this answer is correct

But when it becomes narrow or aggressive, it can increase conflict.

Step 3

Exam Tip

Understand both sides in a balanced way for exams. चरण 1: राष्ट्रवाद लोगों को साझा पहचान और एकता दे सकता है। चरण 2: पर जब यह संकीर्ण या आक्रामक हो जाए तो संघर्ष बढ़ा सकता है। चरण 3: परीक्षा में दोनों पक्षों को संतुलित रूप से समझें।

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Question Expert Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 1

यदि सकारात्मक और नकारात्मक आकृतियां दोनों पढ़ी जा रही हैं तो इसे किस समझ का उदाहरण माना जाएगा?

If both positive and negative shapes are being read what understanding does this show?

Explanation opens after your attempt

Correct Answer

B. आकृति पृष्ठभूमि द्विअर्थताFigure-ground ambiguity

Step 1

Concept

In figure-ground ambiguity both areas give meaning. Exam tip: identify dual reading.

Step 2

Why this answer is correct

The correct answer is B. आकृति पृष्ठभूमि द्विअर्थता / Figure-ground ambiguity. In figure-ground ambiguity both areas give meaning. Exam tip: identify dual reading.

Step 3

Exam Tip

आकृति पृष्ठभूमि द्विअर्थता में दोनों क्षेत्र अर्थ देते हैं। परीक्षा में दोहरी पढ़त को पहचानें।

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Question Hard Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 9

यदि सकारात्मक और ऋणात्मक आकार दोनों समान रूप से आकर्षक हैं तो दर्शक पर क्या प्रभाव होगा?

If positive and negative shapes are equally attractive what effect will it have on viewer?

Explanation opens after your attempt

Correct Answer

A. दर्शक दोनों अर्थों को पढ़ सकता हैViewer may read both meanings

Step 1

Concept

Figure-ground ambiguity can create two meanings. Exam tip: identify dual reading.

Step 2

Why this answer is correct

The correct answer is A. दर्शक दोनों अर्थों को पढ़ सकता है / Viewer may read both meanings. Figure-ground ambiguity can create two meanings. Exam tip: identify dual reading.

Step 3

Exam Tip

figure ground ambiguity दो अर्थ बना सकती है। परीक्षा में dual reading पहचानें।

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Question Easy General Knowledge World History Colonization and Decolonization Class 10 Level 77

औपनिवेशिक शासन में शिक्षा का एक सकारात्मक अनपेक्षित प्रभाव क्या था?

What was one unintended positive effect of education under colonial rule?

Explanation opens after your attempt

Correct Answer

D. राजनीतिक जागरूकता और राष्ट्रीय चेतना का बढ़नाGrowth of political awareness and national consciousness

Step 1

Concept

Education introduced many people to ideas of rights and freedom. For exams remember education with nationalism.

Step 2

Why this answer is correct

The correct answer is D. राजनीतिक जागरूकता और राष्ट्रीय चेतना का बढ़ना / Growth of political awareness and national consciousness. Education introduced many people to ideas of rights and freedom. For exams remember education with nationalism.

Step 3

Exam Tip

शिक्षा ने कई लोगों को अधिकार और स्वतंत्रता के विचारों से परिचित कराया। परीक्षा में शिक्षा और राष्ट्रवाद साथ याद रखें।

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Question Hard General Knowledge Indian History Indian Freedom Movement Class 10 Level 23

उदारवादी नेताओं की संवैधानिक पद्धति का सकारात्मक योगदान क्या था?

What was the positive contribution of the constitutional method of Moderate leaders?

Explanation opens after your attempt

Correct Answer

A. राजनीतिक प्रशिक्षण और सार्वजनिक बहस की परंपरा विकसित हुईPolitical training and tradition of public debate developed

Step 1

Concept

Moderates gave organised language to national issues. Exam tip: remember both contribution and limitation.

Step 2

Why this answer is correct

The correct answer is A. राजनीतिक प्रशिक्षण और सार्वजनिक बहस की परंपरा विकसित हुई / Political training and tradition of public debate developed. Moderates gave organised language to national issues. Exam tip: remember both contribution and limitation.

Step 3

Exam Tip

उदारवादियों ने राष्ट्रीय मुद्दों को संगठित भाषा दी। परीक्षा में योगदान और सीमा दोनों याद रखें।

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Question Expert General Knowledge Indian History Modern Indian History Class 10 Level 14

उदारवादी कांग्रेस की संवैधानिक राजनीति का एक सकारात्मक योगदान क्या था?

What was one positive contribution of Moderate Congress constitutional politics?

Explanation opens after your attempt

Correct Answer

A. उसने राजनीतिक प्रशिक्षण और सार्वजनिक बहस की परंपरा विकसित कीIt developed political training and tradition of public debate

Step 1

Concept

Moderates gave organised and constitutional language to national issues. Exam tip: remember their contribution along with limitations.

Step 2

Why this answer is correct

The correct answer is A. उसने राजनीतिक प्रशिक्षण और सार्वजनिक बहस की परंपरा विकसित की / It developed political training and tradition of public debate. Moderates gave organised and constitutional language to national issues. Exam tip: remember their contribution along with limitations.

Step 3

Exam Tip

उदारवादियों ने राष्ट्रीय मुद्दों को संगठित और संवैधानिक भाषा दी। परीक्षा में उनकी सीमा के साथ योगदान भी याद रखें।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

पहली (60) धनात्मक विषम संख्याओं का योग कितना होगा?

What is the sum of the first (60) positive odd numbers?

Explanation opens after your attempt

Correct Answer

D. (3600)

Step 1

Concept

The sum of the first (n) odd numbers is $n^2$, so $60^2=3600$. Exam tip: remember this result directly.

Step 2

Why this answer is correct

The correct answer is D. (3600). The sum of the first (n) odd numbers is $n^2$, so $60^2=3600$. Exam tip: remember this result directly.

Step 3

Exam Tip

पहली (n) विषम संख्याओं का योग $n^2$ होता है इसलिए $60^2=3600$। परीक्षा में यह परिणाम सीधे याद रखें।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

पहली (n) धनात्मक सम संख्याओं का योग (650) है। (n) का मान क्या होगा?

The sum of the first (n) positive even numbers is (650). What is (n)?

Explanation opens after your attempt

Correct Answer

D. (25)

Step 1

Concept

The sum of the first (n) even numbers is (n(n+1)), so (n=25). Exam tip: you can also treat it as the AP $2,4,6,\ldots$.

Step 2

Why this answer is correct

The correct answer is D. (25). The sum of the first (n) even numbers is (n(n+1)), so (n=25). Exam tip: you can also treat it as the AP $2,4,6,\ldots$.

Step 3

Exam Tip

पहली (n) सम संख्याओं का योग (n(n+1)) होता है इसलिए (n=25)। परीक्षा में इसे समान्तर श्रेणी $2,4,6,\ldots$ भी मान सकते हैं।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समान्तर श्रेणी $150,141,132,\ldots$ के कितने आरम्भिक पदों का योग धनात्मक रहेगा?

For the arithmetic progression $150,141,132,\ldots$, the sum of how many initial terms will remain positive?

Explanation opens after your attempt

Correct Answer

B. (34)

Step 1

Concept

(S_n=\frac{n}{2}(309-9n)) is positive up to (n=34). Exam tip: solve the inequality and then take the integer limit.

