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visual algebra MCQ Questions for Class 9

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37 questions tagged with visual algebra.

Question 1/37 Medium Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

यदि आयत मॉडल की भुजाएं (x-3) और (x+9) हैं तो कुल क्षेत्रफल क्या होगा?

If the sides of a rectangle model are (x-3) and (x+9), what will be the total area?

Explanation opens after your attempt
Correct Answer

A. \(x^2+6x-27\)correct signed product

Step 1

Concept

The middle strips are (9x) and (-3x), whose sum is (6x). In exams subtract the negative strip.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+6x-27\) / correct signed product. The middle strips are (9x) and (-3x), whose sum is (6x). In exams subtract the negative strip.

Step 3

Exam Tip

मध्य पट्टियां (9x) और (-3x) हैं, जिनका योग (6x) है। परीक्षा में ऋणात्मक पट्टी को घटाएं।

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Question 2/37 Medium Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक टाइल मॉडल में \(x^2\), (-4x), (7x), और (-28) हैं। कुल क्षेत्रफल क्या है?

A tile model has \(x^2\), (-4x), (7x), and (-28). What is the total area?

Explanation opens after your attempt
Correct Answer

A. \(x^2+3x-28\)correct signed sum

Step 1

Concept

The middle term is (-4x+7x=3x), and the corner remains (-28). In exams add with signs.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+3x-28\) / correct signed sum. The middle term is (-4x+7x=3x), and the corner remains (-28). In exams add with signs.

Step 3

Exam Tip

मध्य पद (-4x+7x=3x) है और कोना (-28) रहता है। परीक्षा में चिन्ह सहित जोड़ करें।

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Question 3/37 Medium Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

यदि एक आयत का क्षेत्रफल मॉडल \(x^2+10x+21\) है तो कौन-सी भुजाएं सही होंगी?

If a rectangle area model is \(x^2+10x+21\), which sides will be correct?

Explanation opens after your attempt
Correct Answer

B. (x+3) और (x+7)correct factors

Step 1

Concept

Since (3+7=10) and \(3\cdot7=21\), the sides are (x+3) and (x+7). In exams check both sum and product.

Step 2

Why this answer is correct

The correct answer is B. (x+3) और (x+7) / correct factors. Since (3+7=10) and \(3\cdot7=21\), the sides are (x+3) and (x+7). In exams check both sum and product.

Step 3

Exam Tip

(3+7=10) और \(3\cdot7=21\), इसलिए भुजाएं (x+3) और (x+7) हैं। परीक्षा में योग और गुणनफल दोनों देखें।

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Question 4/37 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 73

यदि भुजा (g-1) वाले वर्ग का मॉडल बने, तो कुल क्षेत्रफल क्या होगा?

If a model of a square with side (g-1) is made, what will be the total area?

Explanation opens after your attempt
Correct Answer

C. \(g^2-2g+1\)

Step 1

Concept

((g-1)2=g-2-2g+1). Exam tip: remember the two removed strips of (1).

Step 2

Why this answer is correct

The correct answer is C. \(g^2-2g+1\). ((g-1)2=g-2-2g+1). Exam tip: remember the two removed strips of (1).

Step 3

Exam Tip

((g-1)2=g-2-2g+1) होता है। परीक्षा में (1) की दो घटाई गई पट्टियाँ याद रखें।

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Question 5/37 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 73

एक आयत में लंबाई (2a+1) और चौड़ाई (a) है। क्षेत्रफल मॉडल का विस्तार क्या होगा?

A rectangle has length (2a+1) and breadth (a). What is the expansion of its area model?

Explanation opens after your attempt
Correct Answer

A. \(2a^2+a\)

Step 1

Concept

(a(2a+1)=2a-2+a). Exam tip: multiply one side by both parts of the other side.

Step 2

Why this answer is correct

The correct answer is A. \(2a^2+a\). (a(2a+1)=2a-2+a). Exam tip: multiply one side by both parts of the other side.

Step 3

Exam Tip

(a(2a+1)=2a-2+a) होता है। परीक्षा में एक भुजा को दोनों भागों से गुणा करें।

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Question 6/37 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 73

यदि आयत मॉडल की एक भुजा (t) और दूसरी (t+7) है, तो क्षेत्रफल क्या होगा?

If one side of a rectangle model is (t) and the other is (t+7), what will be the area?

