Search: Algebraic Identities

Question Hard Social Science The Age of Industrialisation The French Revolution and the Idea of the Nation Class 10 Level 8

फ्रांसीसी क्रांति के बाद राष्ट्र की धारणा में क्षेत्रीय पहचानों की भूमिका को कैसे समझना चाहिए?

How should the role of regional identities in the idea of nation after the French Revolution be understood?

Explanation opens after your attempt

Correct Answer

A. उन्हें पूरी तरह मिटाने के बजाय एक बड़ी राष्ट्रीय पहचान में जोड़ने की कोशिश हुईThey were not simply erased but were brought under a larger national identity

Step 1

Concept

Different regions of France had their own identities.

Step 2

Why this answer is correct

The Revolution tried to connect them within a shared civic nation.

Step 3

Exam Tip

Understand nationalism as a process of bringing diversity into one framework. चरण 1: फ्रांस में अलग-अलग क्षेत्रों की अपनी पहचानें थीं। चरण 2: क्रांति ने उन्हें साझा नागरिक राष्ट्र के अंदर जोड़ने की कोशिश की। चरण 3: राष्ट्रवाद को विविधता को एक ढांचे में बांधने की प्रक्रिया के रूप में समझें।

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Question Hard General Knowledge Indian Geography Mountains and Plateaus Class 10 Level 97

कंचनजंगा और नंदा देवी की अलग-अलग क्षेत्रीय पहचान का सही आधार क्या है?

What is the correct basis of the different regional identities of Kanchenjunga and Nanda Devi?

Explanation opens after your attempt

Correct Answer

D. कंचनजंगा सिक्किम से और नंदा देवी उत्तराखंड से जुड़ी हैKanchenjunga is linked with Sikkim and Nanda Devi with Uttarakhand

Step 1

Concept

Kanchenjunga is linked with Eastern Himalaya and Sikkim, while Nanda Devi is linked with Uttarakhand. For exams, remember peak-state relations separately.

Step 2

Why this answer is correct

The correct answer is D. कंचनजंगा सिक्किम से और नंदा देवी उत्तराखंड से जुड़ी है / Kanchenjunga is linked with Sikkim and Nanda Devi with Uttarakhand. Kanchenjunga is linked with Eastern Himalaya and Sikkim, while Nanda Devi is linked with Uttarakhand. For exams, remember peak-state relations separately.

Step 3

Exam Tip

कंचनजंगा पूर्वी हिमालय और सिक्किम से जुड़ी है जबकि नंदा देवी उत्तराखंड से। परीक्षा में चोटी-राज्य संबंध अलग-अलग याद रखें।

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

औपनिवेशिक जनगणना ने सामाजिक पहचानों को राजनीतिक प्रश्न कैसे बनाया?

How did colonial census turn social identities into political questions?

Explanation opens after your attempt

Correct Answer

A. समूहों को प्रशासनिक श्रेणियों में बांटकर प्रतिनिधित्व और अधिकार की बहस बढ़ाईBy dividing groups into administrative categories and increasing debate on representation and rights

Step 1

Concept

Census was linked with classification and rule. For exams write the relation between knowledge and power.

Step 2

Why this answer is correct

The correct answer is A. समूहों को प्रशासनिक श्रेणियों में बांटकर प्रतिनिधित्व और अधिकार की बहस बढ़ाई / By dividing groups into administrative categories and increasing debate on representation and rights. Census was linked with classification and rule. For exams write the relation between knowledge and power.

Step 3

Exam Tip

जनगणना वर्गीकरण और शासन से जुड़ी थी। परीक्षा में ज्ञान और सत्ता का संबंध लिखें।

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Question Expert Social Science Chapter 2: Nationalism in India The Sense of Collective Belonging Class 10 Level 26

स्थानीय और राष्ट्रीय पहचान के संबंध को सामूहिक अपनेपन में कैसे समझना चाहिए?

How should the relation between local and national identities be understood in collective belonging?

Explanation opens after your attempt

Correct Answer

D. स्थानीय संस्कृतियों को व्यापक राष्ट्रीय पहचान से जोड़ने का प्रयास हुआAn effort was made to connect local cultures with wider national identity

Step 1

Concept

India had rich local traditions.

Step 2

Why this answer is correct

Nationalists tried to connect them with wider national identity.

Step 3

Exam Tip

In exams understand local and national identities as connected not opposite. चरण 1: भारत में स्थानीय परंपराएँ बहुत समृद्ध थीं। चरण 2: राष्ट्रवादियों ने इन्हें व्यापक राष्ट्रीय पहचान से जोड़ने की कोशिश की। चरण 3: परीक्षा में स्थानीय और राष्ट्रीय को विरोधी नहीं बल्कि जुड़े हुए रूप में समझें।

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Question Expert Social Science Chapter 2: Nationalism in India The Sense of Collective Belonging Class 10 Level 25

सामूहिक अपनेपन की भावना में स्थानीय और राष्ट्रीय पहचान का संबंध कैसा था?

What was the relation between local and national identities in the sense of collective belonging?

Explanation opens after your attempt

Correct Answer

A. स्थानीय संस्कृतियों को व्यापक राष्ट्रीय पहचान से जोड़ने का प्रयास हुआAn effort was made to link local cultures with wider national identity

Step 1

Concept

India had rich local traditions.

Step 2

Why this answer is correct

Nationalists tried to connect them with a wider national identity.

Step 3

Exam Tip

In exams understand local and national identities as connected not opposite. चरण 1: भारत में स्थानीय परंपराएँ बहुत समृद्ध थीं। चरण 2: राष्ट्रवादियों ने उन्हें व्यापक राष्ट्रीय पहचान से जोड़ने की कोशिश की। चरण 3: परीक्षा में स्थानीय और राष्ट्रीय को विरोधी नहीं बल्कि जुड़े हुए रूप में समझें।

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Question Expert Social Science The Age of Industrialisation The French Revolution and the Idea of the Nation Class 10 Level 10

फ्रांस में पुरानी प्रांतीय पहचान से ऊपर राष्ट्रीय पहचान बनाने में कौन सा उपाय सहायक था?

Which measure helped create a national identity above old provincial identities in France?

Explanation opens after your attempt

Correct Answer

A. साझा कानून और साझा प्रशासनCommon laws and common administration

Step 1

Concept

Provincial separation was an obstacle to national unity.

Step 2

Why this answer is correct

Common laws and administration connected people in one political framework.

Step 3

Exam Tip

Treat it as an institutional process of nation-building. चरण 1: प्रांतीय अलगाव राष्ट्रीय एकता में बाधा था। चरण 2: साझा कानून और प्रशासन ने लोगों को एक राजनीतिक ढांचे में जोड़ा। चरण 3: इसे राष्ट्र निर्माण की संस्थागत प्रक्रिया मानें।

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Question Easy Social Science The Age of Industrialisation Nationalism and Imperialism Class 10 Level 4

बाल्कन में जातीय समूहों की पहचान किससे जुड़ी थी?

With what were ethnic identities in the Balkans linked?

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Correct Answer

A. भाषा संस्कृति और इतिहास सेLanguage, culture, and history

Step 1

Concept

National identity is not formed only by politics.

Step 2

Why this answer is correct

Language, culture, and history also create identity.

Step 3

Exam Tip

Balkan groups asserted their identities on these bases. चरण 1: राष्ट्रवादी पहचान केवल राजनीति से नहीं बनती। चरण 2: भाषा संस्कृति और इतिहास भी पहचान बनाते हैं। चरण 3: बाल्कन समूहों ने इन्हीं आधारों पर अपनी अलग पहचान जताई।

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि \(y \neq 0\), तो (\dfrac{(x+y)³-(x-y)³}{2y}) का सरल रूप क्या है?

If \(y \neq 0\), what is the simplified form of (\dfrac{(x+y)³-(x-y)³}{2y})?

Explanation opens after your attempt

Correct Answer

A. \(,3x^2+y^2,\)

Step 1

Concept

The numerator difference is (6x^-2y+2y^-3=2y\(3x^2+y^2\)), so division gives \(3x^2+y^2\). In exams, take out the common factor.

Step 2

Why this answer is correct

The correct answer is A. \(,3x^2+y^2,\). The numerator difference is (6x^-2y+2y^-3=2y\(3x^2+y^2\)), so division gives \(3x^2+y^2\). In exams, take out the common factor.

Step 3

Exam Tip

ऊपर का अंतर (6x^-2y+2y^-3=2y\(3x^2+y^2\)) है, इसलिए भाग देने पर \(3x^2+y^2\) मिलता है। परीक्षा में common factor निकालें।

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((x+1)³-(x-1)³) का सरल रूप क्या है?

What is the simplified form of ((x+1)³-(x-1)³)?

Explanation opens after your attempt

Correct Answer

A. \(,6x^2+2,\)

Step 1

Concept

On expansion, ((x+1)³=x^-3+3x^-2+3x+1) and ((x-1)³=x^-3-3x^-2+3x-1), so the difference is \(6x^2+2\). In exams, expand cubes carefully.

Step 2

Why this answer is correct

The correct answer is A. \(,6x^2+2,\). On expansion, ((x+1)³=x^-3+3x^-2+3x+1) and ((x-1)³=x^-3-3x^-2+3x-1), so the difference is \(6x^2+2\). In exams, expand cubes carefully.

Step 3

Exam Tip

विस्तार करने पर ((x+1)³=x^-3+3x^-2+3x+1) और ((x-1)³=x^-3-3x^-2+3x-1), इसलिए अंतर \(6x^2+2\) है। परीक्षा में cube expansion ध्यान से करें।

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\(8x^3+1\)) को ((2x+1)) से भाग देने पर भागफल क्या है?

What is the quotient when (\(8x^3+1\)) is divided by ((2x+1))?

Explanation opens after your attempt

Correct Answer

A. \(,4x^2-2x+1,\)

Step 1

Concept

Because (8x^-3+1=(2x)³+1³=(2x+1)\(4x^2-2x+1\)). In exams, remember the identity for sum of cubes.

Step 2

Why this answer is correct

The correct answer is A. \(,4x^2-2x+1,\). Because (8x^-3+1=(2x)³+1³=(2x+1)\(4x^2-2x+1\)). In exams, remember the identity for sum of cubes.

Step 3

Exam Tip

क्योंकि (8x^-3+1=(2x)³+1³=(2x+1)\(4x^2-2x+1\))। परीक्षा में sum of cubes की identity याद रखें।

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((3x+2)²-(3x-2)²) का सरल रूप क्या है?

