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Mathematics Quiz - Class 9 Mathematics Easy Level 72 Quiz

Question 1/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

भुजा (x+4) वाले वर्ग के दृश्य मॉडल में कुल क्षेत्र कौन सा होगा?

What is the total area in the visual model of a square with side (x+4)?

Explanation opens after your attempt

Correct Answer

B. \(x^2+8x+16\)

Step 1

Concept

The two equal rectangles have total area (8x), and the small square has area (16). Exam tip: the middle term comes from two rectangles.

Step 2

Why this answer is correct

The correct answer is B. \(x^2+8x+16\). The two equal rectangles have total area (8x), and the small square has area (16). Exam tip: the middle term comes from two rectangles.

Step 3

Exam Tip

दो समान आयतों का कुल क्षेत्र (8x) और छोटे वर्ग का क्षेत्र (16) है। परीक्षा में बीच का पद दो आयतों से बनता है।

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Question 2/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

यदि किसी वर्ग मॉडल में \(x^2\), दो (6x) आयत और (36) छोटा वर्ग हैं, तो बाहरी भुजा क्या होगी?

If a square model has \(x^2\), two (6x) rectangles, and a small square (36), what is the outer side?

Explanation opens after your attempt

Correct Answer

A. (x+6)

Step 1

Concept

The small square has side (6), and the large part is (x). Exam tip: take the sum of the side parts.

Step 2

Why this answer is correct

The correct answer is A. (x+6). The small square has side (6), and the large part is (x). Exam tip: take the sum of the side parts.

Step 3

Exam Tip

छोटे वर्ग की भुजा (6) है और बड़ा भाग (x) है। परीक्षा में बाहरी भुजा भागों का योग लें।

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Question 3/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

भुजा (a+5) वाले वर्ग में दोनों समान आयतों का कुल क्षेत्र क्या होगा?

In a square with side (a+5), what will be the total area of the two equal rectangles?

Explanation opens after your attempt

Correct Answer

C. (10a)

Step 1

Concept

Each rectangle has area (5a), so the total is (10a). Exam tip: double the equal rectangles.

Step 2

Why this answer is correct

The correct answer is C. (10a). Each rectangle has area (5a), so the total is (10a). Exam tip: double the equal rectangles.

Step 3

Exam Tip

प्रत्येक आयत का क्षेत्र (5a) है इसलिए कुल (10a) होगा। परीक्षा में समान आयतों को दोगुना करें।

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Question 4/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

आयत मॉडल में ((x+2)(x+5)) के चार भागों का योग क्या है?

What is the sum of the four parts in the rectangle model of ((x+2)(x+5))?

Explanation opens after your attempt

Correct Answer

A. \(x^2+7x+10\)

Step 1

Concept

The parts are \(x^2\), (5x), (2x), and (10). Exam tip: add like (x)-terms.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+7x+10\). The parts are \(x^2\), (5x), (2x), and (10). Exam tip: add like (x)-terms.

Step 3

Exam Tip

भाग \(x^2\), (5x), (2x) और (10) हैं। परीक्षा में समान (x) पदों को जोड़ें।

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Question 5/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

भुजा (y-3) वाले वर्ग के क्षेत्र मॉडल में सही विस्तार कौन सा है?

Which expansion is correct in the area model of a square with side (y-3)?

Explanation opens after your attempt

Correct Answer

C. \(y^2-6y+9\)

Step 1

Concept

Two (3y) strips are subtracted, and (9) is added back. Exam tip: keep the middle term negative in ((a-b)²).

Step 2

Why this answer is correct

The correct answer is C. \(y^2-6y+9\). Two (3y) strips are subtracted, and (9) is added back. Exam tip: keep the middle term negative in ((a-b)²).

Step 3

Exam Tip

दो (3y) पट्टियां घटती हैं और (9) वापस जुड़ता है। परीक्षा में ((a-b)²) में बीच का पद ऋणात्मक रखें।

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Question 6/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

एक बड़े वर्ग की भुजा (m) है और छोटे हटाए गए वर्ग की भुजा (n) है। बचा क्षेत्र किस पहचान से जुड़ता है?

A large square has side (m), and the removed small square has side (n). The remaining area is linked to which identity?

Explanation opens after your attempt

Correct Answer

B. (m^-2-n^-2=(m+n)(m-n))

Step 1

Concept

The small square area is subtracted from the large square, and the remainder can be rearranged into a rectangle. Exam tip: link difference of squares with rearrangement.

Step 2

Why this answer is correct

The correct answer is B. (m^-2-n^-2=(m+n)(m-n)). The small square area is subtracted from the large square, and the remainder can be rearranged into a rectangle. Exam tip: link difference of squares with rearrangement.

Step 3

Exam Tip

बड़े वर्ग से छोटे वर्ग का क्षेत्र घटता है और शेष आयत में बदला जा सकता है। परीक्षा में अंतर के वर्गों को पुनर्व्यवस्था से जोड़ें।

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Question 7/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

भुजा (p+q) वाले वर्ग में \(p^2\) और \(q^2\) के अलावा कौन सा कुल क्षेत्र आता है?

In a square with side (p+q), besides \(p^2\) and \(q^2\), what total area appears?

Explanation opens after your attempt

Correct Answer

D. (2pq)

Step 1

Concept

The two equal rectangles have areas (pq) and (pq). Exam tip: add them to write (2pq).

Step 2

Why this answer is correct

The correct answer is D. (2pq). The two equal rectangles have areas (pq) and (pq). Exam tip: add them to write (2pq).

Step 3

Exam Tip

दो समान आयतों का क्षेत्र (pq) और (pq) होता है। परीक्षा में इन्हें जोड़कर (2pq) लिखें।

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Question 8/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

यदि वर्ग मॉडल का कुल क्षेत्र \(x^2+2x+1\) है, तो उसकी भुजा क्या होगी?