Step 2

Why this answer is correct

The correct answer is B. (34). (S_n=\frac{n}{2}(309-9n)) is positive up to (n=34). Exam tip: solve the inequality and then take the integer limit.

Step 3

Exam Tip

(S_n=\frac{n}{2}(309-9n)) धनात्मक होने पर अधिकतम (n=34) है। परीक्षा में असमानता हल करके पूर्णांक सीमा लें।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 68

समान्तर श्रेणी $120,113,106,\ldots$ के कितने आरम्भिक पदों का योग धनात्मक रहेगा?

For the arithmetic progression $120,113,106,\ldots$, the sum of how many initial terms will remain positive?

Explanation opens after your attempt

Correct Answer

C. (35)

Step 1

Concept

(S_n=\frac{n}{2}(247-7n)) is positive up to (n=35). Exam tip: solve the inequality and then take the integer limit.

Step 2

Why this answer is correct

The correct answer is C. (35). (S_n=\frac{n}{2}(247-7n)) is positive up to (n=35). Exam tip: solve the inequality and then take the integer limit.

Step 3

Exam Tip

(S_n=\frac{n}{2}(247-7n)) धनात्मक होने पर अधिकतम (n=35) है। परीक्षा में असमानता हल करके पूर्णांक सीमा लें।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

यदि (a=25), (d=-4) और $S_n=105$, तो (n) का सही धनात्मक मान क्या है?

If (a=25), (d=-4), and $S_n=105$, what is the correct positive value of (n)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

From (\frac{n}{2}[50-4(n-1)]=105), (n=7). Even in a decreasing AP, (n) must be a positive integer.

Step 2

Why this answer is correct

The correct answer is C. (7). From (\frac{n}{2}[50-4(n-1)]=105), (n=7). Even in a decreasing AP, (n) must be a positive integer.

Step 3

Exam Tip

(\frac{n}{2}[50-4(n-1)]=105) से (n=7) मिलता है। घटती श्रेढ़ी में भी (n) धनात्मक पूर्णांक होता है।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

(50) से कम (4) के सभी धनात्मक गुणजों का योग कितना है?

What is the sum of all positive multiples of (4) less than (50)?

Explanation opens after your attempt

Correct Answer

C. (312)

Step 1

Concept

The AP is $4,8,\ldots,48$ with (12) terms, and the sum is (312). Identifying the last allowed multiple is important.

Step 2

Why this answer is correct

The correct answer is C. (312). The AP is $4,8,\ldots,48$ with (12) terms, and the sum is (312). Identifying the last allowed multiple is important.

Step 3

Exam Tip

श्रेढ़ी $4,8,\ldots,48$ है जिसमें (12) पद हैं और योग (312) है। अंतिम स्वीकार्य गुणज पहचानना जरूरी है।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

पहले (40) धनात्मक सम संख्याओं का योग क्या है?

What is the sum of the first (40) positive even numbers?

Explanation opens after your attempt

Correct Answer

C. (1640)

Step 1

Concept

The sum of the first (n) even numbers is (n(n+1)), so $40\times41=1640$. Remember it for even-number AP questions.

Step 2

Why this answer is correct

The correct answer is C. (1640). The sum of the first (n) even numbers is (n(n+1)), so $40\times41=1640$. Remember it for even-number AP questions.

Step 3

Exam Tip

पहली (n) सम संख्याओं का योग (n(n+1)) होता है, इसलिए $40\times41=1640$। इसे सम संख्या वाले प्रश्नों में याद रखें।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

(7) से (140) तक (7) के सभी धनात्मक गुणजों का योग ज्ञात कीजिए।

Find the sum of all positive multiples of (7) from (7) to (140).

Explanation opens after your attempt

Correct Answer

D. (1470)

Step 1

Concept

The AP is $7,14,\ldots,140$ with (20) terms, and its sum is (1470). Finding (n) from the last term is an easy method.

Step 2

Why this answer is correct

The correct answer is D. (1470). The AP is $7,14,\ldots,140$ with (20) terms, and its sum is (1470). Finding (n) from the last term is an easy method.

Step 3

Exam Tip

यह श्रेढ़ी $7,14,\ldots,140$ है जिसमें (20) पद हैं और योग (1470) है। अंतिम पद से (n) निकालना आसान तरीका है।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

पहली (25) धनात्मक विषम संख्याओं का योग कितना है?

What is the sum of the first (25) positive odd numbers?

Explanation opens after your attempt

Correct Answer

C. (625)

Step 1

Concept

The sum of the first (n) odd numbers is $n^2$, so $25^2=625$. This result is useful for quick calculation.

Step 2

Why this answer is correct

The correct answer is C. (625). The sum of the first (n) odd numbers is $n^2$, so $25^2=625$. This result is useful for quick calculation.

Step 3

Exam Tip

पहली (n) विषम संख्याओं का योग $n^2$ होता है, इसलिए $25^2=625$। यह परिणाम तेज गणना में उपयोगी है।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 68

दो अंकों की (4) से विभाज्य सभी धनात्मक संख्याओं का योग ज्ञात कीजिए।

Find the sum of all two-digit positive numbers divisible by (4).

Explanation opens after your attempt

Correct Answer

D. (1188)

Step 1

Concept

The numbers are $12,16,\ldots,96$, and there are (22) terms, so the sum is (1188). Apply the two-digit limit carefully.

Step 2

Why this answer is correct

The correct answer is D. (1188). The numbers are $12,16,\ldots,96$, and there are (22) terms, so the sum is (1188). Apply the two-digit limit carefully.

Step 3

Exam Tip

संख्याएँ $12,16,\ldots,96$ हैं और (22) पद हैं, इसलिए योग (1188) है। दो अंकों की सीमा ध्यान से लगाएँ।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 67

(100) से कम (6) के सभी धनात्मक गुणजों का योग ज्ञात कीजिए।

Find the sum of all positive multiples of (6) less than (100).

Explanation opens after your attempt

Correct Answer

A. (816)

Step 1

Concept

The multiples are from (6) to (96), and there are (16) terms, so the sum is (816). In boundary questions, decide the last term first.

Step 2

Why this answer is correct

The correct answer is A. (816). The multiples are from (6) to (96), and there are (16) terms, so the sum is (816). In boundary questions, decide the last term first.

Step 3

Exam Tip

गुणज (6) से (96) तक हैं और (16) पद हैं, इसलिए योग (816) है। सीमा वाले प्रश्न में अंतिम पद पहले तय करें।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

(5000) से कम (41) के धनात्मक गुणजों की समान्तर श्रेणी में अंतिम पद क्या होगा?

What will be the last term in the AP of positive multiples of (41) less than (5000)?

Explanation opens after your attempt

Correct Answer

B. (4961)

Step 1

Concept

In (41n<5000), the greatest (n=121). The last term will be $41\times121=4961$.

Step 2

Why this answer is correct

The correct answer is B. (4961). In (41n<5000), the greatest (n=121). The last term will be $41\times121=4961$.

Step 3

Exam Tip

(41n<5000) में सबसे बड़ा (n=121) है। अंतिम पद $41\times121=4961$ होगा।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

(3600) से कम (37) के धनात्मक गुणजों की समान्तर श्रेणी में अंतिम पद क्या होगा?

What will be the last term in the AP of positive multiples of (37) less than (3600)?

Explanation opens after your attempt

Correct Answer

C. (3589)

Step 1

Concept

In (37n<3600), the greatest (n=97). The last term will be $37\times97=3589$.