What is the simplified form of ((3x+2)²-(3x-2)²)?

Explanation opens after your attempt

Correct Answer

A. (,24x,)

Step 1

Concept

This is of the form ((A+B)²-(A-B)²=4AB), where (A=3x) and (B=2), so the answer is (24x). In exams, identities save time.

Step 2

Why this answer is correct

The correct answer is A. (,24x,). This is of the form ((A+B)²-(A-B)²=4AB), where (A=3x) and (B=2), so the answer is (24x). In exams, identities save time.

Step 3

Exam Tip

यह ((A+B)²-(A-B)²=4AB) का रूप है, जहां (A=3x) और (B=2), इसलिए उत्तर (24x) है। परीक्षा में identity से समय बचता है।

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((x-2)\(x^2+2x+4\)) का विस्तार क्या है?

What is the expansion of ((x-2)\(x^2+2x+4\))?

Explanation opens after your attempt

Correct Answer

A. \(,x^3-8,\)

Step 1

Concept

This matches ((a-b)\(a^2+ab+b^2\)=a^-3-b^-3), so the answer is \(x^3-8\). In exams, identifying the identity makes expansion faster.

Step 2

Why this answer is correct

The correct answer is A. \(,x^3-8,\). This matches ((a-b)\(a^2+ab+b^2\)=a^-3-b^-3), so the answer is \(x^3-8\). In exams, identifying the identity makes expansion faster.

Step 3

Exam Tip

यह ((a-b)\(a^2+ab+b^2\)=a^-3-b^-3) का रूप है, इसलिए उत्तर \(x^3-8\) है। परीक्षा में identity पहचानने से विस्तार जल्दी होता है।

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((2m-n)²-(m+n)²) का सरल रूप क्या है?

What is the simplified form of ((2m-n)²-(m+n)²)?

Explanation opens after your attempt

Correct Answer

A. \(,3m^2-6mn,\)

Step 1

Concept

On expansion, ((2m-n)²=4m^-2-4mn+n^-2) and ((m+n)²=m^-2+2mn+n^-2), so the difference is \(3m^2-6mn\). In exams, check the signs carefully.

Step 2

Why this answer is correct

The correct answer is A. \(,3m^2-6mn,\). On expansion, ((2m-n)²=4m^-2-4mn+n^-2) and ((m+n)²=m^-2+2mn+n^-2), so the difference is \(3m^2-6mn\). In exams, check the signs carefully.

Step 3

Exam Tip

विस्तार करने पर ((2m-n)²=4m^-2-4mn+n^-2) और ((m+n)²=m^-2+2mn+n^-2), इसलिए अंतर \(3m^2-6mn\) है। परीक्षा में चिन्हों की जांच करें।

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\(x^3-27\)) को ((x-3)) से भाग देने पर भागफल क्या होगा?

What is the quotient when (\(x^3-27\)) is divided by ((x-3))?

Explanation opens after your attempt

Correct Answer

A. \(,x^2+3x+9,\)

Step 1

Concept

Because (x^-3-27=(x-3)\(x^2+3x+9\)), the quotient is \(x^2+3x+9\). In exams, identify the difference of cubes.

Step 2

Why this answer is correct

The correct answer is A. \(,x^2+3x+9,\). Because (x^-3-27=(x-3)\(x^2+3x+9\)), the quotient is \(x^2+3x+9\). In exams, identify the difference of cubes.

Step 3

Exam Tip

क्योंकि (x^-3-27=(x-3)\(x^2+3x+9\)), इसलिए भागफल \(x^2+3x+9\) है। परीक्षा में घन के अंतर की पहचान करें।

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

((m+n)²+(m-n)²) का सरल रूप क्या है?

What is the simplified form of ((m+n)²+(m-n)²)?

Explanation opens after your attempt

Correct Answer

A. \(,2m^2+2n^2,\)

Step 1

Concept

When both expansions are added, (2mn) and (-2mn) cancel, giving \(2m^2+2n^2\). In exams, notice opposite middle terms.

Step 2

Why this answer is correct

The correct answer is A. \(,2m^2+2n^2,\). When both expansions are added, (2mn) and (-2mn) cancel, giving \(2m^2+2n^2\). In exams, notice opposite middle terms.

Step 3

Exam Tip

दोनों विस्तारों को जोड़ने पर (2mn) और (-2mn) कट जाते हैं, इसलिए \(2m^2+2n^2\) मिलता है। परीक्षा में opposite middle terms पर ध्यान दें।

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\(\sqrt{5}+\sqrt{2}\)\(\sqrt{5}-\sqrt{2}\)) का मान क्या है?

What is the value of (\(\sqrt{5}+\sqrt{2}\)\(\sqrt{5}-\sqrt{2}\))?

Explanation opens after your attempt

Correct Answer

A. (,3,)

Step 1

Concept

This is ((a+b)(a-b)=a^-2-b^-2), so (5-2=3). In exams, identify a conjugate product.

Step 2

Why this answer is correct

The correct answer is A. (,3,). This is ((a+b)(a-b)=a^-2-b^-2), so (5-2=3). In exams, identify a conjugate product.

Step 3

Exam Tip

यह ((a+b)(a-b)=a^-2-b^-2) है, इसलिए (5-2=3)। परीक्षा में conjugate product को पहचानें।

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\(x^3-8\)) को ((x-2)) से भाग देने पर भागफल क्या होगा?

What is the quotient when (\(x^3-8\)) is divided by ((x-2))?

Explanation opens after your attempt

Correct Answer

A. \(,x^2+2x+4,\)

Step 1

Concept

Because (x^-3-8=(x-2)\(x^2+2x+4\)), the quotient is \(x^2+2x+4\). In exams, remember the identity for cubes.

Step 2

Why this answer is correct

The correct answer is A. \(,x^2+2x+4,\). Because (x^-3-8=(x-2)\(x^2+2x+4\)), the quotient is \(x^2+2x+4\). In exams, remember the identity for cubes.

Step 3

Exam Tip

क्योंकि (x^-3-8=(x-2)\(x^2+2x+4\)), इसलिए भागफल \(x^2+2x+4\) है। परीक्षा में cubes की identity याद रखें।

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

((p+q)²-(p-q)²) का सरल रूप क्या है?

What is the simplified form of ((p+q)²-(p-q)²)?

Explanation opens after your attempt

Correct Answer

A. (,4pq,)

Step 1

Concept

On expansion, ((p+q)²=p^-2+2pq+q^-2) and ((p-q)²=p^-2-2pq+q^-2), so the difference is (4pq). In exams, apply standard identities directly.

Step 2

Why this answer is correct

The correct answer is A. (,4pq,). On expansion, ((p+q)²=p^-2+2pq+q^-2) and ((p-q)²=p^-2-2pq+q^-2), so the difference is (4pq). In exams, apply standard identities directly.

Step 3

Exam Tip

विस्तार करने पर ((p+q)²=p^-2+2pq+q^-2) और ((p-q)²=p^-2-2pq+q^-2), इसलिए अंतर (4pq) है। परीक्षा में standard identities सीधे लगाएं।

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

यदि \(x \neq y\), तो \(\dfrac{x^2-y^2}{x-y}\) का सरल रूप क्या होगा?

If \(x \neq y\), what is the simplified form of \(\dfrac{x^2-y^2}{x-y}\)?

Explanation opens after your attempt

Correct Answer

A. (,x+y,)

Step 1

Concept

Because (x^-2-y^-2=(x-y)(x+y)), the simplified form is (x+y). In exams, identifying difference of squares is very useful.

Step 2

Why this answer is correct

The correct answer is A. (,x+y,). Because (x^-2-y^-2=(x-y)(x+y)), the simplified form is (x+y). In exams, identifying difference of squares is very useful.

Step 3

Exam Tip

क्योंकि (x^-2-y^-2=(x-y)(x+y)), इसलिए सरल रूप (x+y) है। परीक्षा में difference of squares पहचानना बहुत उपयोगी है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

संपाती रेखाओं के लिए सही बीजीय शर्त कौन-सी है?

Which algebraic condition is correct for coincident lines?

Explanation opens after your attempt

Correct Answer

C. \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)

Step 1

Concept

Coincident lines represent the same line. Hence all three ratios are equal and infinitely many solutions occur.

Step 2

Why this answer is correct

The correct answer is C. \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\). Coincident lines represent the same line. Hence all three ratios are equal and infinitely many solutions occur.

Step 3

Exam Tip

संपाती रेखाएँ एक ही रेखा को दर्शाती हैं। इसलिए तीनों अनुपात समान होते हैं और अनंत हल मिलते हैं।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

समीकरणों (18x-7y=31) और (6x+7y=41) के हल में (x+2y) का मान क्या है?

For (18x-7y=31) and (6x+7y=41), what is the value of (x+2y) in the solution?

Explanation opens after your attempt

Correct Answer

B. (12)

Step 1

Concept

Adding gives (24x=72), so (x=3). From the second equation \(y=\frac{23}{7}\), so \(x+2y=\frac{67}{7}\).

Step 2

Why this answer is correct

The correct answer is B. (12). Adding gives (24x=72), so (x=3). From the second equation \(y=\frac{23}{7}\), so \(x+2y=\frac{67}{7}\).

Step 3

Exam Tip

जोड़ने पर (24x=72), इसलिए (x=3)। दूसरे से (18+7y=41), इसलिए \(y=\frac{23}{7}\) और \(x+2y=\frac{67}{7}\)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (y=2x+3) और (5x-2y=1), तो (x) का मान क्या है?

If (y=2x+3) and (5x-2y=1), what is the value of (x)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

Substituting (y=2x+3) gives (5x-2(2x+3)=1). This gives (x=7); handle the negative sign outside brackets carefully.

Step 2

Why this answer is correct

The correct answer is C. (7). Substituting (y=2x+3) gives (5x-2(2x+3)=1). This gives (x=7); handle the negative sign outside brackets carefully.

Step 3

Exam Tip

(y=2x+3) रखने पर (5x-2(2x+3)=1)। इससे (x=7) मिलता है, कोष्ठक खोलते समय चिन्ह ध्यान रखें।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (6x+5y=64) और (3x-5y=-4), तो (y) का मान क्या है?

If (6x+5y=64) and (3x-5y=-4), what is the value of (y)?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

Adding gives (9x=60), so \(x=\frac{20}{3}\). Substitute back carefully to avoid arithmetic errors.

Step 2

Why this answer is correct

The correct answer is C. (8). Adding gives (9x=60), so \(x=\frac{20}{3}\). Substitute back carefully to avoid arithmetic errors.