If the total area of a square model is \(x^2+2x+1\), what will be its side?

Explanation opens after your attempt

Correct Answer

A. (x+1)

Step 1

Concept

This is the area of ((x+1)²). Exam tip: identify (1) as \(1^2\) and (2x) as two (x) rectangles.

Step 2

Why this answer is correct

The correct answer is A. (x+1). This is the area of ((x+1)²). Exam tip: identify (1) as \(1^2\) and (2x) as two (x) rectangles.

Step 3

Exam Tip

यह ((x+1)²) का क्षेत्र है। परीक्षा में (1) को \(1^2\) और (2x) को दो (x) आयतों से पहचानें।

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Question 9/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

आयाम (a+3) और (a+7) वाले आयत का क्षेत्र मॉडल कौन सा विस्तार देता है?

Which expansion is given by the area model of a rectangle with dimensions (a+3) and (a+7)?

Explanation opens after your attempt

Correct Answer

C. \(a^2+10a+21\)

Step 1

Concept

The four parts are \(a^2\), (7a), (3a), and (21). Exam tip: check the sum and product of the outside numbers.

Step 2

Why this answer is correct

The correct answer is C. \(a^2+10a+21\). The four parts are \(a^2\), (7a), (3a), and (21). Exam tip: check the sum and product of the outside numbers.

Step 3

Exam Tip

चार भाग \(a^2\), (7a), (3a) और (21) हैं। परीक्षा में बाहरी संख्याओं का योग और गुणनफल देखें।

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Question 10/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

भुजा (10+2) वाले वर्ग का क्षेत्र दृश्य पहचान से कितना होगा?

Using the visual identity, what is the area of a square with side (10+2)?

Explanation opens after your attempt

Correct Answer

B. (144)

Step 1

Concept

((10+2)²=100+40+4=144). Exam tip: use square identities for fast calculation.

Step 2

Why this answer is correct

The correct answer is B. (144). ((10+2)²=100+40+4=144). Exam tip: use square identities for fast calculation.

Step 3

Exam Tip

((10+2)²=100+40+4=144) होता है। परीक्षा में वर्ग पहचान से तेज गणना करें।

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Question 11/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

किस आकृति का क्षेत्र सीधे ((u-v)²) दिखाता है?

Which figure directly shows the area ((u-v)²)?

Explanation opens after your attempt

Correct Answer

A. भुजा (u-v) वाला वर्गSquare with side (u-v)

Step 1

Concept

The area of a square equals the square of its side. Exam tip: connect ((u-v)²) with a subtraction square.

Step 2

Why this answer is correct

The correct answer is A. भुजा (u-v) वाला वर्ग / Square with side (u-v). The area of a square equals the square of its side. Exam tip: connect ((u-v)²) with a subtraction square.

Step 3

Exam Tip

किसी वर्ग का क्षेत्र उसकी भुजा के वर्ग के बराबर होता है। परीक्षा में ((u-v)²) को घटाव वाले वर्ग से जोड़ें।

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Question 12/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

यदि \(x^2+12x+36\) को पूर्ण वर्ग मॉडल से पढ़ा जाए, तो छोटे वर्ग की भुजा क्या होगी?

If \(x^2+12x+36\) is read through a complete square model, what is the side of the small square?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

The small square has area (36), so its side is (6). Exam tip: take the square root of the last term.

Step 2

Why this answer is correct

The correct answer is C. (6). The small square has area (36), so its side is (6). Exam tip: take the square root of the last term.

Step 3

Exam Tip

छोटे वर्ग का क्षेत्र (36) है इसलिए उसकी भुजा (6) है। परीक्षा में अंतिम पद की वर्गमूल लें।

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Question 13/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

दृश्य मॉडल में ((r+s)(r-s)) के बीच के पद क्यों नहीं बचते?

In the visual model of ((r+s)(r-s)), why do the middle terms not remain?

Explanation opens after your attempt

Correct Answer

A. क्योंकि वे बराबर और विपरीत चिन्ह वाले होते हैंBecause they are equal and have opposite signs

Step 1

Concept

One term is (rs) and the other is (-rs), so they cancel. Exam tip: watch the middle terms in conjugate multiplication.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि वे बराबर और विपरीत चिन्ह वाले होते हैं / Because they are equal and have opposite signs. One term is (rs) and the other is (-rs), so they cancel. Exam tip: watch the middle terms in conjugate multiplication.

Step 3

Exam Tip

एक पद (rs) और दूसरा (-rs) होता है, इसलिए वे कट जाते हैं। परीक्षा में संयुग्म गुणन में बीच के पदों को देखें।

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Question 14/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

आयत मॉडल में (x(x+9)) का क्षेत्र कौन सा है?

What is the area of (x(x+9)) in the rectangle model?

Explanation opens after your attempt

Correct Answer

C. \(x^2+9x\)

Step 1

Concept

Splitting the rectangle into (x) and (9) parts gives \(x^2\) and (9x). Exam tip: understand the distributive law through area.

Step 2

Why this answer is correct

The correct answer is C. \(x^2+9x\). Splitting the rectangle into (x) and (9) parts gives \(x^2\) and (9x). Exam tip: understand the distributive law through area.

Step 3

Exam Tip

आयत को (x) और (9) भागों में बांटने पर \(x^2\) और (9x) मिलते हैं। परीक्षा में वितरण नियम को क्षेत्र से समझें।

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Question 15/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

भुजा (2x+1) वाले वर्ग के दृश्य मॉडल में कुल क्षेत्र क्या होगा?

What is the total area in the visual model of a square with side (2x+1)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

The square of (2x) is \(4x^2\), and the two rectangles have total area (4x). Exam tip: do not forget to square the coefficient.