Step 2

Why this answer is correct

The correct answer is C. (3589). In (37n<3600), the greatest (n=97). The last term will be $37\times97=3589$.

Step 3

Exam Tip

(37n<3600) में सबसे बड़ा (n=97) है। अंतिम पद $37\times97=3589$ होगा।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

(2500) से कम (29) के धनात्मक गुणजों की समान्तर श्रेणी में अंतिम पद क्या होगा?

What will be the last term in the AP of positive multiples of (29) less than (2500)?

Explanation opens after your attempt

Correct Answer

B. (2494)

Step 1

Concept

In (29n<2500), the greatest (n=86). The last term will be $29\times86=2494$.

Step 2

Why this answer is correct

The correct answer is B. (2494). In (29n<2500), the greatest (n=86). The last term will be $29\times86=2494$.

Step 3

Exam Tip

(29n<2500) में सबसे बड़ा (n=86) है। अंतिम पद $29\times86=2494$ होगा।

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

(2000) से कम (23) के धनात्मक गुणजों की समान्तर श्रेणी में अंतिम पद क्या है?

What is the last term in the AP of positive multiples of (23) less than (2000)?

Explanation opens after your attempt

Correct Answer

B. (1978)

Step 1

Concept

In (23n<2000), the greatest (n=86). The last term will be $23\times86=1978$.

Step 2

Why this answer is correct

The correct answer is B. (1978). In (23n<2000), the greatest (n=86). The last term will be $23\times86=1978$.

Step 3

Exam Tip

(23n<2000) में सबसे बड़ा (n=86) है। अंतिम पद $23\times86=1978$ होगा।

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

(1500) से कम (19) के धनात्मक गुणजों की समान्तर श्रेणी में अंतिम पद क्या है?

What is the last term in the AP of positive multiples of (19) less than (1500)?

Explanation opens after your attempt

Correct Answer

A. (1482)

Step 1

Concept

In (19n<1500), the greatest (n=78). The last term will be $19\times78=1482$.

Step 2

Why this answer is correct

The correct answer is A. (1482). In (19n<1500), the greatest (n=78). The last term will be $19\times78=1482$.

Step 3

Exam Tip

(19n<1500) में सबसे बड़ा (n=78) है। अंतिम पद $19\times78=1482$ होगा।

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

(1000) से कम (17) के धनात्मक गुणजों की AP में अंतिम पद क्या है?

What is the last term in the AP of positive multiples of (17) less than (1000)?

Explanation opens after your attempt

Correct Answer

B. (986)

Step 1

Concept

In (17n<1000), the greatest (n=58). The last term will be $17\times58=986$.

Step 2

Why this answer is correct

The correct answer is B. (986). In (17n<1000), the greatest (n=58). The last term will be $17\times58=986$.

Step 3

Exam Tip

(17n<1000) में सबसे बड़ा (n=58) है। अंतिम पद $17\times58=986$ होगा।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

(600) से कम (13) के धनात्मक गुणजों में अंतिम पद क्या है?

What is the last term among the positive multiples of (13) less than (600)?

Explanation opens after your attempt

Correct Answer

B. (598)

Step 1

Concept

In (13n<600), the greatest (n=46) so the term is $13\times46=598$. Take the greatest integer below the limit.

Step 2

Why this answer is correct

The correct answer is B. (598). In (13n<600), the greatest (n=46) so the term is $13\times46=598$. Take the greatest integer below the limit.

Step 3

Exam Tip

(13n<600) में सबसे बड़ा (n=46) है इसलिए पद $13\times46=598$। सीमा से कम सबसे बड़ा पूर्णांक लें।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

(500) से कम (11) के धनात्मक गुणजों में अंतिम पद क्या है?

What is the last term among the positive multiples of (11) less than (500)?

Explanation opens after your attempt

Correct Answer

B. (495)

Step 1

Concept

In (11n<500), the greatest (n=45), so the term is $11\times45=495$. Take the greatest integer below the limit.

Step 2

Why this answer is correct

The correct answer is B. (495). In (11n<500), the greatest (n=45), so the term is $11\times45=495$. Take the greatest integer below the limit.

Step 3

Exam Tip

(11n<500) में सबसे बड़ा (n=45) है इसलिए पद $11\times45=495$। सीमा से कम सबसे बड़ा पूर्णांक लें।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

(200) से कम (9) के धनात्मक गुणजों में अंतिम पद क्या है?

What is the last term among the positive multiples of (9) less than (200)?

Explanation opens after your attempt

Correct Answer

C. (198)

Step 1

Concept

In $9,18,27,\ldots$, (9n<200), so the greatest (n=22) and the term is (198). For multiples, take the largest integer below the limit.

Step 2

Why this answer is correct

The correct answer is C. (198). In $9,18,27,\ldots$, (9n<200), so the greatest (n=22) and the term is (198). For multiples, take the largest integer below the limit.

Step 3

Exam Tip

$9,18,27,\ldots$ में (9n<200), इसलिए सबसे बड़ा (n=22) और पद (198) है। गुणजों में सीमा से कम सबसे बड़ा पूर्णांक लें।

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Question Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x^-2-kx+36) के शून्यक धनात्मक और अनुपात (1:4) में हैं, तो (k) क्या है?

If the zeroes of (p(x)=x^-2-kx+36) are positive and in the ratio (1:4), what is (k)?

Explanation opens after your attempt

Correct Answer

A. (15)

Step 1

Concept

Let the zeroes be (t) and (4t), then $4t^2=36$ gives (t=3). The sum is (15), so (k=15).

Step 2

Why this answer is correct

The correct answer is A. (15). Let the zeroes be (t) and (4t), then $4t^2=36$ gives (t=3). The sum is (15), so (k=15).

Step 3

Exam Tip

शून्यक (t) और (4t) मानें, तो $4t^2=36$ से (t=3) है। योग (15) है, इसलिए (k=15)।

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Question Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)=x^-2+kx+16) का एक शून्यक दूसरे का दुगुना है और दोनों धनात्मक हैं, तो (k) क्या होगा?

If one zero of (p(x)=x^-2+kx+16) is twice the other and both are positive, what is (k)?

Explanation opens after your attempt

Correct Answer

A. -$6\sqrt{2}$

Step 1

Concept

Let the zeroes be (t) and (2t), then $2t^2=16$ gives $t=2\sqrt{2}$. The sum is $6\sqrt{2}$, so $-k=6\sqrt{2}$ and $k=-6\sqrt{2}$.

Step 2

Why this answer is correct

The correct answer is A. -$6\sqrt{2}$. Let the zeroes be (t) and (2t), then $2t^2=16$ gives $t=2\sqrt{2}$. The sum is $6\sqrt{2}$, so $-k=6\sqrt{2}$ and $k=-6\sqrt{2}$.

Step 3

Exam Tip

शून्यक (t) और (2t) मानें, तो $2t^2=16$ से $t=2\sqrt{2}$ है। योग $6\sqrt{2}$ है, इसलिए $-k=6\sqrt{2}$ और $k=-6\sqrt{2}$।

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

किस (k) के लिए $x^2+kx+9$ का एक शून्यक दूसरे का तीन गुना है और दोनों धनात्मक हैं?

For which (k) does $x^2+kx+9$ have one zero three times the other and both positive?