Step 3

Exam Tip

जोड़ने पर (9x=60), इसलिए \(x=\frac{20}{3}\)। दूसरे समीकरण में रखने पर (20-5y=-4), इसलिए \(y=\frac{24}{5}\) नहीं; पुनः जांच करें।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

समीकरणों (7x+11y=103) और (14x-11y=23) को हल करने पर (x) का मान क्या है?

Solving (7x+11y=103) and (14x-11y=23), what is the value of (x)?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

Adding gives (21x=126), so (x=6). In such questions, one variable is eliminated immediately.

Step 2

Why this answer is correct

The correct answer is C. (6). Adding gives (21x=126), so (x=6). In such questions, one variable is eliminated immediately.

Step 3

Exam Tip

जोड़ने पर (21x=126), इसलिए (x=6)। ऐसे प्रश्नों में एक चर तुरंत समाप्त हो जाता है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि \(\frac{x-1}{2}+\frac{y+1}{3}=8\) और \(\frac{x-1}{3}-\frac{y+1}{2}=-1\), तो (x) का मान क्या है?

If \(\frac{x-1}{2}+\frac{y+1}{3}=8\) and \(\frac{x-1}{3}-\frac{y+1}{2}=-1\), what is the value of (x)?

Explanation opens after your attempt

Correct Answer

D. (13)

Step 1

Concept

Let (u=x-1) and (v=y+1). Solve (3u+2v=48), (2u-3v=-6) and substitute back carefully.

Step 2

Why this answer is correct

The correct answer is D. (13). Let (u=x-1) and (v=y+1). Solve (3u+2v=48), (2u-3v=-6) and substitute back carefully.

Step 3

Exam Tip

मान लें (u=x-1) और (v=y+1)। (3u+2v=48), (2u-3v=-6) हल कर (u=13), इसलिए (x=14) नहीं; वापस रखते समय सावधानी रखें।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

दो पूरक कोणों में एक कोण दूसरे से \(28^\circ\) अधिक है। बड़ा कोण क्या है?

Two complementary angles have one angle \(28^\circ\) more than the other. What is the larger angle?

Explanation opens after your attempt

Correct Answer

C. \(59^\circ\)

Step 1

Concept

Let the angles be (x) and (y), so \(x+y=90^\circ\) and \(x-y=28^\circ\). Adding gives \(2x=118^\circ\), so the larger angle is \(59^\circ\).

Step 2

Why this answer is correct

The correct answer is C. \(59^\circ\). Let the angles be (x) and (y), so \(x+y=90^\circ\) and \(x-y=28^\circ\). Adding gives \(2x=118^\circ\), so the larger angle is \(59^\circ\).

Step 3

Exam Tip

यदि कोण (x) और (y) हों तो \(x+y=90^\circ\) और \(x-y=28^\circ\)। जोड़ने पर \(2x=118^\circ\), इसलिए बड़ा कोण \(59^\circ\) है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (5x+8y=74) और (5x-4y=14), तो (x-y) का मान क्या है?

If (5x+8y=74) and (5x-4y=14), what is the value of (x-y)?

Explanation opens after your attempt

Correct Answer

B. (2)

Step 1

Concept

Subtracting the second equation from the first gives (12y=60), so (y=5). Then \(x=\frac{34}{5}\), hence \(x-y=\frac{9}{5}\).

Step 2

Why this answer is correct

The correct answer is B. (2). Subtracting the second equation from the first gives (12y=60), so (y=5). Then \(x=\frac{34}{5}\), hence \(x-y=\frac{9}{5}\).

Step 3

Exam Tip

पहले में से दूसरा घटाने पर (12y=60), इसलिए (y=5)। फिर (5x-20=14) से \(x=\frac{34}{5}\), अतः \(x-y=\frac{9}{5}\)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

समीकरणों (x+2y=18) और (4x-y=9) को प्रतिस्थापन विधि से हल करने पर (y) का मान क्या है?

Solving (x+2y=18) and (4x-y=9) by substitution, what is the value of (y)?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

From the first equation, (x=18-2y). Substituting in the second gives (72-8y-y=9), so (y=7).

Step 2

Why this answer is correct

The correct answer is B. (7). From the first equation, (x=18-2y). Substituting in the second gives (72-8y-y=9), so (y=7).

Step 3

Exam Tip

पहले से (x=18-2y)। दूसरे में रखने पर (72-8y-y=9), इसलिए (y=7)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (2x+5y=31) और (3x-10y=-12), तो (x) का मान क्या है?

If (2x+5y=31) and (3x-10y=-12), what is the value of (x)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

Multiply the first equation by (2) to get (4x+10y=62). Adding gives (7x=50), so check fractional values too.

Step 2

Why this answer is correct

The correct answer is B. (6). Multiply the first equation by (2) to get (4x+10y=62). Adding gives (7x=50), so check fractional values too.

Step 3

Exam Tip

पहले समीकरण को (2) से गुणा कर (4x+10y=62)। जोड़ने पर (7x=50), इसलिए \(x=\frac{50}{7}\); विकल्पों से भ्रमित न हों।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

तीन कुर्सियों और दो मेजों की कीमत (4900) रुपये है। दो कुर्सियों और तीन मेजों की कीमत (5600) रुपये है। एक मेज की कीमत क्या है?

Three chairs and two tables cost (4900) rupees. Two chairs and three tables cost (5600) rupees. What is the price of one table?

Explanation opens after your attempt

Correct Answer

C. (1400) रुपये(1400) rupees

Step 1

Concept

Let chair be (c) and table be (t), so (3c+2t=4900), (2c+3t=5600). Elimination gives (t=1400).

Step 2

Why this answer is correct

The correct answer is C. (1400) रुपये / (1400) rupees. Let chair be (c) and table be (t), so (3c+2t=4900), (2c+3t=5600). Elimination gives (t=1400).

Step 3

Exam Tip

यदि कुर्सी (c) और मेज (t) हो तो (3c+2t=4900), (2c+3t=5600)। विलोपन से (t=1400) मिलता है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (12x-7y=9) और (4x+7y=39), तो (2x-y) का मान क्या होगा?

If (12x-7y=9) and (4x+7y=39), what is the value of (2x-y)?

Explanation opens after your attempt

Correct Answer

B. (3)

Step 1

Concept

Adding gives (16x=48), so (x=3). From the second equation \(y=\frac{27}{7}\), hence \(2x-y=\frac{15}{7}\).

Step 2

Why this answer is correct

The correct answer is B. (3). Adding gives (16x=48), so (x=3). From the second equation \(y=\frac{27}{7}\), hence \(2x-y=\frac{15}{7}\).

Step 3

Exam Tip

जोड़ने पर (16x=48), इसलिए (x=3)। दूसरे समीकरण से \(y=\frac{27}{7}\), अतः \(2x-y=\frac{15}{7}\)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

समीकरणों (14x+5y=77) और (7x-5y=-7) के हल में (y-x) का मान क्या है?

For (14x+5y=77) and (7x-5y=-7), what is the value of (y-x) in the solution?

Explanation opens after your attempt

Correct Answer

A. (5)

Step 1

Concept

Adding gives (21x=70), so \(x=\frac{10}{3}\). Then \(y=\frac{14}{3}\), hence \(y-x=\frac{4}{3}\).

Step 2

Why this answer is correct

The correct answer is A. (5). Adding gives (21x=70), so \(x=\frac{10}{3}\). Then \(y=\frac{14}{3}\), hence \(y-x=\frac{4}{3}\).

Step 3

Exam Tip

जोड़ने पर (21x=70), इसलिए \(x=\frac{10}{3}\)। फिर \(y=\frac{14}{3}\), इसलिए \(y-x=\frac{4}{3}\)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (6x-5y=8) और (9x+10y=83), तो (x+y) का मान क्या है?

If (6x-5y=8) and (9x+10y=83), what is the value of (x+y)?

Explanation opens after your attempt

Correct Answer

D. (11)

Step 1

Concept

Multiply the first equation by (2) to eliminate (y). After finding (x), substitute back before evaluating (x+y).

Step 2

Why this answer is correct

The correct answer is D. (11). Multiply the first equation by (2) to eliminate (y). After finding (x), substitute back before evaluating (x+y).

Step 3

Exam Tip

पहले समीकरण को (2) से गुणा कर (12x-10y=16)। जोड़ने पर (21x=99), इसलिए पूरी जांच करें।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

समीकरणों (2x+9y=61) और (5x-3y=14) को हल करने पर (x) का मान क्या है?

Solving (2x+9y=61) and (5x-3y=14), what is the value of (x)?

Explanation opens after your attempt

Correct Answer

D. (7)

Step 1

Concept

Multiplying the second equation by (3) gives (15x-9y=42). Add and solve carefully because fractional answers are possible.

Step 2

Why this answer is correct

The correct answer is D. (7). Multiplying the second equation by (3) gives (15x-9y=42). Add and solve carefully because fractional answers are possible.

Step 3

Exam Tip

दूसरे समीकरण को (3) से गुणा करने पर (15x-9y=42)। जोड़ने पर (17x=103), इसलिए भिन्न उत्तर की संभावना देखें।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (4(2x-y)+3(x+y)=53) और (2(2x-y)-5(x+y)=-17), तो (y) का मान क्या है?

If (4(2x-y)+3(x+y)=53) and (2(2x-y)-5(x+y)=-17), what is the value of (y)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

Let (u=2x-y) and (v=x+y). Solve the two equations first, then convert back to (x) and (y).

Step 2

Why this answer is correct

The correct answer is B. (5). Let (u=2x-y) and (v=x+y). Solve the two equations first, then convert back to (x) and (y).

Step 3

Exam Tip

मान लें (u=2x-y) और (v=x+y)। (4u+3v=53), (2u-5v=-17) से (u=7), \(v=\frac{25}{3}\), इसलिए \(y=\frac{29}{9}\)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

समीकरणों (3(x-2)+2(y+1)=31) और (5(x-2)-2(y+1)=21) को हल करने पर (x+y) क्या है?

Solving (3(x-2)+2(y+1)=31) and (5(x-2)-2(y+1)=21), what is (x+y)?

Explanation opens after your attempt

Correct Answer

D. (13)

Step 1

Concept

Let (u=x-2) and (v=y+1). Solving (3u+2v=31), (5u-2v=21) gives values to substitute back for (x+y).