Step 2

Why this answer is correct

The correct answer is A. \(4x^2+4x+1\). The square of (2x) is \(4x^2\), and the two rectangles have total area (4x). Exam tip: do not forget to square the coefficient.

Step 3

Exam Tip

(2x) का वर्ग \(4x^2\) और दो आयतों का कुल क्षेत्र (4x) है। परीक्षा में गुणांक का वर्ग करना न भूलें।

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Question 16/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

यदि \(a^2-16\) को अंतर के वर्गों के मॉडल से आयत में बदला जाए, तो आयाम क्या होंगे?

If \(a^2-16\) is changed into a rectangle using the difference of squares model, what will the dimensions be?

Explanation opens after your attempt

Correct Answer

B. (a+4) और (a-4)(a+4) and (a-4)

Step 1

Concept

Since \(16=4^2\), (a^-2-16=(a+4)(a-4)). Exam tip: identify the side of the subtracted square.

Step 2

Why this answer is correct

The correct answer is B. (a+4) और (a-4) / (a+4) and (a-4). Since \(16=4^2\), (a^-2-16=(a+4)(a-4)). Exam tip: identify the side of the subtracted square.

Step 3

Exam Tip

\(16=4^2\), इसलिए (a^-2-16=(a+4)(a-4)) है। परीक्षा में घटाए गए वर्ग की भुजा पहचानें।

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Question 17/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

भुजा (x-5) वाले वर्ग के मॉडल में अंतिम छोटा वर्ग किस क्षेत्र का होगा?

In the model of a square with side (x-5), what will be the area of the final small square?

Explanation opens after your attempt

Correct Answer

C. (25)

Step 1

Concept

The small square has side (5), so its area is (25). Exam tip: the square of the negative part is positive.

Step 2

Why this answer is correct

The correct answer is C. (25). The small square has side (5), so its area is (25). Exam tip: the square of the negative part is positive.

Step 3

Exam Tip

छोटे वर्ग की भुजा (5) है इसलिए उसका क्षेत्र (25) है। परीक्षा में ऋणात्मक भाग का वर्ग धनात्मक होता है।

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Question 18/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

किस दृश्य मॉडल में \(a^2+2ab+b^2\) के चार क्षेत्र भाग साफ दिखाई देते हैं?

In which visual model are the four area parts of \(a^2+2ab+b^2\) clearly visible?

Explanation opens after your attempt

Correct Answer

A. भुजा (a+b) वाला वर्गSquare with side (a+b)

Step 1

Concept

A square of side (a+b) splits into \(a^2\), (ab), (ab), and \(b^2\). Exam tip: add the four parts to form the identity.

Step 2

Why this answer is correct

The correct answer is A. भुजा (a+b) वाला वर्ग / Square with side (a+b). A square of side (a+b) splits into \(a^2\), (ab), (ab), and \(b^2\). Exam tip: add the four parts to form the identity.

Step 3

Exam Tip

भुजा (a+b) वाला वर्ग \(a^2\), (ab), (ab) और \(b^2\) में बंटता है। परीक्षा में चार भागों को जोड़कर पहचान बनाएं।

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Question 19/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

यदि आयत मॉडल में भाग \(x^2\), (4x), (5x) और (20) हैं, तो बाहरी आयाम क्या हो सकते हैं?

If a rectangle model has parts \(x^2\), (4x), (5x), and (20), what can the outer dimensions be?

Explanation opens after your attempt

Correct Answer

B. (x+4) और (x+5)(x+4) and (x+5)

Step 1

Concept

The numbers (4) and (5) make (4x), (5x), and (20). Exam tip: the corner area is the product of numerical parts.

Step 2

Why this answer is correct

The correct answer is B. (x+4) और (x+5) / (x+4) and (x+5). The numbers (4) and (5) make (4x), (5x), and (20). Exam tip: the corner area is the product of numerical parts.

Step 3

Exam Tip

(4) और (5) से (4x), (5x) और (20) बनते हैं। परीक्षा में कोने का क्षेत्र संख्यात्मक भागों का गुणनफल होता है।

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Question 20/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

एक विद्यार्थी ((x+3)²) को \(x^2+9\) लिखता है। दृश्य मॉडल के अनुसार क्या छूट गया?

A student writes ((x+3)²) as \(x^2+9\). According to the visual model, what is missing?

Explanation opens after your attempt

Correct Answer

A. दो (3x) आयतTwo (3x) rectangles

Step 1

Concept

A complete square has two (3x) rectangles along with \(x^2\) and (9). Exam tip: do not omit the middle term (6x).

Step 2

Why this answer is correct

The correct answer is A. दो (3x) आयत / Two (3x) rectangles. A complete square has two (3x) rectangles along with \(x^2\) and (9). Exam tip: do not omit the middle term (6x).

Step 3

Exam Tip

पूर्ण वर्ग में \(x^2\) और (9) के साथ दो (3x) आयत भी होते हैं। परीक्षा में बीच का (6x) पद न छोड़ें।

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Question 21/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

किस पहचान को भुजा (a+b) वाले वर्ग का क्षेत्र और उसके अंदर के भागों का योग बराबर रखकर सिद्ध किया जाता है?

Which identity is proved by equating the area of a square with side (a+b) and the sum of its inner parts?

Explanation opens after your attempt

Correct Answer

C. (a^-2+2ab+b^-2=(a+b)²)

Step 1

Concept

The same square has outside area ((a+b)²) and inside area \(a^2+2ab+b^2\). Exam tip: remember two forms of the same area.

Step 2

Why this answer is correct

The correct answer is C. (a^-2+2ab+b^-2=(a+b)²). The same square has outside area ((a+b)²) and inside area \(a^2+2ab+b^2\). Exam tip: remember two forms of the same area.