Explanation opens after your attempt
Correct Answer

A. \(t^2+7t\)

Step 1

Concept

The area is (t(t+7)=t-2+7t). Exam tip: multiply both sides of the rectangle.

Step 2

Why this answer is correct

The correct answer is A. \(t^2+7t\). The area is (t(t+7)=t-2+7t). Exam tip: multiply both sides of the rectangle.

Step 3

Exam Tip

क्षेत्रफल (t(t+7)=t-2+7t) है। परीक्षा में आयत की दोनों भुजाएँ गुणा करें।

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Question 7/37 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 73

क्षेत्रफल चित्र में भुजा (a+1) वाले वर्ग को चार भागों में बाँटा गया है। कुल क्षेत्रफल कौन सा होगा?

In an area diagram, a square of side (a+1) is divided into four parts. What will be the total area?

Explanation opens after your attempt
Correct Answer

A. \(a^2+2a+1\)

Step 1

Concept

The side is (a+1), so the area is ((a+1)2). Exam tip: check the sum of all four parts.

Step 2

Why this answer is correct

The correct answer is A. \(a^2+2a+1\). The side is (a+1), so the area is ((a+1)2). Exam tip: check the sum of all four parts.

Step 3

Exam Tip

भुजा (a+1) है इसलिए क्षेत्रफल ((a+1)2) होगा। परीक्षा में चारों भागों का योग देखें।

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Question 8/37 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 9/37 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 10/37 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 71

दृश्य मॉडल में \(x^2+5x+6\) किस आयत से बन सकता है?

In a visual model, \(x^2+5x+6\) can be formed by which rectangle?

Explanation opens after your attempt
Correct Answer

B. ((x+2)(x+3))

Step 1

Concept

((x+2)(x+3)=x-2+3x+2x+6=x-2+5x+6). Exam tip: check that the two factors add to (5) and multiply to (6).

Step 2

Why this answer is correct

The correct answer is B. ((x+2)(x+3)). ((x+2)(x+3)=x-2+3x+2x+6=x-2+5x+6). Exam tip: check that the two factors add to (5) and multiply to (6).

Step 3

Exam Tip

((x+2)(x+3)=x-2+3x+2x+6=x-2+5x+6) है। परीक्षा में दो कारकों का योग (5) और गुणन (6) देखें।

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Question 11/37 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 71

किस आयत मॉडल से \(x^2+6x+8\) मिलता है?

Which rectangle model gives \(x^2+6x+8\)?

Explanation opens after your attempt
Correct Answer

B. ((x+2)(x+4))

Step 1

Concept

((x+2)(x+4)=x-2+4x+2x+8=x-2+6x+8). Exam tip: look at the factors of the constant term.

Step 2

Why this answer is correct

The correct answer is B. ((x+2)(x+4)). ((x+2)(x+4)=x-2+4x+2x+8=x-2+6x+8). Exam tip: look at the factors of the constant term.

Step 3

Exam Tip

((x+2)(x+4)=x-2+4x+2x+8=x-2+6x+8) है। परीक्षा में स्थिर पद के कारक देखें।

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Question 12/37 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 71

यदि क्षेत्र मॉडल में \(x^2+8x+16\) दिखता है तो यह किसका पूर्ण वर्ग है?

If an area model shows \(x^2+8x+16\), whose perfect square is it?

Explanation opens after your attempt
Correct Answer

B. ((x+4)2)

Step 1

Concept

\(16=4^2\) and \(8x=2\cdot4x\). Therefore it is ((x+4)2).

Step 2

Why this answer is correct

The correct answer is B. ((x+4)2). \(16=4^2\) and \(8x=2\cdot4x\). Therefore it is ((x+4)2).

Step 3

Exam Tip

\(16=4^2\) और \(8x=2\cdot4x\) है। इसलिए यह ((x+4)2) है।

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Question 13/37 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 71

एक वर्ग मॉडल में भुजा (x+1) है। इसका क्षेत्रफल किसके बराबर होगा?

In a square model, the side is (x+1). What will its area be equal to?

Explanation opens after your attempt
Correct Answer

B. \(x^2+2x+1\)

Step 1

Concept

The area is ((x+1)2), and the expansion is \(x^2+2x+1\). Exam tip: remember to add the two (x)-rectangles.

Step 2

Why this answer is correct

The correct answer is B. \(x^2+2x+1\). The area is ((x+1)2), and the expansion is \(x^2+2x+1\). Exam tip: remember to add the two (x)-rectangles.