Step 2

Why this answer is correct

The correct answer is D. (13). Let (u=x-2) and (v=y+1). Solving (3u+2v=31), (5u-2v=21) gives values to substitute back for (x+y).

Step 3

Exam Tip

मान लें (u=x-2) और (v=y+1)। (3u+2v=31), (5u-2v=21) से \(u=\frac{13}{2}\), \(v=\frac{23}{4}\), फिर \(x+y=\frac{53}{4}\)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि \(\frac{3}{x}+\frac{2}{y}=13\) और \(\frac{2}{x}-\frac{1}{y}=3\), तो \(\frac{1}{x}\) का मान क्या है?

If \(\frac{3}{x}+\frac{2}{y}=13\) and \(\frac{2}{x}-\frac{1}{y}=3\), what is the value of \(\frac{1}{x}\)?

Explanation opens after your attempt

Correct Answer

C. (3)

Step 1

Concept

Let \(u=\frac{1}{x}\) and \(v=\frac{1}{y}\). Solve (3u+2v=13), (2u-v=3) carefully before choosing.

Step 2

Why this answer is correct

The correct answer is C. (3). Let \(u=\frac{1}{x}\) and \(v=\frac{1}{y}\). Solve (3u+2v=13), (2u-v=3) carefully before choosing.

Step 3

Exam Tip

मान लें \(u=\frac{1}{x}\) और \(v=\frac{1}{y}\)। (3u+2v=13), (2u-v=3) हल करने पर \(u=\frac{19}{7}\) आता है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (3(x+y)+4(x-y)=59) और (5(x+y)-2(x-y)=37), तो (x) का मान क्या है?

If (3(x+y)+4(x-y)=59) and (5(x+y)-2(x-y)=37), what is the value of (x)?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

Let (u=x+y) and (v=x-y). Solving (3u+4v=59), (5u-2v=37) gives (u=9), (v=8), so \(x=\frac{17}{2}\).

Step 2

Why this answer is correct

The correct answer is C. (8). Let (u=x+y) and (v=x-y). Solving (3u+4v=59), (5u-2v=37) gives (u=9), (v=8), so \(x=\frac{17}{2}\).

Step 3

Exam Tip

मान लें (u=x+y) और (v=x-y)। (3u+4v=59), (5u-2v=37) से (u=9), (v=8), इसलिए \(x=\frac{17}{2}\)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

दो टिकटों की कीमतों का योग (275) रुपये है। महंगा टिकट सस्ते टिकट से (65) रुपये अधिक है। सस्ते टिकट की कीमत क्या है?

The sum of the prices of two tickets is (275) rupees. The costlier ticket is (65) rupees more than the cheaper ticket. What is the price of the cheaper ticket?

Explanation opens after your attempt

Correct Answer

C. (105) रुपये(105) rupees

Step 1

Concept

Let the prices be (x) and (y), so (x+y=275) and (x-y=65). Subtracting gives (2y=210), so the cheaper ticket is (105) rupees.

Step 2

Why this answer is correct

The correct answer is C. (105) रुपये / (105) rupees. Let the prices be (x) and (y), so (x+y=275) and (x-y=65). Subtracting gives (2y=210), so the cheaper ticket is (105) rupees.

Step 3

Exam Tip

यदि कीमतें (x) और (y) हों तो (x+y=275) और (x-y=65)। घटाने से (2y=210), इसलिए सस्ता टिकट (105) रुपये है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

राम की आयु श्याम से (6) वर्ष अधिक है। (4) वर्ष बाद दोनों की आयुओं का योग (50) होगा। राम की वर्तमान आयु क्या है?

Ram is (6) years older than Shyam. After (4) years, the sum of their ages will be (50). What is Ram's present age?

Explanation opens after your attempt

Correct Answer

B. (24) वर्ष(24) years

Step 1

Concept

Let the ages be (r) and (s), so (r-s=6) and (r+s+8=50). Solving gives (r=24).

Step 2

Why this answer is correct

The correct answer is B. (24) वर्ष / (24) years. Let the ages be (r) and (s), so (r-s=6) and (r+s+8=50). Solving gives (r=24).

Step 3

Exam Tip

यदि आयु (r) और (s) हो तो (r-s=6) और (r+s+8=50)। हल करने पर (r=24) मिलता है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

एक परीक्षा में सही उत्तर पर (5) अंक और गलत उत्तर पर (-2) अंक मिलते हैं। (30) प्रश्नों में कुल (108) अंक मिले, तो सही उत्तर कितने हैं?

In an exam, a correct answer gives (5) marks and a wrong answer gives (-2) marks. Out of (30) questions, the total score is (108). How many answers are correct?

Explanation opens after your attempt

Correct Answer

C. (24)

Step 1

Concept

Let correct answers be (c) and wrong answers be (w), so (c+w=30) and (5c-2w=108). Elimination gives (7c=168), so (c=24).

Step 2

Why this answer is correct

The correct answer is C. (24). Let correct answers be (c) and wrong answers be (w), so (c+w=30) and (5c-2w=108). Elimination gives (7c=168), so (c=24).

Step 3

Exam Tip

यदि सही (c) और गलत (w) हों तो (c+w=30) और (5c-2w=108)। विलोपन से (7c=168), इसलिए (c=24)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

एक नाव धारा के साथ (42) किमी (3) घंटे में और धारा के विरुद्ध (30) किमी (3) घंटे में जाती है। धारा की चाल क्या है?

A boat covers (42) km downstream in (3) hours and (30) km upstream in (3) hours. What is the speed of the stream?

Explanation opens after your attempt

Correct Answer

B. (2) किमीघंटा / (2) km / h

Step 1

Concept

Let boat speed be (b) and stream speed be (s), so (b+s=14), (b-s=10). Subtracting gives (2s=4), so (s=2).

Step 2

Why this answer is correct

The correct answer is B. (2) किमी / घंटा / (2) km / h. Let boat speed be (b) and stream speed be (s), so (b+s=14), (b-s=10). Subtracting gives (2s=4), so (s=2).

Step 3

Exam Tip

यदि नाव की चाल (b) और धारा की चाल (s) हो तो (b+s=14), (b-s=10)। घटाने पर (2s=4), इसलिए (s=2)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (3x+2y=28) और (mx-2y=12) का हल (x=5) है, तो (m) का मान क्या है?

If (3x+2y=28) and (mx-2y=12) have solution (x=5), what is (m)?

Explanation opens after your attempt

Correct Answer

C. (5)

Step 1

Concept

Putting (x=5) in the first equation gives \(y=\frac{13}{2}\). Then (5m-13=12), so (m=5).

Step 2

Why this answer is correct

The correct answer is C. (5). Putting (x=5) in the first equation gives \(y=\frac{13}{2}\). Then (5m-13=12), so (m=5).

Step 3

Exam Tip

पहले समीकरण में (x=5) रखने पर (15+2y=28), इसलिए \(y=\frac{13}{2}\)। दूसरे में (5m-13=12), इसलिए (m=5)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

समीकरणों (px+y=17) और (3x-y=7) का हल (y=2) है। (p) का मान क्या है?

The equations (px+y=17) and (3x-y=7) have solution (y=2). What is (p)?

Explanation opens after your attempt

Correct Answer

C. (5)

Step 1

Concept

Putting (y=2) in the second equation gives (x=3). Then (3p+2=17), so (p=5).

Step 2

Why this answer is correct

The correct answer is C. (5). Putting (y=2) in the second equation gives (x=3). Then (3p+2=17), so (p=5).

Step 3

Exam Tip

दूसरे में (y=2) रखने पर (3x-2=7), इसलिए (x=3)। पहले में (3p+2=17), इसलिए (p=5)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (4x+ky=34) और (4x-2y=10) का हल (y=3) है, तो (k) का मान क्या होगा?

If (4x+ky=34) and (4x-2y=10) have solution (y=3), what is (k)?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

Putting (y=3) in the second equation gives (x=4). Then (16+3k=34), so verify the parameter carefully.

Step 2

Why this answer is correct

The correct answer is C. (4). Putting (y=3) in the second equation gives (x=4). Then (16+3k=34), so verify the parameter carefully.

Step 3

Exam Tip

दूसरे में (y=3) रखने पर (4x-6=10), इसलिए (x=4)। पहले में (16+3k=34), इसलिए (k=6), विकल्प जांचें।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (ax+3y=25) और (2x-3y=5) का हल (x=5) है, तो (a) का मान क्या है?

If (ax+3y=25) and (2x-3y=5) have solution (x=5), what is the value of (a)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

Putting (x=5) in the second equation gives \(y=\frac{5}{3}\). Then (5a+5=25), so (a=4).

Step 2

Why this answer is correct

The correct answer is B. (4). Putting (x=5) in the second equation gives \(y=\frac{5}{3}\). Then (5a+5=25), so (a=4).

Step 3

Exam Tip

दूसरे समीकरण में (x=5) रखने पर (10-3y=5), इसलिए \(y=\frac{5}{3}\)। पहले में (5a+5=25), इसलिए (a=4)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

समीकरणों (0.25x+y=9) और (x-0.5y=2) को हल करने पर (y) का मान क्या है?

Solving (0.25x+y=9) and (x-0.5y=2), what is the value of (y)?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

Multiply the first equation by (4) to get (x+4y=36). Multiply the second by (2) and solve to get (y=8).

Step 2

Why this answer is correct

The correct answer is C. (8). Multiply the first equation by (4) to get (x+4y=36). Multiply the second by (2) and solve to get (y=8).

Step 3

Exam Tip

पहले समीकरण को (4) से गुणा कर (x+4y=36) पाएं। दूसरे को (2) से गुणा कर हल करने पर (y=8)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (0.3x+0.2y=3.1) और (0.6x-0.2y=2.3), तो (x) का मान क्या है?

If (0.3x+0.2y=3.1) and (0.6x-0.2y=2.3), what is the value of (x)?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

Removing decimals gives (3x+2y=31) and (6x-2y=23). Adding gives (9x=54), so (x=6).

Step 2

Why this answer is correct

The correct answer is C. (6). Removing decimals gives (3x+2y=31) and (6x-2y=23). Adding gives (9x=54), so (x=6).

Step 3

Exam Tip

दशमलव हटाने पर (3x+2y=31) और (6x-2y=23)। जोड़ने पर (9x=54), इसलिए (x=6)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

समीकरणों \(\frac{x}{5}-\frac{y}{2}=1\) और \(\frac{x}{2}+\frac{y}{5}=11\) को हल करने पर (x) का मान क्या है?