Step 3

Exam Tip

एक ही वर्ग का क्षेत्र बाहर से ((a+b)²) और अंदर से \(a^2+2ab+b^2\) मिलता है। परीक्षा में एक ही क्षेत्र के दो रूप याद रखें।

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Question 22/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

भुजा (8-1) वाले वर्ग का क्षेत्र पहचान से कितना होगा?

Using identity, what is the area of a square with side (8-1)?

Explanation opens after your attempt

Correct Answer

D. (49)

Step 1

Concept

((8-1)²=64-16+1=49). Exam tip: use ((a-b)²) for mental calculation.

Step 2

Why this answer is correct

The correct answer is D. (49). ((8-1)²=64-16+1=49). Exam tip: use ((a-b)²) for mental calculation.

Step 3

Exam Tip

((8-1)²=64-16+1=49) होता है। परीक्षा में ((a-b)²) से मानसिक गणना करें।

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Question 23/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

किस दृश्य मॉडल में एक \(a^2\) वर्ग और एक (ab) आयत मिलकर (a(a+b)) दिखाते हैं?

Which visual model shows (a(a+b)) by combining one \(a^2\) square and one (ab) rectangle?

Explanation opens after your attempt

Correct Answer

A. लंबाई (a+b) और चौड़ाई (a) वाला आयतRectangle with length (a+b) and breadth (a)

Step 1

Concept

The rectangle area is (a(a+b)), and the sum of parts is \(a^2+ab\). Exam tip: identify the common factor from the figure.

Step 2

Why this answer is correct

The correct answer is A. लंबाई (a+b) और चौड़ाई (a) वाला आयत / Rectangle with length (a+b) and breadth (a). The rectangle area is (a(a+b)), and the sum of parts is \(a^2+ab\). Exam tip: identify the common factor from the figure.

Step 3

Exam Tip

आयत का क्षेत्र (a(a+b)) है और भागों का योग \(a^2+ab\) है। परीक्षा में सामान्य गुणनखंड को चित्र से पहचानें।

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Question 24/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

यदि ((x+4)(x-4)) को आयत मॉडल से देखें, तो क्षेत्र कौन सा होगा?

If ((x+4)(x-4)) is viewed through a rectangle model, what will the area be?

Explanation opens after your attempt

Correct Answer

C. \(x^2-16\)

Step 1

Concept

This is a conjugate product, and the middle terms cancel. Exam tip: identify ((a+b)(a-b)=a^-2-b^-2).

Step 2

Why this answer is correct

The correct answer is C. \(x^2-16\). This is a conjugate product, and the middle terms cancel. Exam tip: identify ((a+b)(a-b)=a^-2-b^-2).

Step 3

Exam Tip

यह संयुग्म गुणन है और बीच के पद कट जाते हैं। परीक्षा में ((a+b)(a-b)=a^-2-b^-2) पहचानें।

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Question 25/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

भुजा (3x+2) वाले वर्ग में छोटे वर्ग का क्षेत्र क्या होगा?

In a square with side (3x+2), what will be the area of the small square?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

The small square has side (2), so its area is \(2^2=4\). Exam tip: square the constant part.

Step 2

Why this answer is correct

The correct answer is B. (4). The small square has side (2), so its area is \(2^2=4\). Exam tip: square the constant part.

Step 3

Exam Tip

छोटे वर्ग की भुजा (2) है इसलिए क्षेत्र \(2^2=4\) होगा। परीक्षा में स्थिर भाग का वर्ग करें।

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Question 26/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

दृश्य मॉडल में \(x^2-10x+25\) किस वर्ग की भुजा को दिखाता है?

In a visual model, \(x^2-10x+25\) shows the side of which square?

Explanation opens after your attempt

Correct Answer

C. (x-5)

Step 1

Concept

Since \(25=5^2\) and \(-10x=-2\times x\times5\), the side is (x-5). Exam tip: look at the negative middle term.

Step 2

Why this answer is correct

The correct answer is C. (x-5). Since \(25=5^2\) and \(-10x=-2\times x\times5\), the side is (x-5). Exam tip: look at the negative middle term.

Step 3

Exam Tip

\(25=5^2\) और \(-10x=-2\times x\times5\), इसलिए भुजा (x-5) है। परीक्षा में ऋणात्मक बीच का पद देखें।

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Question 27/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

यदि \(6^2-2^2\) को दृश्य आयत में बदला जाए, तो आयाम क्या होंगे?

If \(6^2-2^2\) is changed into a visual rectangle, what will the dimensions be?

Explanation opens after your attempt

Correct Answer

A. (6+2) और (6-2)(6+2) and (6-2)

Step 1

Concept

In difference of squares, the dimensions become ((a+b)) and ((a-b)). Exam tip: compute \(6^2-2^2=8\times4\).

Step 2

Why this answer is correct

The correct answer is A. (6+2) और (6-2) / (6+2) and (6-2). In difference of squares, the dimensions become ((a+b)) and ((a-b)). Exam tip: compute \(6^2-2^2=8\times4\).

Step 3

Exam Tip

अंतर के वर्गों में आयाम ((a+b)) और ((a-b)) बनते हैं। परीक्षा में \(6^2-2^2=8\times4\) करें।

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Question 28/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

किस मॉडल में \(x^2+5x\) को (x) और (5) चौड़ाई वाले दो भागों से दिखाया जा सकता है?

In which model can \(x^2+5x\) be shown by two parts with widths (x) and (5)?

Explanation opens after your attempt

Correct Answer

B. लंबाई (x+5) और चौड़ाई (x) वाला आयतRectangle with length (x+5) and breadth (x)

Step 1

Concept

The rectangle area is (x(x+5)=x^-2+5x). Exam tip: see the common (x) as the breadth.