Step 3

Exam Tip

वर्ग का क्षेत्रफल ((x+1)2) है और विस्तार \(x^2+2x+1\) मिलता है। परीक्षा में दो (x) आयतों को जोड़ना याद रखें।

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Question 14/37 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक टाइल मॉडल में \(x^2+6x+9\) और \(x^2+8x+16\) दो अलग पूर्ण वर्ग हैं। पहले वर्ग की भुजा दूसरे से कितनी कम है?

In a tile model, \(x^2+6x+9\) and \(x^2+8x+16\) are two separate perfect squares. By how much is the side of the first square less than the second?

Explanation opens after your attempt
Correct Answer

A. (1)

Step 1

Concept

The first side is (x+3) and the second is (x+4), so the difference is (1). Exam tip: find the side before comparing areas.

Step 2

Why this answer is correct

The correct answer is A. (1). The first side is (x+3) and the second is (x+4), so the difference is (1). Exam tip: find the side before comparing areas.

Step 3

Exam Tip

पहली भुजा (x+3) और दूसरी (x+4) है इसलिए अंतर (1) है। परीक्षा में क्षेत्रफल से पहले भुजा निकालें।

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Question 15/37 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक वर्गाकार मॉडल में क्षेत्रफल \(16p^2-40pq+25q^2\) है। यह किस भुजा वाले वर्ग को दिखाता है?

A square model has area \(16p^2-40pq+25q^2\). It represents a square with which side?

Explanation opens after your attempt
Correct Answer

C. (4p-5q)

Step 1

Concept

Here (16p-2=(4p)2) and (25q-2=(5q)2), and the middle term is negative. Exam tip: check both signs and square roots.

Step 2

Why this answer is correct

The correct answer is C. (4p-5q). Here (16p-2=(4p)2) and (25q-2=(5q)2), and the middle term is negative. Exam tip: check both signs and square roots.

Step 3

Exam Tip

(16p-2=(4p)2) और (25q-2=(5q)2) हैं तथा मध्य पद ऋण है। परीक्षा में संकेत और वर्गमूल दोनों जांचें।

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Question 16/37 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

आयताकार मॉडल में \(x^2+13x+36\) को दो रैखिक भागों में बांटना है। कौन सा जोड़ा सही है?

In a rectangle model, \(x^2+13x+36\) must be split into two linear parts. Which pair is correct?

Explanation opens after your attempt
Correct Answer

A. (4x) और (9x)(4x) and (9x)

Step 1

Concept

Since (4+9=13) and \(4\cdot9=36\), the strips are (4x) and (9x). Exam tip: find factors of the constant term.

Step 2

Why this answer is correct

The correct answer is A. (4x) और (9x) / (4x) and (9x). Since (4+9=13) and \(4\cdot9=36\), the strips are (4x) and (9x). Exam tip: find factors of the constant term.

Step 3

Exam Tip

(4+9=13) और \(4\cdot9=36\) है इसलिए पट्टियां (4x) और (9x) होंगी। परीक्षा में स्थिर पद के गुणनखंड खोजें।

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Question 17/37 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 66

किस दृश्य मॉडल में \(a^2+2ab+b^2-c^2\) को दो आयत भुजाओं में बदला जा सकता है?

In which visual model can \(a^2+2ab+b^2-c^2\) be changed into two rectangle sides?

Explanation opens after your attempt
Correct Answer

A. ((a+b+c)(a+b-c))difference after grouping

Step 1

Concept

First (a-2+2ab+b-2=(a+b)2), then \(c^2\) is subtracted. In exams group first and then apply difference of squares.

Step 2

Why this answer is correct

The correct answer is A. ((a+b+c)(a+b-c)) / difference after grouping. First (a-2+2ab+b-2=(a+b)2), then \(c^2\) is subtracted. In exams group first and then apply difference of squares.

Step 3

Exam Tip

पहले (a-2+2ab+b-2=(a+b)2), फिर \(c^2\) घटता है। परीक्षा में समूह बनाकर वर्गों का अंतर लगाएं।

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Question 18/37 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 66

एक दृश्य ग्रिड \(x^2-xy-6y^2\) बनाता है। कौन-सी भुजाएं सही हैं?

A visual grid forms \(x^2-xy-6y^2\). Which sides are correct?