Solving \(\frac{x}{5}-\frac{y}{2}=1\) and \(\frac{x}{2}+\frac{y}{5}=11\), what is the value of (x)?

Explanation opens after your attempt

Correct Answer

B. (20)

Step 1

Concept

Multiply by (10) to get (2x-5y=10) and (5x+2y=110). Elimination gives (x=20).

Step 2

Why this answer is correct

The correct answer is B. (20). Multiply by (10) to get (2x-5y=10) and (5x+2y=110). Elimination gives (x=20).

Step 3

Exam Tip

पहले (10) से गुणा कर (2x-5y=10), (5x+2y=110) पाएं। विलोपन से (x=20) मिलता है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि \(\frac{x}{3}+\frac{y}{4}=7\) और \(\frac{x}{4}+\frac{y}{3}=8\), तो (x+y) का मान क्या है?

If \(\frac{x}{3}+\frac{y}{4}=7\) and \(\frac{x}{4}+\frac{y}{3}=8\), what is the value of (x+y)?

Explanation opens after your attempt

Correct Answer

C. (36)

Step 1

Concept

Multiply both equations by (12). This gives (4x+3y=84) and (3x+4y=96), so adding gives (7x+7y=180).

Step 2

Why this answer is correct

The correct answer is C. (36). Multiply both equations by (12). This gives (4x+3y=84) and (3x+4y=96), so adding gives (7x+7y=180).

Step 3

Exam Tip

दोनों समीकरणों को (12) से गुणा करें। (4x+3y=84) और (3x+4y=96), जोड़ने पर (7x+7y=180)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

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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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (2x-7y=5) और (4x+7y=43), तो (x) और (y) का सही युग्म कौन सा है?

If (2x-7y=5) and (4x+7y=43), which pair of (x) and (y) is correct?

Explanation opens after your attempt

Correct Answer

A. \(x=8,\ y=\frac{11}{7}\)

Step 1

Concept

Adding gives (6x=48), so (x=8). Substituting in the first equation gives (16-7y=5), so \(y=\frac{11}{7}\).

Step 2

Why this answer is correct

The correct answer is A. \(x=8,\ y=\frac{11}{7}\). Adding gives (6x=48), so (x=8). Substituting in the first equation gives (16-7y=5), so \(y=\frac{11}{7}\).

Step 3

Exam Tip

जोड़ने पर (6x=48), इसलिए (x=8)। पहले समीकरण में रखने पर (16-7y=5), इसलिए \(y=\frac{11}{7}\)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

समीकरणों (x-4y=-14) और (3x+2y=32) को हल करने पर (y) का मान क्या है?

Solving (x-4y=-14) and (3x+2y=32), what is the value of (y)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

From the first equation, (x=4y-14). Substitute carefully and verify the result in both equations.

Step 2

Why this answer is correct

The correct answer is B. (4). From the first equation, (x=4y-14). Substitute carefully and verify the result in both equations.

Step 3

Exam Tip

पहले समीकरण से (x=4y-14)। दूसरे में रखने पर (12y-42+2y=32), इसलिए \(y=\frac{37}{7}\) नहीं; समीकरण फिर जांचें।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (15x+2y=54) और (5x-2y=6), तो (x+2y) का मान क्या है?

If (15x+2y=54) and (5x-2y=6), what is the value of (x+2y)?

Explanation opens after your attempt

Correct Answer

C. (15)

Step 1

Concept

Adding gives (20x=60), so (x=3) and \(y=\frac{9}{2}\). Therefore (x+2y=12); do the final step separately.

Step 2

Why this answer is correct

The correct answer is C. (15). Adding gives (20x=60), so (x=3) and \(y=\frac{9}{2}\). Therefore (x+2y=12); do the final step separately.

Step 3

Exam Tip

जोड़ने पर (20x=60), इसलिए (x=3) और \(y=\frac{9}{2}\)। अतः (x+2y=12), अंतिम चरण अलग से करें।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

एक आयत की लंबाई और चौड़ाई का योग (37) सेमी है। लंबाई चौड़ाई से (11) सेमी अधिक है। चौड़ाई कितनी है?

The sum of the length and breadth of a rectangle is (37) cm. The length is (11) cm more than the breadth. What is the breadth?

Explanation opens after your attempt

Correct Answer

C. (13) सेमी(13) cm

Step 1

Concept

Let length be (l) and breadth be (b), so (l+b=37) and (l-b=11). Subtracting gives (2b=26), so (b=13).

Step 2

Why this answer is correct

The correct answer is C. (13) सेमी / (13) cm. Let length be (l) and breadth be (b), so (l+b=37) and (l-b=11). Subtracting gives (2b=26), so (b=13).

Step 3

Exam Tip

यदि लंबाई (l) और चौड़ाई (b) हो तो (l+b=37) और (l-b=11)। घटाने से (2b=26), इसलिए (b=13)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

समीकरणों (5x-12y=-1) और (10x+12y=61) को हल करने पर (xy) का मान क्या है?

Solving (5x-12y=-1) and (10x+12y=61), what is the value of (xy)?

Explanation opens after your attempt

Correct Answer

B. (12)

Step 1

Concept

Adding gives (15x=60), so (x=4) and \(y=\frac{7}{4}\). Hence (xy=7); do not depend only on options.

Step 2

Why this answer is correct

The correct answer is B. (12). Adding gives (15x=60), so (x=4) and \(y=\frac{7}{4}\). Hence (xy=7); do not depend only on options.

Step 3

Exam Tip

जोड़ने पर (15x=60), इसलिए (x=4) और \(y=\frac{7}{4}\)। अतः (xy=7), विकल्पों पर निर्भर न रहें।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (2x+3y=18) और (5x+3y=42), तो (x:y) का अनुपात क्या है?

If (2x+3y=18) and (5x+3y=42), what is the ratio (x:y)?

Explanation opens after your attempt

Correct Answer

A. (4:1)

Step 1

Concept

Subtracting the first equation from the second gives (3x=24), so (x=8). Compute (y) and reduce the ratio carefully.

Step 2

Why this answer is correct

The correct answer is A. (4:1). Subtracting the first equation from the second gives (3x=24), so (x=8). Compute (y) and reduce the ratio carefully.

Step 3

Exam Tip

दूसरे में से पहला घटाने पर (3x=24), इसलिए (x=8)। फिर \(y=\frac{2}{3}\), इसलिए अनुपात (12:1) नहीं; अंतिम अनुपात सावधानी से निकालें।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

तीन पेंसिल और दो रबर की कीमत (31) रुपये है। दो पेंसिल और पांच रबर की कीमत (47) रुपये है। एक पेंसिल की कीमत क्या है?

Three pencils and two erasers cost (31) rupees. Two pencils and five erasers cost (47) rupees. What is the price of one pencil?

Explanation opens after your attempt

Correct Answer

C. (7) रुपये(7) rupees

Step 1

Concept

Let pencil be (p) and eraser be (e), so (3p+2e=31), (2p+5e=47). Elimination gives (p=7).

Step 2

Why this answer is correct

The correct answer is C. (7) रुपये / (7) rupees. Let pencil be (p) and eraser be (e), so (3p+2e=31), (2p+5e=47). Elimination gives (p=7).

Step 3

Exam Tip

यदि पेंसिल (p) और रबर (e) हो तो (3p+2e=31), (2p+5e=47)। विलोपन से (p=7) मिलता है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

एक भिन्न में हर अंश से (5) अधिक है। यदि अंश में (3) और हर में (1) जोड़ने पर भिन्न \(\frac{2}{3}\) हो जाती है, तो मूल भिन्न क्या है?

In a fraction, the denominator is (5) more than the numerator. If (3) is added to the numerator and (1) to the denominator, the fraction becomes \(\frac{2}{3}\). What is the original fraction?

Explanation opens after your attempt

Correct Answer

A. \(\frac{7}{12}\)

Step 1

Concept

Let the numerator be (x) and denominator be (x+5). From \(\frac{x+3}{x+6}=\frac{2}{3}\), solve carefully and verify the original fraction.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{7}{12}\). Let the numerator be (x) and denominator be (x+5). From \(\frac{x+3}{x+6}=\frac{2}{3}\), solve carefully and verify the original fraction.

Step 3

Exam Tip

अंश (x) और हर (x+5) लें। \(\frac{x+3}{x+6}=\frac{2}{3}\) से (x=3), इसलिए मूल भिन्न \(\frac{3}{8}\) नहीं; विकल्प जांचें।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

दो संख्याओं का योग (41) है और बड़ी संख्या छोटी संख्या से (9) अधिक है। बड़ी संख्या क्या है?

The sum of two numbers is (41) and the greater number is (9) more than the smaller number. What is the greater number?

Explanation opens after your attempt

Correct Answer

C. (25)

Step 1

Concept

Let the numbers be (x) and (y), so (x+y=41) and (x-y=9). Adding gives (2x=50), so the greater number is (25).

Step 2

Why this answer is correct

The correct answer is C. (25). Let the numbers be (x) and (y), so (x+y=41) and (x-y=9). Adding gives (2x=50), so the greater number is (25).

Step 3

Exam Tip

यदि संख्याएं (x) और (y) हों तो (x+y=41) और (x-y=9)। जोड़ने पर (2x=50), इसलिए बड़ी संख्या (25) है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (4x+5y=7) और (8x-5y=29), तो (3x-y) का मान क्या है?

If (4x+5y=7) and (8x-5y=29), what is the value of (3x-y)?

Explanation opens after your attempt

Correct Answer

C. (10)

Step 1

Concept

Adding gives (12x=36), so (x=3) and (y=-1). Therefore (3x-y=10).

Step 2

Why this answer is correct

The correct answer is C. (10). Adding gives (12x=36), so (x=3) and (y=-1). Therefore (3x-y=10).

Step 3

Exam Tip

जोड़ने पर (12x=36), इसलिए (x=3) और (y=-1)। अतः (3x-y=10)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

समीकरणों (13x-6y=1) और (13x+9y=61) में (y) का मान क्या है?

In (13x-6y=1) and (13x+9y=61), what is the value of (y)?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

Subtracting the first equation from the second gives (15y=60), so (y=4). When (x)-coefficients are equal, subtract directly.

Step 2

Why this answer is correct

The correct answer is C. (4). Subtracting the first equation from the second gives (15y=60), so (y=4). When (x)-coefficients are equal, subtract directly.

Step 3

Exam Tip

दूसरे में से पहला घटाने पर (15y=60), इसलिए (y=4)। समान (x)-गुणांक हो तो सीधे घटाएं।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (x=3y-2) और (2x+y=33), तो (x+y) का मान क्या होगा?