Step 2

Why this answer is correct

The correct answer is B. लंबाई (x+5) और चौड़ाई (x) वाला आयत / Rectangle with length (x+5) and breadth (x). The rectangle area is (x(x+5)=x^-2+5x). Exam tip: see the common (x) as the breadth.

Step 3

Exam Tip

आयत का क्षेत्र (x(x+5)=x^-2+5x) है। परीक्षा में सामान्य (x) को चौड़ाई की तरह देखें।

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Question 29/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

भुजा (a+b+c) वाले वर्ग के दृश्य मॉडल में (bc) आयत कितनी बार आएगा?

In the visual model of a square with side (a+b+c), how many times will the (bc) rectangle appear?

Explanation opens after your attempt

Correct Answer

B. दो बारTwice

Step 1

Concept

Each different pair forms two equal rectangles, so (bc) appears twice. Exam tip: count paired rectangles.

Step 2

Why this answer is correct

The correct answer is B. दो बार / Twice. Each different pair forms two equal rectangles, so (bc) appears twice. Exam tip: count paired rectangles.

Step 3

Exam Tip

हर अलग जोड़ी के दो समान आयत बनते हैं इसलिए (bc) दो बार आता है। परीक्षा में जोड़ीदार आयत गिनें।

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Question 30/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

यदि \(x^2+16x+64\) पूर्ण वर्ग मॉडल है, तो बाहरी भुजा क्या होगी?

If \(x^2+16x+64\) is a complete square model, what is the outer side?

Explanation opens after your attempt

Correct Answer

C. (x+8)

Step 1

Concept

Since \(64=8^2\) and \(16x=2\times8\times x\), the side is (x+8). Exam tip: check using the square root of the last term.

Step 2

Why this answer is correct

The correct answer is C. (x+8). Since \(64=8^2\) and \(16x=2\times8\times x\), the side is (x+8). Exam tip: check using the square root of the last term.

Step 3

Exam Tip

\(64=8^2\) और \(16x=2\times8\times x\), इसलिए भुजा (x+8) है। परीक्षा में अंतिम पद की वर्गमूल से जांचें।

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Question 31/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

दृश्य क्षेत्र मॉडल में \(a^2\), (2ab) और \(b^2\) किस प्रकार के भाग हैं?

In the visual area model, what type of parts are \(a^2\), (2ab), and \(b^2\)?

Explanation opens after your attempt

Correct Answer

B. क्षेत्र के भागArea parts

Step 1

Concept

All these represent areas of squares or rectangles. Exam tip: understand identity terms as area parts.

Step 2

Why this answer is correct

The correct answer is B. क्षेत्र के भाग / Area parts. All these represent areas of squares or rectangles. Exam tip: understand identity terms as area parts.

Step 3

Exam Tip

ये सभी वर्ग या आयत के क्षेत्र को दर्शाते हैं। परीक्षा में पहचान के पदों को क्षेत्र भागों की तरह समझें।

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Question 32/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

यदि एक वर्ग को \(r^2\), (2rs) और \(s^2\) में पढ़ा जा रहा है, तो उसकी भुजा क्या होगी?

If a square is read as \(r^2\), (2rs), and \(s^2\), what will be its side?

Explanation opens after your attempt

Correct Answer

A. (r+s)

Step 1

Concept

These terms come from the area model of ((r+s)²). Exam tip: identify (2rs) from two equal rectangles.

Step 2

Why this answer is correct

The correct answer is A. (r+s). These terms come from the area model of ((r+s)²). Exam tip: identify (2rs) from two equal rectangles.

Step 3

Exam Tip

ये पद ((r+s)²) के क्षेत्र मॉडल से आते हैं। परीक्षा में (2rs) को दो समान आयतों से पहचानें।

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Question 33/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

भुजा (9+1) वाले वर्ग का क्षेत्र दृश्य पहचान से किस योग के बराबर है?

Using the visual identity, the area of a square with side (9+1) equals which sum?

Explanation opens after your attempt

Correct Answer

B. (81+18+1)

Step 1

Concept

In ((9+1)²), \(9^2\), two (9) rectangles, and \(1^2\) are added. Exam tip: do not forget the two equal rectangles.

Step 2

Why this answer is correct

The correct answer is B. (81+18+1). In ((9+1)²), \(9^2\), two (9) rectangles, and \(1^2\) are added. Exam tip: do not forget the two equal rectangles.

Step 3

Exam Tip

((9+1)²) में \(9^2\), दो (9) आयत और \(1^2\) जुड़ते हैं। परीक्षा में दो समान आयतों को न भूलें।

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Question 34/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

किस स्थिति में दृश्य मॉडल का छोटा कोना (12) होगा?

In which situation will the small corner of the visual model be (12)?

Explanation opens after your attempt

Correct Answer

A. आयत ((x+3)(x+4)) मेंIn the rectangle ((x+3)(x+4))

Step 1

Concept

The small corner is formed by \(3\times4=12\). Exam tip: connect the constant term with the corner in a rectangle model.

Step 2

Why this answer is correct

The correct answer is A. आयत ((x+3)(x+4)) में / In the rectangle ((x+3)(x+4)). The small corner is formed by \(3\times4=12\). Exam tip: connect the constant term with the corner in a rectangle model.

Step 3

Exam Tip

छोटा कोना \(3\times4=12\) से बनता है। परीक्षा में आयत मॉडल में स्थिर पद को कोने से जोड़ें।

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Question 35/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

यदि \(x^2-4\) को दृश्य रूप से देखें, तो कौन सा छोटा वर्ग हटाया गया है?

If \(x^2-4\) is viewed visually, which small square has been removed?