Explanation opens after your attempt

Correct Answer

A. $-4\sqrt{3}$

Step 1

Concept

Let the zeroes be (t) and (3t), so $3t^2=9$ gives $t=\sqrt{3}$. The sum is $4\sqrt{3}$, hence $k=-4\sqrt{3}$.

Step 2

Why this answer is correct

The correct answer is A. $-4\sqrt{3}$. Let the zeroes be (t) and (3t), so $3t^2=9$ gives $t=\sqrt{3}$. The sum is $4\sqrt{3}$, hence $k=-4\sqrt{3}$.

Step 3

Exam Tip

शून्यक (t) और (3t) मानें, तो $3t^2=9$ से $t=\sqrt{3}$ है। योग $4\sqrt{3}$ है इसलिए $k=-4\sqrt{3}$।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक संख्या अपने व्युत्क्रम से $\frac{15}{4}$ अधिक है। धनात्मक संख्या क्या है?

A number exceeds its reciprocal by $\frac{15}{4}$. What is the positive number?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

The equation is $x-\frac{1}{x}=\frac{15}{4}$. This gives $4x^2-15x-4=0$, so the positive root is (x=4).

Step 2

Why this answer is correct

The correct answer is B. (4). The equation is $x-\frac{1}{x}=\frac{15}{4}$. This gives $4x^2-15x-4=0$, so the positive root is (x=4).

Step 3

Exam Tip

समीकरण $x-\frac{1}{x}=\frac{15}{4}$ है। इससे $4x^2-15x-4=0$ और धनात्मक हल (x=4) है।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक संख्या के वर्ग में उस संख्या का (9) गुना जोड़ने पर (400) मिलता है। धनात्मक संख्या क्या है?

When (9) times a number is added to its square, the result is (400). What is the positive number?

Explanation opens after your attempt

Correct Answer

A. (16)

Step 1

Concept

The equation is $x^2+9x=400$. From $x^2+9x-400=0$, the positive root is (x=16).

Step 2

Why this answer is correct

The correct answer is A. (16). The equation is $x^2+9x=400$. From $x^2+9x-400=0$, the positive root is (x=16).

Step 3

Exam Tip

समीकरण $x^2+9x=400$ है। $x^2+9x-400=0$ से धनात्मक हल (x=16) है।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

दो क्रमागत विषम धनात्मक पूर्णांकों का गुणनफल (483) है। बड़ी संख्या क्या है?

The product of two consecutive positive odd integers is (483). What is the larger integer?

Explanation opens after your attempt

Correct Answer

B. (23)

Step 1

Concept

The integers are (x) and (x+2). From (x(x+2)=483), (x=21), so the larger integer is (23).

Step 2

Why this answer is correct

The correct answer is B. (23). The integers are (x) and (x+2). From (x(x+2)=483), (x=21), so the larger integer is (23).

Step 3

Exam Tip

संख्याएँ (x) और (x+2) हैं। (x(x+2)=483) से (x=21) मिलता है इसलिए बड़ी संख्या (23) है।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

दो क्रमागत सम धनात्मक पूर्णांकों का गुणनफल (360) है। छोटी संख्या क्या है?

The product of two consecutive positive even integers is (360). What is the smaller integer?

Explanation opens after your attempt

Correct Answer

B. (18)

Step 1

Concept

Let the integers be (x) and (x+2). From (x(x+2)=360), $x^2+2x-360=0$, so (x=18).

Step 2

Why this answer is correct

The correct answer is B. (18). Let the integers be (x) and (x+2). From (x(x+2)=360), $x^2+2x-360=0$, so (x=18).

Step 3

Exam Tip

संख्याएँ (x) और (x+2) मानें। (x(x+2)=360) से $x^2+2x-360=0$ और (x=18) मिलता है।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

दो क्रमागत धनात्मक पूर्णांकों का गुणनफल (552) है। वे पूर्णांक कौन-से हैं?

The product of two consecutive positive integers is (552). Which are the integers?

Explanation opens after your attempt

Correct Answer

B. (23) और (24)(23) and (24)

Step 1

Concept

Let the numbers be (x) and (x+1). From (x(x+1)=552), we get (x=23).

Step 2

Why this answer is correct

The correct answer is B. (23) और (24) / (23) and (24). Let the numbers be (x) and (x+1). From (x(x+1)=552), we get (x=23).

Step 3

Exam Tip

मान लें संख्याएँ (x) और (x+1) हैं। (x(x+1)=552) से (x=23) मिलता है।

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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

दो क्रमागत धनात्मक विषम संख्याओं के वर्गों का योग (394) है। छोटी संख्या क्या है?

The sum of the squares of two consecutive positive odd numbers is (394). What is the smaller number?

Explanation opens after your attempt

Correct Answer

B. (13)

Step 1

Concept

If the numbers are (x) and (x+2), then (x^-2+(x+2)²=394). This gives (x=13).

Step 2

Why this answer is correct

The correct answer is B. (13). If the numbers are (x) and (x+2), then (x^-2+(x+2)²=394). This gives (x=13).

Step 3

Exam Tip

संख्याएँ (x) और (x+2) हों तो (x^-2+(x+2)²=394)। इससे (x=13) है।

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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक धनात्मक संख्या और उसके व्युत्क्रम का अंतर $\frac{3}{2}$ है। संख्या क्या है?

The difference between a positive number and its reciprocal is $\frac{3}{2}$. What is the number?

Explanation opens after your attempt

Correct Answer

C. (2)

Step 1

Concept

The equation is $x-\frac{1}{x}=\frac{3}{2}$. It gives $2x^2-3x-2=0$ and (x=2).

Step 2

Why this answer is correct

The correct answer is C. (2). The equation is $x-\frac{1}{x}=\frac{3}{2}$. It gives $2x^2-3x-2=0$ and (x=2).

Step 3

Exam Tip

समीकरण $x-\frac{1}{x}=\frac{3}{2}$ है। इससे $2x^2-3x-2=0$ और (x=2) मिलता है।

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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

(3) के दो क्रमागत धनात्मक गुणजों का गुणनफल (270) है। वे गुणज कौन से हैं?

The product of two consecutive positive multiples of (3) is (270). Which multiples are they?

Explanation opens after your attempt

Correct Answer

C. (15) और (18)(15) and (18)

Step 1

Concept

Let the multiples be (x) and (x+3). From (x(x+3)=270), we get (x=15).

Step 2

Why this answer is correct

The correct answer is C. (15) और (18) / (15) and (18). Let the multiples be (x) and (x+3). From (x(x+3)=270), we get (x=15).

Step 3

Exam Tip

गुणज (x) और (x+3) मानें। (x(x+3)=270) से (x=15) मिलता है।

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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

दो धनात्मक संख्याओं में अंतर (9) है और उनके वर्गों का योग (585) है। छोटी संख्या क्या है?

Two positive numbers differ by (9) and the sum of their squares is (585). What is the smaller number?

Explanation opens after your attempt

Correct Answer

C. (12)

Step 1

Concept

If the smaller number is (x), then (x^-2+(x+9)²=585). This gives (x=12).

Step 2

Why this answer is correct

The correct answer is C. (12). If the smaller number is (x), then (x^-2+(x+9)²=585). This gives (x=12).

Step 3

Exam Tip

छोटी संख्या (x) हो तो (x^-2+(x+9)²=585)। इससे (x=12) मिलता है।

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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

दो धनात्मक संख्याओं का योग (19) और गुणनफल (84) है। वे संख्याएँ कौन सी हैं?