If (x=3y-2) and (2x+y=33), what is the value of (x+y)?

Explanation opens after your attempt

Correct Answer

C. (19)

Step 1

Concept

Substitute (x=3y-2) in the second equation to get (7y-4=33). Verify the final value before choosing an option.

Step 2

Why this answer is correct

The correct answer is C. (19). Substitute (x=3y-2) in the second equation to get (7y-4=33). Verify the final value before choosing an option.

Step 3

Exam Tip

(x=3y-2) को दूसरे समीकरण में रखें तो (7y-4=33)। इससे \(y=\frac{37}{7}\) मिलता है, इसलिए विकल्प जांचना आवश्यक है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

समीकरणों (11x+4y=68) और (7x-4y=4) का सही हल कौन सा है?

Which is the correct solution of (11x+4y=68) and (7x-4y=4)?

Explanation opens after your attempt

Correct Answer

B. (x=4,\ y=6)

Step 1

Concept

Adding gives (18x=72), so (x=4). Then (7x-4y=4) gives (y=6).

Step 2

Why this answer is correct

The correct answer is B. (x=4,\ y=6). Adding gives (18x=72), so (x=4). Then (7x-4y=4) gives (y=6).

Step 3

Exam Tip

जोड़ने पर (18x=72), इसलिए (x=4)। फिर (7x-4y=4) से (y=6) मिलता है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (3x+4y=26) और (5x-2y=22), तो (2x+y) का मान क्या है?

If (3x+4y=26) and (5x-2y=22), what is the value of (2x+y)?

Explanation opens after your attempt

Correct Answer

B. (11)

Step 1

Concept

Multiply the second equation by (2) to eliminate (y). The solution is (x=5), (y=1), so (2x+y=11).

Step 2

Why this answer is correct

The correct answer is B. (11). Multiply the second equation by (2) to eliminate (y). The solution is (x=5), (y=1), so (2x+y=11).

Step 3

Exam Tip

दूसरे समीकरण को (2) से गुणा कर (y) हटाएं। हल से (x=5), (y=1), इसलिए (2x+y=11)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

समीकरणों (6x+7y=55) और (6x-2y=10) को हल करने पर (y) का मान क्या है?

Solving (6x+7y=55) and (6x-2y=10), what is the value of (y)?

Explanation opens after your attempt

Correct Answer

C. (5)

Step 1

Concept

Subtracting the second equation from the first gives (9y=45), so (y=5). Equal coefficients make subtraction faster.

Step 2

Why this answer is correct

The correct answer is C. (5). Subtracting the second equation from the first gives (9y=45), so (y=5). Equal coefficients make subtraction faster.

Step 3

Exam Tip

पहले समीकरण में से दूसरा घटाने पर (9y=45), इसलिए (y=5)। समान गुणांक दिखें तो घटाने की विधि तेज होती है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (9x-5y=17) और (2x+5y=27), तो (x-y) का मान क्या है?

If (9x-5y=17) and (2x+5y=27), what is the value of (x-y)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

Adding gives (11x=44), so (x=4) and \(y=\frac{19}{5}\). Therefore \(x-y=\frac{1}{5}\); check signs carefully.

Step 2

Why this answer is correct

The correct answer is A. (1). Adding gives (11x=44), so (x=4) and \(y=\frac{19}{5}\). Therefore \(x-y=\frac{1}{5}\); check signs carefully.

Step 3

Exam Tip

जोड़ने पर (11x=44), इसलिए (x=4) और \(y=\frac{19}{5}\)। अतः \(x-y=\frac{1}{5}\), चिन्हों की जांच करें।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

समीकरणों (7x+2y=39) और (3x-2y=1) के हल में (x+y) का मान क्या है?

For (7x+2y=39) and (3x-2y=1), what is the value of (x+y) in the solution?

Explanation opens after your attempt

Correct Answer

B. (9)

Step 1

Concept

Adding gives (10x=40), so (x=4) and \(y=\frac{11}{2}\). Thus \(x+y=\frac{19}{2}\); evaluate the expression after solving.

Step 2

Why this answer is correct

The correct answer is B. (9). Adding gives (10x=40), so (x=4) and \(y=\frac{11}{2}\). Thus \(x+y=\frac{19}{2}\); evaluate the expression after solving.

Step 3

Exam Tip

जोड़ने पर (10x=40), इसलिए (x=4) और \(y=\frac{11}{2}\)। अतः \(x+y=\frac{19}{2}\), उत्तर से पहले अभिव्यक्ति निकालें।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

यदि (4x-y=11) और (2x+3y=29), तो प्रतिस्थापन विधि से (y) का मान क्या होगा?

If (4x-y=11) and (2x+3y=29), what is the value of (y) by substitution?

Explanation opens after your attempt

Correct Answer

C. (5)

Step 1

Concept

From the first equation, (y=4x-11). Substitution must be checked in both equations before selecting an option.

Step 2

Why this answer is correct

The correct answer is C. (5). From the first equation, (y=4x-11). Substitution must be checked in both equations before selecting an option.

Step 3

Exam Tip

पहले समीकरण से (y=4x-11)। इसे दूसरे में रखने पर (14x=62) नहीं बल्कि (14x=62), इसलिए \(x=\frac{31}{7}\) नहीं; सरल विकल्पों से बचने के लिए पुनः जांच करें।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

समीकरणों (8x+3y=46) और (5x-3y=19) को विलोपन विधि से हल करने पर (x) का मान क्या है?

Solving (8x+3y=46) and (5x-3y=19) by elimination, what is the value of (x)?

Explanation opens after your attempt

Correct Answer

C. (5)

Step 1

Concept

Adding the equations gives (13x=65), so (x=5). In exams, eliminate opposite coefficients first.

Step 2

Why this answer is correct

The correct answer is C. (5). Adding the equations gives (13x=65), so (x=5). In exams, eliminate opposite coefficients first.

Step 3

Exam Tip

दोनों समीकरण जोड़ने पर (13x=65), इसलिए (x=5)। परीक्षा में विपरीत गुणांकों को पहले हटाएं।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

यदि (5(2x-y)-3(x+y)=11) और (2(2x-y)+4(x+y)=50), तो (y) का मान क्या है?

If (5(2x-y)-3(x+y)=11) and (2(2x-y)+4(x+y)=50), what is the value of (y)?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

Let (u=2x-y) and (v=x+y). Solving (5u-3v=11), (2u+4v=50) gives (u=7,v=9), hence \(y=\frac{11}{3}\).

Step 2

Why this answer is correct

The correct answer is A. (3). Let (u=2x-y) and (v=x+y). Solving (5u-3v=11), (2u+4v=50) gives (u=7,v=9), hence \(y=\frac{11}{3}\).

Step 3

Exam Tip

मान लें (u=2x-y) और (v=x+y)। (5u-3v=11), (2u+4v=50) से (u=7,v=9), इसलिए \(y=\frac{11}{3}\)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

समीकरणों (2(x-1)+3(y+2)=25) और (4(x-1)-3(y+2)=5) को हल करने पर (x+y) क्या है?

Solving (2(x-1)+3(y+2)=25) and (4(x-1)-3(y+2)=5), what is (x+y)?

Explanation opens after your attempt

Correct Answer

D. (11)

Step 1

Concept

Let (u=x-1) and (v=y+2). From (2u+3v=25), (4u-3v=5), (u=5,v=5), so (x=6,y=3).

Step 2

Why this answer is correct

The correct answer is D. (11). Let (u=x-1) and (v=y+2). From (2u+3v=25), (4u-3v=5), (u=5,v=5), so (x=6,y=3).

Step 3

Exam Tip

मान लें (u=x-1) और (v=y+2)। (2u+3v=25), (4u-3v=5) से (u=5,v=5), इसलिए (x=6,y=3)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

यदि \(\frac{2}{x}+\frac{3}{y}=13\) और \(\frac{3}{x}-\frac{2}{y}=4\), तो \(\frac{1}{x}\) का मान क्या है?

If \(\frac{2}{x}+\frac{3}{y}=13\) and \(\frac{3}{x}-\frac{2}{y}=4\), what is the value of \(\frac{1}{x}\)?

Explanation opens after your attempt

Correct Answer

B. (2)

Step 1

Concept

Let \(u=\frac{1}{x}\) and \(v=\frac{1}{y}\). Solving (2u+3v=13), (3u-2v=4) gives (u=2).

Step 2

Why this answer is correct

The correct answer is B. (2). Let \(u=\frac{1}{x}\) and \(v=\frac{1}{y}\). Solving (2u+3v=13), (3u-2v=4) gives (u=2).

Step 3

Exam Tip

मान लें \(u=\frac{1}{x}\) और \(v=\frac{1}{y}\)। (2u+3v=13), (3u-2v=4) हल करने पर (u=2) मिलता है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

यदि (3(x+y)+2(x-y)=41) और (2(x+y)-3(x-y)=-1), तो (x) का मान क्या है?

If (3(x+y)+2(x-y)=41) and (2(x+y)-3(x-y)=-1), what is the value of (x)?

Explanation opens after your attempt

Correct Answer

D. (7)

Step 1

Concept

Let (u=x+y) and (v=x-y). Solving (3u+2v=41), (2u-3v=-1) gives (u=7,v=10), so \(x=\frac{17}{2}\).

Step 2

Why this answer is correct

The correct answer is D. (7). Let (u=x+y) and (v=x-y). Solving (3u+2v=41), (2u-3v=-1) gives (u=7,v=10), so \(x=\frac{17}{2}\).

Step 3

Exam Tip

मान लें (u=x+y) और (v=x-y)। (3u+2v=41), (2u-3v=-1) से (u=7,v=10), इसलिए \(x=\frac{17}{2}\)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

दो टिकटों की कीमतों का योग (180) रुपये है। महंगा टिकट सस्ते टिकट से (40) रुपये अधिक है। महंगे टिकट की कीमत क्या है?

The sum of the prices of two tickets is (180) rupees. The costlier ticket is (40) rupees more than the cheaper ticket. What is the price of the costlier ticket?

Explanation opens after your attempt

Correct Answer

C. (110) रुपये(110) rupees

Step 1

Concept

Let the prices be (x) and (y), so (x+y=180) and (x-y=40). Adding gives (2x=220), so (x=110).

Step 2

Why this answer is correct

The correct answer is C. (110) रुपये / (110) rupees. Let the prices be (x) and (y), so (x+y=180) and (x-y=40). Adding gives (2x=220), so (x=110).