Explanation opens after your attempt
Correct Answer

D. (x+2y) और (x-3y)signed sides

Step 1

Concept

Here (2y+(-3y)=-y) and (2y\cdot(-3y)=-6y-2). In exams add negative tiles carefully.

Step 2

Why this answer is correct

The correct answer is D. (x+2y) और (x-3y) / signed sides. Here (2y+(-3y)=-y) and (2y\cdot(-3y)=-6y-2). In exams add negative tiles carefully.

Step 3

Exam Tip

(2y+(-3y)=-y) और (2y\cdot(-3y)=-6y-2) है। परीक्षा में ऋणात्मक टाइलों का योग सावधानी से करें।

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Question 19/37 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 66

एक घटाव मॉडल \(16x^2-40xy+25y^2\) दिखाता है। यह किस भुजा वाले वर्ग का क्षेत्रफल है?

A subtraction model shows \(16x^2-40xy+25y^2\). It is the area of a square with which side?

Explanation opens after your attempt
Correct Answer

B. (4x-5y)reduced side

Step 1

Concept

(16x-2=(4x)2), (25y-2=(5y)2), and the middle term is \(-2\cdot4x\cdot5y\). In exams check all three parts of a perfect square.

Step 2

Why this answer is correct

The correct answer is B. (4x-5y) / reduced side. (16x-2=(4x)2), (25y-2=(5y)2), and the middle term is \(-2\cdot4x\cdot5y\). In exams check all three parts of a perfect square.

Step 3

Exam Tip

(16x-2=(4x)2), (25y-2=(5y)2), और मध्य पद \(-2\cdot4x\cdot5y\) है। परीक्षा में पूर्ण वर्ग के तीनों भाग जांचें।

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Question 20/37 Hard Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 67

एक आयत मॉडल में ((4x+3)(x+2)) के सभी भाग जोड़ने पर क्या मिलेगा?

What is obtained by adding all parts in the rectangle model of ((4x+3)(x+2))?

Explanation opens after your attempt
Correct Answer

A. \(4x^2+11x+6\)

Step 1

Concept

The parts are \(4x^2\), (8x), (3x), and (6), giving \(4x^2+11x+6\). Exam tip: add like (x)-terms.

Step 2

Why this answer is correct

The correct answer is A. \(4x^2+11x+6\). The parts are \(4x^2\), (8x), (3x), and (6), giving \(4x^2+11x+6\). Exam tip: add like (x)-terms.

Step 3

Exam Tip

भाग \(4x^2\), (8x), (3x) और (6) हैं, जिनसे \(4x^2+11x+6\) मिलता है। परीक्षा में समान (x) पद जोड़ें।

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Question 21/37 Hard Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 66

यदि ((x+8)2) के मॉडल से \(x^2+16x\) पहले से बना है, तो पूर्ण वर्ग पूरा करने के लिए कितनी स्थिर टाइलें चाहिए?

If \(x^2+16x\) is already made from the model of ((x+8)2), how many constant tiles are needed to complete the square?

Explanation opens after your attempt
Correct Answer

D. (64)

Step 1

Concept

((x+8)2=x-2+16x+64). Therefore (64) constant tiles are needed.

Step 2

Why this answer is correct

The correct answer is D. (64). ((x+8)2=x-2+16x+64). Therefore (64) constant tiles are needed.

Step 3

Exam Tip

((x+8)2=x-2+16x+64) है। इसलिए (64) स्थिर टाइलें चाहिए।

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Question 22/37 Medium Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 67

आयत मॉडल में \(x^2+2x-15\) को दो बाइनोमियल भुजाओं से दिखाना है। कौन सी भुजाएं सही हैं?

In a rectangle model \(x^2+2x-15\) must be shown using two binomial sides. Which sides are correct?

Explanation opens after your attempt
Correct Answer

A. (x+5) और (x-3)(x+5) and (x-3)

Step 1

Concept

\(5\cdot -3=-15\) and (5+(-3)=2) so the sides are (x+5) and (x-3). Exam tip: check both product and sum.

Step 2

Why this answer is correct

The correct answer is A. (x+5) और (x-3) / (x+5) and (x-3). \(5\cdot -3=-15\) and (5+(-3)=2) so the sides are (x+5) and (x-3). Exam tip: check both product and sum.