The sum of two positive numbers is (19) and their product is (84). Which numbers are they?

Explanation opens after your attempt

Correct Answer

B. (7) और (12)(7) and (12)

Step 1

Concept

If one number is (x), the other is (19-x). From (x(19-x)=84), we get (7) and (12).

Step 2

Why this answer is correct

The correct answer is B. (7) और (12) / (7) and (12). If one number is (x), the other is (19-x). From (x(19-x)=84), we get (7) and (12).

Step 3

Exam Tip

यदि एक संख्या (x) है तो दूसरी (19-x) है। (x(19-x)=84) से (7) और (12) मिलते हैं।

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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

दो क्रमागत धनात्मक सम संख्याओं का गुणनफल (224) है। वे संख्याएँ कौन सी हैं?

The product of two consecutive positive even numbers is (224). Which numbers are they?

Explanation opens after your attempt

Correct Answer

C. (14) और (16)(14) and (16)

Step 1

Concept

Let the numbers be (x) and (x+2). From (x(x+2)=224), (x=14).

Step 2

Why this answer is correct

The correct answer is C. (14) और (16) / (14) and (16). Let the numbers be (x) and (x+2). From (x(x+2)=224), (x=14).

Step 3

Exam Tip

संख्याएँ (x) और (x+2) मानें। (x(x+2)=224) से (x=14) है।

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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

दो धनात्मक संख्याओं में अंतर (6) है और उनका गुणनफल (216) है। छोटी संख्या क्या है?

Two positive numbers differ by (6) and their product is (216). What is the smaller number?

Explanation opens after your attempt

Correct Answer

C. (12)

Step 1

Concept

If the smaller number is (x), then (x(x+6)=216). The positive solution is (x=12).

Step 2

Why this answer is correct

The correct answer is C. (12). If the smaller number is (x), then (x(x+6)=216). The positive solution is (x=12).

Step 3

Exam Tip

छोटी संख्या (x) हो तो (x(x+6)=216)। धनात्मक हल (x=12) है।

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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक धनात्मक संख्या और उसके व्युत्क्रम का योग $\frac{5}{2}$ है। वह संख्या क्या हो सकती है?

The sum of a positive number and its reciprocal is $\frac{5}{2}$. What can the number be?

Explanation opens after your attempt

Correct Answer

C. (2) या $\frac{1}{2}$(2) or $\frac{1}{2}$

Step 1

Concept

The equation $x+\frac{1}{x}=\frac{5}{2}$ gives $2x^2-5x+2=0$. The solutions are (x=2) or $x=\frac{1}{2}$.

Step 2

Why this answer is correct

The correct answer is C. (2) या $\frac{1}{2}$ / (2) or $\frac{1}{2}$. The equation $x+\frac{1}{x}=\frac{5}{2}$ gives $2x^2-5x+2=0$. The solutions are (x=2) or $x=\frac{1}{2}$.

Step 3

Exam Tip

समीकरण $x+\frac{1}{x}=\frac{5}{2}$ से $2x^2-5x+2=0$ बनता है। हल (x=2) या $x=\frac{1}{2}$ हैं।

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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

दो क्रमागत धनात्मक विषम संख्याओं का गुणनफल (255) है। वे संख्याएँ कौन सी हैं?

The product of two consecutive positive odd numbers is (255). Which numbers are they?

Explanation opens after your attempt

Correct Answer

C. (15) और (17)(15) and (17)

Step 1

Concept

Let the numbers be (x) and (x+2). From (x(x+2)=255), we get (x=15).

Step 2

Why this answer is correct

The correct answer is C. (15) और (17) / (15) and (17). Let the numbers be (x) and (x+2). From (x(x+2)=255), we get (x=15).

Step 3

Exam Tip

संख्याएँ (x) और (x+2) मानें। (x(x+2)=255) से (x=15) मिलता है।

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Question Medium Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

दो क्रमागत धनात्मक पूर्णांकों का गुणनफल (240) है। वे पूर्णांक कौन से हैं?

The product of two consecutive positive integers is (240). Which integers are they?

Explanation opens after your attempt

Correct Answer

B. (15) और (16)(15) and (16)

Step 1

Concept

Let the integers be (x) and (x+1). From (x(x+1)=240), we get (x=15).

Step 2

Why this answer is correct

The correct answer is B. (15) और (16) / (15) and (16). Let the integers be (x) and (x+1). From (x(x+1)=240), we get (x=15).

Step 3

Exam Tip

मान लें पूर्णांक (x) और (x+1) हैं। (x(x+1)=240) से (x=15) मिलता है।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

एक धनात्मक संख्या और उसके वर्ग का योग (156) है। संख्या क्या है?

The sum of a positive number and its square is (156). What is the number?

Explanation opens after your attempt

Correct Answer

C. (12)

Step 1

Concept

Let the number be (x), then $x^2+x=156$. This gives $x^2+x-156=0$, so the positive root is (12).

Step 2

Why this answer is correct

The correct answer is C. (12). Let the number be (x), then $x^2+x=156$. This gives $x^2+x-156=0$, so the positive root is (12).

Step 3

Exam Tip

संख्या (x) हो, तो $x^2+x=156$। इससे $x^2+x-156=0$, इसलिए धनात्मक मूल (12) है।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

एक धनात्मक भिन्न का हर अंश से (4) अधिक है। भिन्न और उसके व्युत्क्रम का योग $\frac{41}{20}$ है। भिन्न क्या है?

In a positive fraction, the denominator is (4) more than the numerator. The sum of the fraction and its reciprocal is $\frac{41}{20}$. What is the fraction?

Explanation opens after your attempt

Correct Answer

B. $\frac{5}{9}$

Step 1

Concept

Let the fraction be $\frac{x}{x+4}$, then $\frac{x}{x+4}+\frac{x+4}{x}=\frac{41}{20}$. This gives (x=5), so the fraction is $\frac{5}{9}$.

Step 2

Why this answer is correct

The correct answer is B. $\frac{5}{9}$. Let the fraction be $\frac{x}{x+4}$, then $\frac{x}{x+4}+\frac{x+4}{x}=\frac{41}{20}$. This gives (x=5), so the fraction is $\frac{5}{9}$.

Step 3

Exam Tip

भिन्न $\frac{x}{x+4}$ हो, तो $\frac{x}{x+4}+\frac{x+4}{x}=\frac{41}{20}$। इससे (x=5), इसलिए भिन्न $\frac{5}{9}$ है।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

दो धनात्मक संख्याओं का योग (21) है और उनका गुणनफल (108) है। बड़ी संख्या क्या है?

The sum of two positive numbers is (21), and their product is (108). What is the larger number?

Explanation opens after your attempt

Correct Answer

C. (12)

Step 1

Concept

Let the numbers be (x) and (21-x), then (x(21-x)=108). The roots are (9) and (12), so the larger number is (12).

Step 2

Why this answer is correct

The correct answer is C. (12). Let the numbers be (x) and (21-x), then (x(21-x)=108). The roots are (9) and (12), so the larger number is (12).

Step 3

Exam Tip

संख्याएँ (x) और (21-x) हों, तो (x(21-x)=108)। मूल (9) और (12) हैं, इसलिए बड़ी संख्या (12) है।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

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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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

दो क्रमागत विषम धनात्मक पूर्णांकों के वर्गों का योग (394) है। छोटा पूर्णांक क्या है?