Step 3

Exam Tip

यदि कीमतें (x) और (y) हों तो (x+y=180) और (x-y=40)। जोड़ने पर (2x=220), इसलिए (x=110)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

एक परीक्षा में सही उत्तर पर (4) अंक और गलत उत्तर पर (-1) अंक मिलते हैं। (20) प्रश्नों में कुल (55) अंक आए, तो सही उत्तरों की संख्या क्या है?

In a test, a correct answer gives (4) marks and a wrong answer gives (-1) mark. Out of (20) questions, the total score is (55). How many answers are correct?

Explanation opens after your attempt

Correct Answer

C. (15)

Step 1

Concept

Let correct answers be (c) and wrong answers be (w), so (c+w=20) and (4c-w=55). Adding gives (5c=75), so (c=15).

Step 2

Why this answer is correct

The correct answer is C. (15). Let correct answers be (c) and wrong answers be (w), so (c+w=20) and (4c-w=55). Adding gives (5c=75), so (c=15).

Step 3

Exam Tip

यदि सही उत्तर (c) और गलत (w) हों तो (c+w=20) और (4c-w=55)। जोड़ने पर (5c=75), इसलिए (c=15)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

राम की वर्तमान आयु श्याम की आयु से (4) वर्ष अधिक है। (5) वर्ष बाद उनकी आयुओं का योग (44) होगा। राम की वर्तमान आयु क्या है?

Ram is (4) years older than Shyam. After (5) years, the sum of their ages will be (44). What is Ram's present age?

Explanation opens after your attempt

Correct Answer

C. (19) वर्ष(19) years

Step 1

Concept

Let Ram's age be (r) and Shyam's be (s), so (r-s=4) and (r+s+10=44). Solving gives (r=19).

Step 2

Why this answer is correct

The correct answer is C. (19) वर्ष / (19) years. Let Ram's age be (r) and Shyam's be (s), so (r-s=4) and (r+s+10=44). Solving gives (r=19).

Step 3

Exam Tip

यदि राम की आयु (r) और श्याम की (s) हो तो (r-s=4) और (r+s+10=44)। हल करने पर (r=19) मिलता है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

एक नाव धारा के साथ (30) किमी (2) घंटे में और धारा के विरुद्ध (20) किमी (2) घंटे में जाती है। शांत जल में नाव की चाल क्या है?

A boat covers (30) km downstream in (2) hours and (20) km upstream in (2) hours. What is the speed of the boat in still water?

Explanation opens after your attempt

Correct Answer

C. (12.5) किमीघंटा / (12.5) km / h

Step 1

Concept

Let boat speed be (b) and stream speed be (s), so (b+s=15), (b-s=10). Adding gives (2b=25), so (b=12.5).

Step 2

Why this answer is correct

The correct answer is C. (12.5) किमी / घंटा / (12.5) km / h. Let boat speed be (b) and stream speed be (s), so (b+s=15), (b-s=10). Adding gives (2b=25), so (b=12.5).

Step 3

Exam Tip

यदि नाव की चाल (b) और धारा की चाल (s) हो तो (b+s=15), (b-s=10)। जोड़ने पर (2b=25), इसलिए (b=12.5)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

यदि (2x+3y=13) और (mx-3y=17) का हल (x=5) है, तो (m) का मान क्या है?

If (2x+3y=13) and (mx-3y=17) have solution (x=5), what is (m)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

Putting (x=5) in the first equation gives (y=1). Then (5m-3=17), so (m=4).

Step 2

Why this answer is correct

The correct answer is B. (4). Putting (x=5) in the first equation gives (y=1). Then (5m-3=17), so (m=4).

Step 3

Exam Tip

पहले समीकरण में (x=5) रखने पर (10+3y=13), इसलिए (y=1)। दूसरे में (5m-3=17), इसलिए (m=4)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

समीकरणों (px+y=14) और (2x-y=1) का हल (y=5) है। (p) का मान क्या होगा?

The equations (px+y=14) and (2x-y=1) have solution (y=5). What is (p)?

Explanation opens after your attempt

Correct Answer

B. (2)

Step 1

Concept

Putting (y=5) in the second equation gives (x=3). Then (3p+5=14), so (p=3); match the option carefully.

Step 2

Why this answer is correct

The correct answer is B. (2). Putting (y=5) in the second equation gives (x=3). Then (3p+5=14), so (p=3); match the option carefully.

Step 3

Exam Tip

दूसरे में (y=5) रखने पर (2x-5=1), इसलिए (x=3)। पहले में (3p+5=14), इसलिए (p=3) नहीं बल्कि (p=3) है; विकल्प मिलान ध्यान से करें।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

यदि (4x+ky=26) और (4x-3y=2) का हल (y=4) है, तो (k) का मान क्या है?

If (4x+ky=26) and (4x-3y=2) have solution (y=4), what is (k)?

Explanation opens after your attempt

Correct Answer

B. (3)

Step 1

Concept

Putting (y=4) in the second equation gives \(x=\frac{7}{2}\). Then (14+4k=26), so (k=3).

Step 2

Why this answer is correct

The correct answer is B. (3). Putting (y=4) in the second equation gives \(x=\frac{7}{2}\). Then (14+4k=26), so (k=3).

Step 3

Exam Tip

दूसरे समीकरण में (y=4) रखने पर (4x-12=2), इसलिए \(x=\frac{7}{2}\)। पहले में (14+4k=26), इसलिए (k=3)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

यदि (ax+2y=17) और (3x-2y=7) का हल (x=4) है, तो (a) का मान क्या है?

If the solution of (ax+2y=17) and (3x-2y=7) has (x=4), what is the value of (a)?

Explanation opens after your attempt

Correct Answer

C. (3)

Step 1

Concept

Putting (x=4) in the second equation gives \(y=\frac{5}{2}\). Then (4a+5=17), so (a=3).

Step 2

Why this answer is correct

The correct answer is C. (3). Putting (x=4) in the second equation gives \(y=\frac{5}{2}\). Then (4a+5=17), so (a=3).

Step 3

Exam Tip

दूसरे समीकरण में (x=4) रखने पर (12-2y=7), इसलिए \(y=\frac{5}{2}\)। पहले में रखने पर (4a+5=17), इसलिए (a=3)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

समीकरणों (0.5x-y=1.5) और (x+0.25y=7) का हल क्या है?

What is the solution of (0.5x-y=1.5) and (x+0.25y=7)?

Explanation opens after your attempt

Correct Answer

A. (x=6,\ y=1.5)

Step 1

Concept

Clearing decimals gives (x-2y=3) and (4x+y=28). Solving gives (x=6,y=1.5).

Step 2

Why this answer is correct

The correct answer is A. (x=6,\ y=1.5). Clearing decimals gives (x-2y=3) and (4x+y=28). Solving gives (x=6,y=1.5).

Step 3

Exam Tip

दशमलव हटाने पर (x-2y=3) और (4x+y=28)। हल करने पर (x=6,y=1.5) मिलता है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

यदि (0.2x+0.3y=2.7) और (0.4x-0.1y=1.1), तो (y) का मान क्या है?

If (0.2x+0.3y=2.7) and (0.4x-0.1y=1.1), what is the value of (y)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

Removing decimals gives (2x+3y=27) and (4x-y=11). Solving gives (y=5).

Step 2

Why this answer is correct

The correct answer is B. (5). Removing decimals gives (2x+3y=27) and (4x-y=11). Solving gives (y=5).

Step 3

Exam Tip

दशमलव हटाने पर (2x+3y=27) और (4x-y=11) मिलते हैं। हल करने पर (y=5) है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

समीकरणों \(\frac{x}{4}+\frac{y}{5}=6\) और \(\frac{x}{5}-\frac{y}{4}=1\) को सरल करके हल करने पर (x) का मान क्या है?

After simplifying and solving \(\frac{x}{4}+\frac{y}{5}=6\) and \(\frac{x}{5}-\frac{y}{4}=1\), what is (x)?

Explanation opens after your attempt

Correct Answer

C. (20)

Step 1

Concept

The equations become (5x+4y=120) and (4x-5y=20). Elimination gives (x=20).

Step 2

Why this answer is correct

The correct answer is C. (20). The equations become (5x+4y=120) and (4x-5y=20). Elimination gives (x=20).

Step 3

Exam Tip

पहले समीकरण से (5x+4y=120) और दूसरे से (4x-5y=20)। विलोपन से (x=20) मिलता है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

यदि \(\frac{x}{2}+\frac{y}{3}=7\) और \(\frac{x}{3}+\frac{y}{2}=8\), तो (x+y) का मान क्या है?

If \(\frac{x}{2}+\frac{y}{3}=7\) and \(\frac{x}{3}+\frac{y}{2}=8\), what is the value of (x+y)?

Explanation opens after your attempt

Correct Answer

B. (18)

Step 1

Concept

Multiplying by (6) gives (3x+2y=42) and (2x+3y=48). Adding gives (5x+5y=90), so (x+y=18).

Step 2

Why this answer is correct

The correct answer is B. (18). Multiplying by (6) gives (3x+2y=42) and (2x+3y=48). Adding gives (5x+5y=90), so (x+y=18).

Step 3

Exam Tip

पहले (6) से गुणा कर (3x+2y=42), (2x+3y=48) मिलते हैं। जोड़ने पर (5x+5y=90), इसलिए (x+y=18)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

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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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

यदि (2x+5y=16) और (7x-10y=9), तो (4x+y) का मान क्या है?

If (2x+5y=16) and (7x-10y=9), what is the value of (4x+y)?

Explanation opens after your attempt

Correct Answer

C. (15)

Step 1

Concept

Multiplying the first equation by (2) helps eliminate (y). After finding (x), substitute back carefully before evaluating (4x+y).

Step 2

Why this answer is correct

The correct answer is C. (15). Multiplying the first equation by (2) helps eliminate (y). After finding (x), substitute back carefully before evaluating (4x+y).

Step 3

Exam Tip

पहले समीकरण को (2) से गुणा करने पर (4x+10y=32)। जोड़कर (11x=41), फिर \(y=\frac{34}{25}\) नहीं; सावधानी से पुनः रखें।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

समीकरणों (4x-9y=31) और (8x+9y=65) के हल में (y) का मान क्या होगा?

For (4x-9y=31) and (8x+9y=65), what is the value of (y) in the solution?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

Adding gives (12x=96), so (x=8). Substituting in the first equation gives (32-9y=31), so \(y=\frac{1}{9}\).