Explanation opens after your attempt

Correct Answer

B. भुजा (2) वाला वर्गSquare with side (2)

Step 1

Concept

Since \(4=2^2\), a small square of side (2) has been removed. Exam tip: find the side of the subtracted square.

Step 2

Why this answer is correct

The correct answer is B. भुजा (2) वाला वर्ग / Square with side (2). Since \(4=2^2\), a small square of side (2) has been removed. Exam tip: find the side of the subtracted square.

Step 3

Exam Tip

\(4=2^2\), इसलिए भुजा (2) का छोटा वर्ग हटाया गया है। परीक्षा में घटाए गए वर्ग की भुजा निकालें।

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Question 36/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

भुजा (x+7) वाले वर्ग में छोटे वर्ग का क्षेत्र और दो आयतों का कुल क्षेत्र कौन सा है?

In a square with side (x+7), what are the small square area and total area of the two rectangles?

Explanation opens after your attempt

Correct Answer

C. (49) और (14x)(49) and (14x)

Step 1

Concept

The small square is \(7^2=49\), and the two rectangles total \(2\times7x=14x\). Exam tip: use the constant part in both square and rectangles.

Step 2

Why this answer is correct

The correct answer is C. (49) और (14x) / (49) and (14x). The small square is \(7^2=49\), and the two rectangles total \(2\times7x=14x\). Exam tip: use the constant part in both square and rectangles.

Step 3

Exam Tip

छोटा वर्ग \(7^2=49\) और दो आयतों का कुल \(2\times7x=14x\) है। परीक्षा में स्थिर भाग को वर्ग और आयत दोनों में उपयोग करें।

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Question 37/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

किस दृश्य पहचान से \(12^2-8^2\) को बिना लंबे गुणन के हल किया जा सकता है?

Which visual identity can solve \(12^2-8^2\) without long multiplication?

Explanation opens after your attempt

Correct Answer

B. अंतर के वर्गों की पहचानDifference of squares identity

Step 1

Concept

(12²-8²=(12+8)(12-8)) gives the area quickly. Exam tip: when a difference appears, multiply sum and difference.

Step 2

Why this answer is correct

The correct answer is B. अंतर के वर्गों की पहचान / Difference of squares identity. (12²-8²=(12+8)(12-8)) gives the area quickly. Exam tip: when a difference appears, multiply sum and difference.

Step 3

Exam Tip

(12²-8²=(12+8)(12-8)) से तुरंत क्षेत्र मिलता है। परीक्षा में अंतर दिखे तो योग और अंतर का गुणन करें।

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Question 38/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

आयत मॉडल में ((x+1)(x+6)) का (x) वाला कुल पद क्या होगा?

In the rectangle model of ((x+1)(x+6)), what will be the total (x)-term?

Explanation opens after your attempt

Correct Answer

B. (7x)

Step 1

Concept

The cross rectangles are (6x) and (x), whose sum is (7x). Exam tip: add both (x) rectangles.

Step 2

Why this answer is correct

The correct answer is B. (7x). The cross rectangles are (6x) and (x), whose sum is (7x). Exam tip: add both (x) rectangles.

Step 3

Exam Tip

क्रॉस आयत (6x) और (x) हैं, जिनका योग (7x) है। परीक्षा में दोनों (x) आयत जोड़ें।

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Question 39/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

यदि भुजा (a-b) वाले वर्ग का क्षेत्र \(a^2-2ab+b^2\) है, तो \(b^2\) का चिन्ह कैसा होगा?

If the area of a square with side (a-b) is \(a^2-2ab+b^2\), what will be the sign of \(b^2\)?

Explanation opens after your attempt

Correct Answer

C. धनात्मकPositive

Step 1

Concept

Because (b) is squared, \(b^2\) remains positive. Exam tip: only the middle term is negative.

Step 2

Why this answer is correct

The correct answer is C. धनात्मक / Positive. Because (b) is squared, \(b^2\) remains positive. Exam tip: only the middle term is negative.

Step 3

Exam Tip

(b) का वर्ग बनने से \(b^2\) धनात्मक रहता है। परीक्षा में केवल बीच का पद ऋणात्मक होता है।

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Question 40/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

एक (x) बाय (x) वर्ग और एक (x) बाय (8) आयत को जोड़ने पर कौन सा क्षेत्र बनता है?

What area is formed by joining an (x) by (x) square and an (x) by (8) rectangle?

Explanation opens after your attempt

Correct Answer

A. \(x^2+8x\)

Step 1

Concept

The areas of the two parts are \(x^2\) and (8x). Exam tip: add the areas of joined shapes.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+8x\). The areas of the two parts are \(x^2\) and (8x). Exam tip: add the areas of joined shapes.

Step 3

Exam Tip

दोनों भागों के क्षेत्र \(x^2\) और (8x) हैं। परीक्षा में जुड़ी आकृतियों के क्षेत्र जोड़ें।

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Question 41/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

यदि \(x^2+20x+100\) को वर्ग टाइलों से बनाया गया है, तो दो समान आयतों में प्रत्येक का क्षेत्र कितना है?

If \(x^2+20x+100\) is made with square tiles, what is the area of each of the two equal rectangles?

Explanation opens after your attempt

Correct Answer

B. (10x)

Step 1

Concept

The total middle term is (20x), so each rectangle has area (10x). Exam tip: split the middle term into two equal parts.

Step 2

Why this answer is correct

The correct answer is B. (10x). The total middle term is (20x), so each rectangle has area (10x). Exam tip: split the middle term into two equal parts.

Step 3

Exam Tip

बीच का कुल पद (20x) है इसलिए प्रत्येक आयत (10x) का होगा। परीक्षा में बीच के पद को दो बराबर भागों में बांटें।

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Question 42/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

किस मॉडल में (x^-2-25=(x+5)(x-5)) को सबसे साफ देखा जा सकता है?