The sum of the squares of two consecutive positive odd integers is (394). What is the smaller integer?

Explanation opens after your attempt

Correct Answer

B. (13)

Step 1

Concept

Let the smaller odd integer be (x), then (x^-2+(x+2)²=394). This gives $x^2+2x-195=0$, so (x=13).

Step 2

Why this answer is correct

The correct answer is B. (13). Let the smaller odd integer be (x), then (x^-2+(x+2)²=394). This gives $x^2+2x-195=0$, so (x=13).

Step 3

Exam Tip

छोटा विषम पूर्णांक (x) हो, तो (x^-2+(x+2)²=394)। इससे $x^2+2x-195=0$, इसलिए (x=13)।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक संख्या के (22) कम मान का वर्ग (2500) है। धनात्मक स्थिति में संख्या क्या है?

The square of (22) less than a number is (2500). In the positive case, what is the number?

Explanation opens after your attempt

Correct Answer

C. (72)

Step 1

Concept

((x-22)²=2500) and (x-22=50), so (x=72). After taking square root, choose the sign according to the condition.

Step 2

Why this answer is correct

The correct answer is C. (72). ((x-22)²=2500) and (x-22=50), so (x=72). After taking square root, choose the sign according to the condition.

Step 3

Exam Tip

((x-22)²=2500) और (x-22=50), इसलिए (x=72) है। वर्गमूल के बाद शर्त के अनुसार चिन्ह चुनें।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक संख्या के (18) अधिक मान का वर्ग (4096) है। धनात्मक स्थिति में संख्या क्या है?

The square of (18) more than a number is (4096). In the positive case, what is the number?

Explanation opens after your attempt

Correct Answer

B. (46)

Step 1

Concept

((x+18)²=4096) and (x+18=64), so (x=46). If the positive case is clear, take the positive square root.

Step 2

Why this answer is correct

The correct answer is B. (46). ((x+18)²=4096) and (x+18=64), so (x=46). If the positive case is clear, take the positive square root.

Step 3

Exam Tip

((x+18)²=4096) और (x+18=64), इसलिए (x=46) है। धनात्मक स्थिति स्पष्ट हो तो धनात्मक वर्गमूल लें।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक संख्या के वर्ग में (975) घटाने पर (2625) मिलता है। धनात्मक संख्या क्या है?

When (975) is subtracted from the square of a number, the result is (2625). What is the positive number?

Explanation opens after your attempt

Correct Answer

C. (60)

Step 1

Concept

$x^2-975=2625$ gives $x^2=3600$, so (x=60). Write the subtraction sign carefully.

Step 2

Why this answer is correct

The correct answer is C. (60). $x^2-975=2625$ gives $x^2=3600$, so (x=60). Write the subtraction sign carefully.

Step 3

Exam Tip

$x^2-975=2625$ से $x^2=3600$, इसलिए (x=60) है। घटाव के चिन्ह को ध्यान से लिखें।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक संख्या के वर्ग में (399) जोड़ने पर (3208) मिलता है। धनात्मक संख्या क्या है?

When (399) is added to the square of a number, the result is (3208). What is the positive number?

Explanation opens after your attempt

Correct Answer

C. (53)

Step 1

Concept

$x^2+399=3208$ gives $x^2=2809$, so (x=53). First move the constant to the other side.

Step 2

Why this answer is correct

The correct answer is C. (53). $x^2+399=3208$ gives $x^2=2809$, so (x=53). First move the constant to the other side.

Step 3

Exam Tip

$x^2+399=3208$ से $x^2=2809$, इसलिए (x=53) है। पहले स्थिर संख्या को दूसरी तरफ ले जाएँ।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक संख्या और उसके वर्ग का योग (2352) है। धनात्मक संख्या क्या है?

The sum of a number and its square is (2352). What is the positive number?

Explanation opens after your attempt

Correct Answer

C. (48)

Step 1

Concept

$x^2+x=2352$ gives $x^2+x-2352=0$. The positive solution is (48).

Step 2

Why this answer is correct

The correct answer is C. (48). $x^2+x=2352$ gives $x^2+x-2352=0$. The positive solution is (48).

Step 3

Exam Tip

$x^2+x=2352$ से $x^2+x-2352=0$ मिलता है। धनात्मक हल (48) है।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक धनात्मक संख्या के वर्ग और संख्या के (40) गुने का अंतर (3825) है। संख्या क्या है?

The difference between the square of a positive number and (40) times the number is (3825). What is the number?

Explanation opens after your attempt

Correct Answer

C. (85)

Step 1

Concept

$x^2-40x=3825$ gives $x^2-40x-3825=0$. The positive solution is (x=85).

Step 2

Why this answer is correct

The correct answer is C. (85). $x^2-40x=3825$ gives $x^2-40x-3825=0$. The positive solution is (x=85).

Step 3

Exam Tip

$x^2-40x=3825$ से $x^2-40x-3825=0$ बनता है। धनात्मक हल (x=85) है।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

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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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

एक संख्या के (11) कम और (20) अधिक मानों का गुणनफल (2112) है। धनात्मक मूल संख्या क्या है?

The product of (11) less and (20) more than a number is (2112). What is the positive original number?

Explanation opens after your attempt

Correct Answer

C. (44)

Step 1

Concept

((x-11)(x+20)=2112) gives (x=44). Use signs for less and more carefully.

Step 2

Why this answer is correct

The correct answer is C. (44). ((x-11)(x+20)=2112) gives (x=44). Use signs for less and more carefully.

Step 3

Exam Tip

((x-11)(x+20)=2112) से (x=44) मिलता है। कम और अधिक के चिन्ह सावधानी से लगाएँ।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

दो धनात्मक संख्याओं का योग (90) है और उनके वर्गों का योग (4068) है। छोटी संख्या क्या है?

The sum of two positive numbers is (90) and the sum of their squares is (4068). What is the smaller number?

Explanation opens after your attempt

Correct Answer

B. (42)

Step 1

Concept

Take the numbers as (x) and (90-x). From (x^-2+(90-x)²=4068), the numbers are (42) and (48).

Step 2

Why this answer is correct

The correct answer is B. (42). Take the numbers as (x) and (90-x). From (x^-2+(90-x)²=4068), the numbers are (42) and (48).

Step 3

Exam Tip

संख्याएँ (x) और (90-x) मानें। (x^-2+(90-x)²=4068) से संख्याएँ (42) और (48) मिलती हैं।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

दो धनात्मक संख्याओं का अंतर (19) है और उनका गुणनफल (1632) है। बड़ी संख्या क्या है?

The difference between two positive numbers is (19) and their product is (1632). What is the larger number?

Explanation opens after your attempt

Correct Answer

C. (51)

Step 1

Concept

If the smaller number is (x) and the larger is (x+19), then (x(x+19)=1632). This gives smaller number (32) and larger number (51).

Step 2

Why this answer is correct

The correct answer is C. (51). If the smaller number is (x) and the larger is (x+19), then (x(x+19)=1632). This gives smaller number (32) and larger number (51).

Step 3

Exam Tip

छोटी संख्या (x) और बड़ी (x+19) हो तो (x(x+19)=1632) बनता है। इससे छोटी संख्या (32) और बड़ी संख्या (51) मिलती है।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

दो लगातार सम धनात्मक संख्याओं के वर्गों का योग (3044) है। बड़ी संख्या क्या है?

The sum of squares of two consecutive even positive numbers is (3044). What is the larger number?