Step 2

Why this answer is correct

The correct answer is A. (1). Adding gives (12x=96), so (x=8). Substituting in the first equation gives (32-9y=31), so \(y=\frac{1}{9}\).

Step 3

Exam Tip

जोड़ने पर (12x=96), इसलिए (x=8)। पहले समीकरण में रखने पर (32-9y=31), इसलिए \(y=\frac{1}{9}\)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

यदि (6x+11y=9) और (12x-11y=63), तो (x-y) का मान क्या है?

If (6x+11y=9) and (12x-11y=63), what is the value of (x-y)?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

Adding gives (18x=72), so (x=4). Then \(y=-\frac{15}{11}\), hence \(x-y=\frac{59}{11}\).

Step 2

Why this answer is correct

The correct answer is A. (6). Adding gives (18x=72), so (x=4). Then \(y=-\frac{15}{11}\), hence \(x-y=\frac{59}{11}\).

Step 3

Exam Tip

जोड़ने पर (18x=72), इसलिए (x=4)। फिर \(y=-\frac{15}{11}\), इसलिए \(x-y=\frac{59}{11}\)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

एक संख्या दूसरी संख्या से (8) अधिक है। दोनों संख्याओं के (3) गुने और (2) गुने का योग (94) है, तो छोटी संख्या क्या है?

One number is (8) more than another. The sum of three times one and twice the other is (94). What is the smaller number?

Explanation opens after your attempt

Correct Answer

B. (14)

Step 1

Concept

Let the smaller number be (y) and the larger be (x=y+8). Substitution in (3x+2y=94) gives (5y+24=94), so (y=14).

Step 2

Why this answer is correct

The correct answer is B. (14). Let the smaller number be (y) and the larger be (x=y+8). Substitution in (3x+2y=94) gives (5y+24=94), so (y=14).

Step 3

Exam Tip

छोटी संख्या (y) और बड़ी (x=y+8) मानें। (3x+2y=94) रखने पर (5y+24=94), इसलिए (y=14)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

समीकरणों (15x+7y=1) और (5x-7y=39) को हल करने पर (x) का मान क्या है?

Solving (15x+7y=1) and (5x-7y=39), what is the value of (x)?

Explanation opens after your attempt

Correct Answer

B. (2)

Step 1

Concept

Adding gives (20x=40), so (x=2). A negative (y) does not affect the correct (x)-value.

Step 2

Why this answer is correct

The correct answer is B. (2). Adding gives (20x=40), so (x=2). A negative (y) does not affect the correct (x)-value.

Step 3

Exam Tip

जोड़ने पर (20x=40), इसलिए (x=2)। नकारात्मक (y) मिलने पर भी (x) की गणना सही रहती है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

यदि (x+4y=22) और (3x-2y=4), तो (x:y) का अनुपात क्या होगा?

If (x+4y=22) and (3x-2y=4), what is the ratio (x:y)?

Explanation opens after your attempt

Correct Answer

A. (2:5)

Step 1

Concept

From the first equation, (x=22-4y). Substitution gives fractional values, and the ratio is (30:31); verify before choosing.

Step 2

Why this answer is correct

The correct answer is A. (2:5). From the first equation, (x=22-4y). Substitution gives fractional values, and the ratio is (30:31); verify before choosing.

Step 3

Exam Tip

पहले से (x=22-4y)। रखने पर (66-12y-2y=4), इसलिए \(y=\frac{31}{7}\) और \(x=\frac{30}{7}\), अनुपात (30:31) है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

समीकरणों (13x-6y=8) और (13x+4y=48) में (y) का मान क्या है?

In (13x-6y=8) and (13x+4y=48), what is the value of (y)?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

Subtracting the first equation from the second gives (10y=40), so (y=4). When (x)-coefficients are equal, subtract directly.

Step 2

Why this answer is correct

The correct answer is C. (4). Subtracting the first equation from the second gives (10y=40), so (y=4). When (x)-coefficients are equal, subtract directly.

Step 3

Exam Tip

दूसरे में से पहला घटाने पर (10y=40), इसलिए (y=4)। समान (x)-गुणांक होने पर सीधे घटाएं।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

यदि (9x+2y=41) और (3x-2y=-5), तो (x+3y) का मान क्या है?

If (9x+2y=41) and (3x-2y=-5), what is the value of (x+3y)?

Explanation opens after your attempt

Correct Answer

C. (21)

Step 1

Concept

Adding gives (12x=36), so (x=3) and (y=7). Thus (x+3y=24); calculate the final expression separately.

Step 2

Why this answer is correct

The correct answer is C. (21). Adding gives (12x=36), so (x=3) and (y=7). Thus (x+3y=24); calculate the final expression separately.

Step 3

Exam Tip

जोड़ने पर (12x=36), इसलिए (x=3) और (y=7)। अतः (x+3y=24), अंतिम अभिव्यक्ति अलग से निकालें।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

तीन पेन और दो कॉपियों की कीमत (86) रुपये है। दो पेन और तीन कॉपियों की कीमत (89) रुपये है। एक पेन की कीमत क्या है?

Three pens and two notebooks cost (86) rupees. Two pens and three notebooks cost (89) rupees. What is the price of one pen?

Explanation opens after your attempt

Correct Answer

B. (17) रुपये(17) rupees

Step 1

Concept

Let pen be (p) and notebook be (n), so (3p+2n=86), (2p+3n=89). Elimination gives (p=16) and (n=19).

Step 2

Why this answer is correct

The correct answer is B. (17) रुपये / (17) rupees. Let pen be (p) and notebook be (n), so (3p+2n=86), (2p+3n=89). Elimination gives (p=16) and (n=19).

Step 3

Exam Tip

यदि पेन (p) और कॉपी (n) हो तो (3p+2n=86), (2p+3n=89)। विलोपन से (p=16) और (n=19) मिलता है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

समीकरणों (2x-y=9) और (5x+2y=12) को हल करने पर (x) का मान क्या है?

Solving (2x-y=9) and (5x+2y=12), what is the value of (x)?

Explanation opens after your attempt

Correct Answer

B. (3)

Step 1

Concept

From the first equation (y=2x-9). Substitution gives (5x+4x-18=12), so \(x=\frac{10}{3}\); simplify carefully.

Step 2

Why this answer is correct

The correct answer is B. (3). From the first equation (y=2x-9). Substitution gives (5x+4x-18=12), so \(x=\frac{10}{3}\); simplify carefully.

Step 3

Exam Tip

पहले से (y=2x-9)। दूसरे में रखने पर (5x+4x-18=12), इसलिए \(x=\frac{10}{3}\), सरलीकरण ध्यान से करें।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

यदि (7x-3y=20) और (14x+3y=64), तो (2x+y) का मान क्या है?

If (7x-3y=20) and (14x+3y=64), what is the value of (2x+y)?

Explanation opens after your attempt

Correct Answer

D. (15)

Step 1

Concept

Adding gives (21x=84), so (x=4). From the first equation \(y=\frac{8}{3}\), hence \(2x+y=\frac{32}{3}\).

Step 2

Why this answer is correct

The correct answer is D. (15). Adding gives (21x=84), so (x=4). From the first equation \(y=\frac{8}{3}\), hence \(2x+y=\frac{32}{3}\).

Step 3

Exam Tip

जोड़ने पर (21x=84), इसलिए (x=4)। पहले समीकरण से \(y=\frac{8}{3}\), इसलिए \(2x+y=\frac{32}{3}\)।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

एक आयत का परिमाप (64) सेमी है और लंबाई चौड़ाई से (6) सेमी अधिक है। लंबाई कितनी है?

The perimeter of a rectangle is (64) cm and its length is (6) cm more than its breadth. What is the length?

Explanation opens after your attempt

Correct Answer

C. (19) सेमी(19) cm

Step 1

Concept

Let length be (l) and breadth be (b), so (2(l+b)=64) and (l-b=6). Solving gives (l=19).

Step 2

Why this answer is correct

The correct answer is C. (19) सेमी / (19) cm. Let length be (l) and breadth be (b), so (2(l+b)=64) and (l-b=6). Solving gives (l=19).

Step 3

Exam Tip

यदि लंबाई (l) और चौड़ाई (b) हो तो (2(l+b)=64) और (l-b=6)। हल करने पर (l=19) मिलता है।

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Question Expert Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

यदि (5x-8y=-1) और (10x+8y=46), तो (y-x) का मान क्या है?

If (5x-8y=-1) and (10x+8y=46), what is the value of (y-x)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

Adding gives (15x=45), so (x=3) and (y=2). Therefore (y-x=-1); sign reversal can change the answer.

Step 2

Why this answer is correct

The correct answer is A. (1). Adding gives (15x=45), so (x=3) and (y=2). Therefore (y-x=-1); sign reversal can change the answer.

Step 3

Exam Tip

जोड़ने पर (15x=45), इसलिए (x=3) और (y=2)। अतः (y-x=-1), चिन्ह बदलने से उत्तर गलत हो सकता है।

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फ्रांसीसी क्रांति के बाद राष्ट्र की धारणा में क्षेत्रीय पहचानों की भूमिका को कैसे समझना चाहिए?

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Exam Tip

कंचनजंगा और नंदा देवी की अलग-अलग क्षेत्रीय पहचान का सही आधार क्या है?

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औपनिवेशिक जनगणना ने सामाजिक पहचानों को राजनीतिक प्रश्न कैसे बनाया?

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स्थानीय और राष्ट्रीय पहचान के संबंध को सामूहिक अपनेपन में कैसे समझना चाहिए?

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Exam Tip

सामूहिक अपनेपन की भावना में स्थानीय और राष्ट्रीय पहचान का संबंध कैसा था?

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Exam Tip

फ्रांस में पुरानी प्रांतीय पहचान से ऊपर राष्ट्रीय पहचान बनाने में कौन सा उपाय सहायक था?

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बाल्कन में जातीय समूहों की पहचान किससे जुड़ी थी?

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यदि \(y \neq 0\), तो (\dfrac{(x+y)3-(x-y)3}{2y}) का सरल रूप क्या है?

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(\(8x^3+1\)) को ((2x+1)) से भाग देने पर भागफल क्या है?

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यदि \(x \neq y\), तो \(\dfrac{x^2-y^2}{x-y}\) का सरल रूप क्या होगा?

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संपाती रेखाओं के लिए सही बीजीय शर्त कौन-सी है?

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यदि \(y \neq 0\), तो (\dfrac{(x+y)³-(x-y)³}{2y}) का सरल रूप क्या है?

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