In which model can (x^-2-25=(x+5)(x-5)) be seen most clearly?

Explanation opens after your attempt

Correct Answer

B. भुजा (x) के वर्ग से भुजा (5) का वर्ग हटाकरBy removing a square of side (5) from a square of side (x)

Step 1

Concept

This is the visual construction of difference of squares. Exam tip: after removing the square, the remaining part forms a rectangle.

Step 2

Why this answer is correct

The correct answer is B. भुजा (x) के वर्ग से भुजा (5) का वर्ग हटाकर / By removing a square of side (5) from a square of side (x). This is the visual construction of difference of squares. Exam tip: after removing the square, the remaining part forms a rectangle.

Step 3

Exam Tip

यह अंतर के वर्गों की दृश्य रचना है। परीक्षा में हटाए गए वर्ग के बाद बचा भाग आयत बनता है।

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Question 43/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

भुजा (a+b) के वर्ग मॉडल में कुल कितने मुख्य भाग बनते हैं?

How many main parts are formed in the square model of side (a+b)?

Explanation opens after your attempt

Correct Answer

C. चारFour

Step 1

Concept

The main parts are \(a^2\), (ab), (ab), and \(b^2\). Exam tip: count all four area parts.

Step 2

Why this answer is correct

The correct answer is C. चार / Four. The main parts are \(a^2\), (ab), (ab), and \(b^2\). Exam tip: count all four area parts.

Step 3

Exam Tip

मुख्य भाग \(a^2\), (ab), (ab) और \(b^2\) होते हैं। परीक्षा में चारों क्षेत्र भाग गिनें।

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Question 44/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

यदि ((2x+3)(2x+3)) को वर्ग के रूप में देखें, तो यह किसके बराबर है?

If ((2x+3)(2x+3)) is viewed as a square, what is it equal to?

Explanation opens after your attempt

Correct Answer

A. \(4x^2+12x+9\)

Step 1

Concept

In ((2x+3)²), \(4x^2\), two (6x), and (9) appear. Exam tip: add both equal rectangles.

Step 2

Why this answer is correct

The correct answer is A. \(4x^2+12x+9\). In ((2x+3)²), \(4x^2\), two (6x), and (9) appear. Exam tip: add both equal rectangles.

Step 3

Exam Tip

((2x+3)²) में \(4x^2\), दो (6x) और (9) आते हैं। परीक्षा में दोनों समान आयत जोड़ें।

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Question 45/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

दृश्य मॉडल में ((a+b+c)²) के वर्गीय भाग कौन से हैं?

In the visual model of ((a+b+c)²), which are the square parts?

Explanation opens after your attempt

Correct Answer

A. \(a^2\), \(b^2\), \(c^2\)

Step 1

Concept

Each of the three side parts forms its own square. Exam tip: distinguish square parts and rectangular parts.

Step 2

Why this answer is correct

The correct answer is A. \(a^2\), \(b^2\), \(c^2\). Each of the three side parts forms its own square. Exam tip: distinguish square parts and rectangular parts.

Step 3

Exam Tip

तीनों अलग भुजा भागों के अपने-अपने वर्ग बनते हैं। परीक्षा में वर्गीय भाग और आयताकार भाग अलग पहचानें।

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Question 46/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

यदि एक आयत की लंबाई (2x+5) और चौड़ाई (x) है, तो क्षेत्र मॉडल क्या देगा?

If a rectangle has length (2x+5) and breadth (x), what will the area model give?

Explanation opens after your attempt

Correct Answer

A. \(2x^2+5x\)

Step 1

Concept

Multiplying (x) by (2x) and (5) gives \(2x^2+5x\). Exam tip: multiply the breadth by both parts.

Step 2

Why this answer is correct

The correct answer is A. \(2x^2+5x\). Multiplying (x) by (2x) and (5) gives \(2x^2+5x\). Exam tip: multiply the breadth by both parts.

Step 3

Exam Tip

(x) को (2x) और (5) से गुणा करने पर \(2x^2+5x\) मिलता है। परीक्षा में चौड़ाई को दोनों भागों से गुणा करें।

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Question 47/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

कौन सा कथन दृश्य मॉडल के लिए सही है?

Which statement is correct for a visual model?

Explanation opens after your attempt

Correct Answer

B. यह बीजीय पदों को क्षेत्रों के रूप में दिखाता हैIt shows algebraic terms as areas

Step 1

Concept

In a visual model, squares and rectangles explain the meaning of algebraic terms. Exam tip: connect the diagram with the formula.

Step 2

Why this answer is correct

The correct answer is B. यह बीजीय पदों को क्षेत्रों के रूप में दिखाता है / It shows algebraic terms as areas. In a visual model, squares and rectangles explain the meaning of algebraic terms. Exam tip: connect the diagram with the formula.

Step 3

Exam Tip

दृश्य मॉडल में वर्ग और आयत बीजीय पदों का अर्थ समझाते हैं। परीक्षा में चित्र को सूत्र से जोड़ें।

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Question 48/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

यदि \(11^2-1^2\) को आयत में बदला जाए, तो क्षेत्र कितना होगा?

If \(11^2-1^2\) is changed into a rectangle, what will be the area?

Explanation opens after your attempt

Correct Answer

C. (120)

Step 1

Concept

(11²-1²=(11+1)(11-1)=12\times10=120). Exam tip: solve quickly using difference of squares.

Step 2

Why this answer is correct

The correct answer is C. (120). (11²-1²=(11+1)(11-1)=12\times10=120). Exam tip: solve quickly using difference of squares.