Explanation opens after your attempt

Correct Answer

C. (40)

Step 1

Concept

Consecutive even numbers are (x) and (x+2). From (x^-2+(x+2)²=3044), (x=38), so the larger number is (40).

Step 2

Why this answer is correct

The correct answer is C. (40). Consecutive even numbers are (x) and (x+2). From (x^-2+(x+2)²=3044), (x=38), so the larger number is (40).

Step 3

Exam Tip

लगातार सम संख्याएँ (x) और (x+2) हैं। (x^-2+(x+2)²=3044) से (x=38), इसलिए बड़ी संख्या (40) है।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

दो लगातार विषम धनात्मक संख्याओं के वर्गों का योग (2314) है। छोटी संख्या क्या है?

The sum of squares of two consecutive odd positive numbers is (2314). What is the smaller number?

Explanation opens after your attempt

Correct Answer

C. (33)

Step 1

Concept

Consecutive odd numbers are (x) and (x+2). From (x^-2+(x+2)²=2314), (x=33).

Step 2

Why this answer is correct

The correct answer is C. (33). Consecutive odd numbers are (x) and (x+2). From (x^-2+(x+2)²=2314), (x=33).

Step 3

Exam Tip

लगातार विषम संख्याएँ (x) और (x+2) होंगी। (x^-2+(x+2)²=2314) से (x=33) है।

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Question Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 40

दो लगातार धनात्मक पूर्णांकों के वर्गों का योग (1513) है। छोटा पूर्णांक क्या है?

The sum of squares of two consecutive positive integers is (1513). What is the smaller integer?

Explanation opens after your attempt

Correct Answer

C. (27)

Step 1

Concept

If the smaller integer is (x), then (x^-2+(x+1)²=1513), giving (x=27). Write consecutive integers as (x) and (x+1).

Step 2

Why this answer is correct

The correct answer is C. (27). If the smaller integer is (x), then (x^-2+(x+1)²=1513), giving (x=27). Write consecutive integers as (x) and (x+1).

Step 3

Exam Tip

छोटा पूर्णांक (x) हो तो (x^-2+(x+1)²=1513), जिससे (x=27) मिलता है। लगातार पूर्णांकों को (x) और (x+1) लिखें।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक संख्या के (15) कम मान का वर्ग (2209) है। धनात्मक स्थिति में संख्या क्या है?

The square of (15) less than a number is (2209). In the positive case, what is the number?

Explanation opens after your attempt

Correct Answer

C. (62)

Step 1

Concept

((x-15)²=2209) and (x-15=47), so (x=62). After taking square root, choose the sign according to the condition.

Step 2

Why this answer is correct

The correct answer is C. (62). ((x-15)²=2209) and (x-15=47), so (x=62). After taking square root, choose the sign according to the condition.

Step 3

Exam Tip

((x-15)²=2209) और (x-15=47), इसलिए (x=62) है। वर्गमूल के बाद शर्त के अनुसार चिन्ह चुनें।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक संख्या के (14) अधिक मान का वर्ग (2500) है। धनात्मक स्थिति में संख्या क्या है?

The square of (14) more than a number is (2500). In the positive case, what is the number?

Explanation opens after your attempt

Correct Answer

C. (36)

Step 1

Concept

((x+14)²=2500) and (x+14=50), so (x=36). If the positive case is clear, take the positive square root.

Step 2

Why this answer is correct

The correct answer is C. (36). ((x+14)²=2500) and (x+14=50), so (x=36). If the positive case is clear, take the positive square root.

Step 3

Exam Tip

((x+14)²=2500) और (x+14=50), इसलिए (x=36) है। धनात्मक स्थिति स्पष्ट हो तो धनात्मक वर्गमूल लें।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक संख्या के वर्ग में (512) घटाने पर (1809) मिलता है। धनात्मक संख्या क्या है?

When (512) is subtracted from the square of a number, the result is (1809). What is the positive number?

Explanation opens after your attempt

Correct Answer

B. (47)

Step 1

Concept

$x^2-512=1809$ gives $x^2=2321$, which is not $47^2$. The given data are not consistent.

Step 2

Why this answer is correct

The correct answer is B. (47). $x^2-512=1809$ gives $x^2=2321$, which is not $47^2$. The given data are not consistent.

Step 3

Exam Tip

$x^2-512=1809$ से $x^2=2321$ बनता है, जो $47^2$ नहीं है। दिए गए आंकड़ों में संगति नहीं है।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक संख्या के वर्ग में (444) जोड़ने पर (1900) मिलता है। धनात्मक संख्या क्या है?

When (444) is added to the square of a number, the result is (1900). What is the positive number?

Explanation opens after your attempt

Correct Answer

C. (38)

Step 1

Concept

$x^2+444=1900$ gives $x^2=1456$, which is not a perfect square. Therefore, none of the options can be correct.

Step 2

Why this answer is correct

The correct answer is C. (38). $x^2+444=1900$ gives $x^2=1456$, which is not a perfect square. Therefore, none of the options can be correct.

Step 3

Exam Tip

$x^2+444=1900$ से $x^2=1456$ नहीं, बल्कि सही घटाव (1900-444=1456) है जो पूर्ण वर्ग नहीं है। इसलिए कोई विकल्प सही नहीं हो सकता।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक संख्या और उसके वर्ग का योग (1892) है। धनात्मक संख्या क्या है?

The sum of a number and its square is (1892). What is the positive number?

Explanation opens after your attempt

Correct Answer

C. (43)

Step 1

Concept

$x^2+x=1892$ gives $x^2+x-1892=0$. The positive solution is (43).

Step 2

Why this answer is correct

The correct answer is C. (43). $x^2+x=1892$ gives $x^2+x-1892=0$. The positive solution is (43).

Step 3

Exam Tip

$x^2+x=1892$ से $x^2+x-1892=0$ मिलता है। धनात्मक हल (43) है।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक धनात्मक संख्या के वर्ग और संख्या के (27) गुने का अंतर (1000) है। संख्या क्या है?

The difference between the square of a positive number and (27) times the number is (1000). What is the number?

Explanation opens after your attempt

Correct Answer

C. (50)

Step 1

Concept

$x^2-27x=1000$ gives $x^2-27x-1000=0$. The positive solution is (x=50).

Step 2

Why this answer is correct

The correct answer is C. (50). $x^2-27x=1000$ gives $x^2-27x-1000=0$. The positive solution is (x=50).

Step 3

Exam Tip

$x^2-27x=1000$ से $x^2-27x-1000=0$ बनता है। धनात्मक हल (x=50) है।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

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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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक संख्या के (9) कम और (16) अधिक मानों का गुणनफल (1110) है। धनात्मक मूल संख्या क्या है?

The product of (9) less and (16) more than a number is (1110). What is the positive original number?

Explanation opens after your attempt

Correct Answer

D. (39)

Step 1

Concept

((x-9)(x+16)=1110) gives (x=39). Use signs for less and more carefully.

Step 2

Why this answer is correct

The correct answer is D. (39). ((x-9)(x+16)=1110) gives (x=39). Use signs for less and more carefully.

Step 3

Exam Tip

((x-9)(x+16)=1110) से (x=39) मिलता है। कम और अधिक के चिन्ह सावधानी से लगाएँ।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

दो धनात्मक संख्याओं का योग (80) है और उनके वर्गों का योग (3232) है। छोटी संख्या क्या है?

The sum of two positive numbers is (80) and the sum of their squares is (3232). What is the smaller number?

Explanation opens after your attempt

Correct Answer

B. (36)

Step 1

Concept

Take the numbers as (x) and (80-x). From (x^-2+(80-x)²=3232), the numbers are (36) and (44).

Step 2

Why this answer is correct

The correct answer is B. (36). Take the numbers as (x) and (80-x). From (x^-2+(80-x)²=3232), the numbers are (36) and (44).

Step 3

Exam Tip

संख्याएँ (x) और (80-x) मानें। (x^-2+(80-x)²=3232) से संख्याएँ (36) और (44) मिलती हैं।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

दो धनात्मक संख्याओं का अंतर (17) है और उनका गुणनफल (1260) है। बड़ी संख्या क्या है?

The difference between two positive numbers is (17) and their product is (1260). What is the larger number?

Explanation opens after your attempt

Correct Answer

D. (45)

Step 1

Concept

If the smaller number is (x) and the larger is (x+17), then (x(x+17)=1260). This gives smaller number (28) and larger number (45).

Step 2

Why this answer is correct

The correct answer is D. (45). If the smaller number is (x) and the larger is (x+17), then (x(x+17)=1260). This gives smaller number (28) and larger number (45).

Step 3

Exam Tip

छोटी संख्या (x) और बड़ी (x+17) हो तो (x(x+17)=1260) बनता है। इससे छोटी संख्या (28) और बड़ी संख्या (45) मिलती है।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

दो लगातार सम धनात्मक संख्याओं के वर्गों का योग (2452) है। बड़ी संख्या क्या है?

The sum of squares of two consecutive even positive numbers is (2452). What is the larger number?

Explanation opens after your attempt

Correct Answer

C. (36)

Step 1

Concept

Consecutive even numbers are (x) and (x+2). From (x^-2+(x+2)²=2452), (x=34), so the larger number is (36).

Step 2

Why this answer is correct

The correct answer is C. (36). Consecutive even numbers are (x) and (x+2). From (x^-2+(x+2)²=2452), (x=34), so the larger number is (36).

Step 3

Exam Tip

लगातार सम संख्याएँ (x) और (x+2) हैं। (x^-2+(x+2)²=2452) से (x=34), इसलिए बड़ी संख्या (36) है।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

दो लगातार विषम धनात्मक संख्याओं के वर्गों का योग (2050) है। छोटी संख्या क्या है?

The sum of squares of two consecutive odd positive numbers is (2050). What is the smaller number?

Explanation opens after your attempt

Correct Answer

C. (31)

Step 1

Concept

Consecutive odd numbers are (x) and (x+2). From (x^-2+(x+2)²=2050), (x=31).

Step 2

Why this answer is correct

The correct answer is C. (31). Consecutive odd numbers are (x) and (x+2). From (x^-2+(x+2)²=2050), (x=31).

Step 3

Exam Tip

लगातार विषम संख्याएँ (x) और (x+2) होंगी। (x^-2+(x+2)²=2050) से (x=31) है।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

दो लगातार धनात्मक पूर्णांकों के वर्गों का योग (1201) है। छोटा पूर्णांक क्या है?

The sum of squares of two consecutive positive integers is (1201). What is the smaller integer?

Explanation opens after your attempt

Correct Answer

C. (24)

Step 1

Concept

If the smaller integer is (x), then (x^-2+(x+1)²=1201), giving (x=24). Write consecutive integers as (x) and (x+1).

Step 2

Why this answer is correct

The correct answer is C. (24). If the smaller integer is (x), then (x^-2+(x+1)²=1201), giving (x=24). Write consecutive integers as (x) and (x+1).

Step 3

Exam Tip

छोटा पूर्णांक (x) हो तो (x^-2+(x+1)²=1201), जिससे (x=24) मिलता है। लगातार पूर्णांकों को (x) और (x+1) लिखें।

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Question Hard Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 41

एक संख्या के (11) कम मान का वर्ग (1156) है। धनात्मक स्थिति में संख्या क्या है?

The square of (11) less than a number is (1156). In the positive case, what is the number?

Explanation opens after your attempt

Correct Answer

C. (45)

Step 1

Concept

((x-11)²=1156) and (x-11=34), so (x=45). After taking square root, choose the sign according to the condition.

Step 2

Why this answer is correct

The correct answer is C. (45). ((x-11)²=1156) and (x-11=34), so (x=45). After taking square root, choose the sign according to the condition.

Step 3

Exam Tip

((x-11)²=1156) और (x-11=34), इसलिए (x=45) है। वर्गमूल के बाद शर्त के अनुसार चिन्ह चुनें।

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यदि दो वास्तविक मूलों का गुणनफल धनात्मक और योग धनात्मक है तो दोनों मूल कैसे होंगे?

Concept

Why this answer is correct

Exam Tip

किस विकल्प में मूलों का योग धनात्मक और गुणनफल धनात्मक होगा?

Concept

Why this answer is correct

Exam Tip

किस स्थिति में सकारात्मक आकार सबसे स्पष्ट होगा?

Concept

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Exam Tip

सकारात्मक और ऋणात्मक स्थान का संतुलन किसमें सबसे अधिक मदद करता है?

Concept

Why this answer is correct

Exam Tip

किस विकल्प में सकारात्मक और ऋणात्मक आकार का संबंध दिखता है?

Concept

Why this answer is correct

Exam Tip

सकारात्मक स्थान किस भाग को कहते हैं?

Concept

Why this answer is correct

Exam Tip

किसी समांतर श्रेढ़ी में \(S_{16}=816\) और (a=6) है। यदि (d) धनात्मक है, तो (d) ज्ञात कीजिए।

Concept

Why this answer is correct

Exam Tip

यदि (d>0) है और प्रथम पद धनात्मक है, तो समांतर श्रेढ़ी के पद सामान्यतः कैसे बदलेंगे?

Concept

Why this answer is correct

Exam Tip

यदि \(x^2+px+64=0\) की जड़ें समान और धनात्मक हैं, तो (p) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(x^2-6x+c=0\) की दोनों जड़ें वास्तविक और धनात्मक हैं, तो (c) पर सही शर्त क्या है?

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Why this answer is correct

Exam Tip

यदि \(x^2+px+36=0\) की जड़ें समान और धनात्मक हैं, तो (p) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(x^2-5x+c=0\) की दोनों जड़ें वास्तविक और धनात्मक हैं, तो (c) पर सही शर्त क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(x^2+px+16=0\) की जड़ें समान और धनात्मक हैं, तो (p) का मान क्या है?

Concept

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Exam Tip

\(x^2-sx+9=0\) की जड़ें समान और धनात्मक हों, तो (s) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2+px+36=0\) के मूल समान और धनात्मक हैं। (p) का मान क्या होगा?

Concept

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Exam Tip

समीकरण \(x^2+px+25=0\) के मूल समान और धनात्मक हैं। (p) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2+px+16=0\) के मूल समान और धनात्मक हैं। (p) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

किस समीकरण में मूल बराबर और धनात्मक होंगे?

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Exam Tip

समीकरण \(x^2+kx+49=0\) में यदि मूल समान और धनात्मक हैं, तो (k) का संभव मान कौन-सा है?

Concept

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Exam Tip

बाल्कन के मामले में राष्ट्रवाद को सकारात्मक और नकारात्मक दोनों रूपों में क्यों देखा जा सकता है?

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