Step 3

Exam Tip

(11²-1²=(11+1)(11-1)=12\times10=120) है। परीक्षा में अंतर के वर्गों से तेजी से हल करें।

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Question 49/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

भुजा (x+2+3) वाले वर्ग को पहले (x+5) की तरह देखने से कौन सा क्षेत्र मिलेगा?

If a square with side (x+2+3) is first viewed as (x+5), what area will be obtained?

Explanation opens after your attempt

Correct Answer

A. \(x^2+10x+25\)

Step 1

Concept

Since (2+3=5), the side becomes (x+5), and the area is \(x^2+10x+25\). Exam tip: simplify side parts first.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+10x+25\). Since (2+3=5), the side becomes (x+5), and the area is \(x^2+10x+25\). Exam tip: simplify side parts first.

Step 3

Exam Tip

क्योंकि (2+3=5), भुजा (x+5) बनती है और क्षेत्र \(x^2+10x+25\) होता है। परीक्षा में पहले भुजा के भाग सरल करें।

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Question 50/50 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 72

क्षेत्र मॉडल में समान आकृति का क्षेत्र दो तरीकों से लिखने का मुख्य निष्कर्ष क्या होता है?

In an area model, what is the main conclusion of writing the area of the same figure in two ways?

Explanation opens after your attempt

Correct Answer

A. दोनों अभिव्यक्तियां बराबर होती हैंBoth expressions are equal

Step 1

Concept

The area of the same figure does not change, so both forms are equal. Exam tip: this idea is the basis of an algebraic identity.

Step 2

Why this answer is correct

The correct answer is A. दोनों अभिव्यक्तियां बराबर होती हैं / Both expressions are equal. The area of the same figure does not change, so both forms are equal. Exam tip: this idea is the basis of an algebraic identity.

Step 3

Exam Tip

एक ही आकृति का क्षेत्र बदलता नहीं है, इसलिए दोनों रूप बराबर होते हैं। परीक्षा में यही विचार बीजीय पहचान का आधार है।

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Class 9 Mathematics Easy Quiz

भुजा (x+4) वाले वर्ग के दृश्य मॉडल में कुल क्षेत्र कौन सा होगा?

Concept

Why this answer is correct

Exam Tip

यदि किसी वर्ग मॉडल में \(x^2\), दो (6x) आयत और (36) छोटा वर्ग हैं, तो बाहरी भुजा क्या होगी?

Concept

Why this answer is correct

Exam Tip

भुजा (a+5) वाले वर्ग में दोनों समान आयतों का कुल क्षेत्र क्या होगा?

Concept

Why this answer is correct

Exam Tip

आयत मॉडल में ((x+2)(x+5)) के चार भागों का योग क्या है?

Concept

Why this answer is correct

Exam Tip

भुजा (y-3) वाले वर्ग के क्षेत्र मॉडल में सही विस्तार कौन सा है?

Concept

Why this answer is correct

Exam Tip

एक बड़े वर्ग की भुजा (m) है और छोटे हटाए गए वर्ग की भुजा (n) है। बचा क्षेत्र किस पहचान से जुड़ता है?

Concept

Why this answer is correct

Exam Tip

भुजा (p+q) वाले वर्ग में \(p^2\) और \(q^2\) के अलावा कौन सा कुल क्षेत्र आता है?

Concept

Why this answer is correct

Exam Tip

यदि वर्ग मॉडल का कुल क्षेत्र \(x^2+2x+1\) है, तो उसकी भुजा क्या होगी?

Concept

Why this answer is correct

Exam Tip

आयाम (a+3) और (a+7) वाले आयत का क्षेत्र मॉडल कौन सा विस्तार देता है?

Concept

Why this answer is correct

Exam Tip

भुजा (10+2) वाले वर्ग का क्षेत्र दृश्य पहचान से कितना होगा?

Concept

Why this answer is correct

Exam Tip

किस आकृति का क्षेत्र सीधे ((u-v)2) दिखाता है?

Concept

Why this answer is correct

Exam Tip

यदि \(x^2+12x+36\) को पूर्ण वर्ग मॉडल से पढ़ा जाए, तो छोटे वर्ग की भुजा क्या होगी?

Concept

Why this answer is correct

Exam Tip

दृश्य मॉडल में ((r+s)(r-s)) के बीच के पद क्यों नहीं बचते?

Concept

Why this answer is correct

Exam Tip

आयत मॉडल में (x(x+9)) का क्षेत्र कौन सा है?

Concept

Why this answer is correct

Exam Tip

भुजा (2x+1) वाले वर्ग के दृश्य मॉडल में कुल क्षेत्र क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(a^2-16\) को अंतर के वर्गों के मॉडल से आयत में बदला जाए, तो आयाम क्या होंगे?

Concept

Why this answer is correct

Exam Tip

भुजा (x-5) वाले वर्ग के मॉडल में अंतिम छोटा वर्ग किस क्षेत्र का होगा?

Concept

Why this answer is correct

Exam Tip

किस दृश्य मॉडल में \(a^2+2ab+b^2\) के चार क्षेत्र भाग साफ दिखाई देते हैं?

Concept

Why this answer is correct

Exam Tip

यदि आयत मॉडल में भाग \(x^2\), (4x), (5x) और (20) हैं, तो बाहरी आयाम क्या हो सकते हैं?

Concept

Why this answer is correct

Exam Tip

एक विद्यार्थी ((x+3)2) को \(x^2+9\) लिखता है। दृश्य मॉडल के अनुसार क्या छूट गया?

Concept

Why this answer is correct

किस आकृति का क्षेत्र सीधे ((u-v)²) दिखाता है?

एक विद्यार्थी ((x+3)²) को \(x^2+9\) लिखता है। दृश्य मॉडल के अनुसार क्या छूट गया?