Step 3

Exam Tip

\(5\cdot -3=-15\) और (5+(-3)=2) इसलिए भुजाएं (x+5) और (x-3) हैं। परीक्षा में गुणनफल और योग दोनों जांचें।

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Question 23/37 Medium Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 67

एक आयत मॉडल में (x+9) और (x-1) भुजाएं हैं। कौन सा क्षेत्रफल सही है?

A rectangle model has sides (x+9) and (x-1). Which area is correct?

Explanation opens after your attempt
Correct Answer

C. \(x^2+8x-9\)

Step 1

Concept

((x+9)(x-1)=x-2-x+9x-9=x-2+8x-9). Exam tip: keep positive and negative strips separate.

Step 2

Why this answer is correct

The correct answer is C. \(x^2+8x-9\). ((x+9)(x-1)=x-2-x+9x-9=x-2+8x-9). Exam tip: keep positive and negative strips separate.

Step 3

Exam Tip

((x+9)(x-1)=x-2-x+9x-9=x-2+8x-9) है। परीक्षा में धन और ऋण पट्टियों को अलग रखें।

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Question 24/37 Medium Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 67

एक आयत मॉडल \(4x^2-9\) क्षेत्रफल दिखाता है। इसे अंतर के वर्ग मॉडल से कौन सा गुणनखंड रूप मिलेगा?

A rectangle model shows area \(4x^2-9\). Which factor form is obtained using the difference of squares model?

Explanation opens after your attempt
Correct Answer

C. ((2x-3)(2x+3))

Step 1

Concept

(4x-2=(2x)2) and \(9=3^2\) so the form is ((2x-3)(2x+3)). Exam tip: rewrite both terms as squares.

Step 2

Why this answer is correct

The correct answer is C. ((2x-3)(2x+3)). (4x-2=(2x)2) and \(9=3^2\) so the form is ((2x-3)(2x+3)). Exam tip: rewrite both terms as squares.

Step 3

Exam Tip

(4x-2=(2x)2) और \(9=3^2\) इसलिए रूप ((2x-3)(2x+3)) है। परीक्षा में दोनों पदों को वर्ग बनाकर देखें।

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Question 25/37 Medium Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 67

आयत मॉडल में लंबाई (x+2) और चौड़ाई (x+7) है। चार भागों का योग कौन सा होगा?

In a rectangle model the length is (x+2) and the breadth is (x+7). What is the sum of the four parts?

Explanation opens after your attempt
Correct Answer

A. \(x^2+9x+14\)

Step 1

Concept

The parts are \(x^2\) (2x) (7x) and (14) so the total is \(x^2+9x+14\). Exam tip: add the cross rectangle areas.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+9x+14\). The parts are \(x^2\) (2x) (7x) and (14) so the total is \(x^2+9x+14\). Exam tip: add the cross rectangle areas.

Step 3

Exam Tip

भाग \(x^2\) (2x) (7x) और (14) हैं इसलिए कुल \(x^2+9x+14\) है। परीक्षा में क्रॉस आयतों के क्षेत्रफल जोड़ें।

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Question 26/37 Medium Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 67

चित्र मॉडल में (m) भुजा वाले वर्ग के भीतर (n) भुजा की दो पट्टियां घटाई गईं और कोने का \(n^2\) भाग वापस जोड़ा गया। पहचान कौन सी बनेगी?

In a visual model two strips of width (n) are subtracted from a square of side (m) and the corner \(n^2\) part is added back. Which identity is formed?

Explanation opens after your attempt
Correct Answer

A. ((m-n)2=m-2-2mn+n-2)

Step 1

Concept

The corner is subtracted twice in the two (mn) strips so \(n^2\) is added back. Exam tip: list removed and added parts separately.

Step 2

Why this answer is correct

The correct answer is A. ((m-n)2=m-2-2mn+n-2). The corner is subtracted twice in the two (mn) strips so \(n^2\) is added back. Exam tip: list removed and added parts separately.

Step 3

Exam Tip

घटाए गए दो (mn) भागों में कोना दो बार घटता है इसलिए \(n^2\) जोड़ा जाता है। परीक्षा में हटाए और जोड़े गए भाग अलग लिखें।

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Question 27/37 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 69

यदि आयत की भुजाएँ (a+b) और (c) हैं, तो क्षेत्रफल मॉडल में दो भाग कौन से होंगे?

If the sides of a rectangle are (a+b) and (c), what two parts appear in the area model?

Explanation opens after your attempt
Correct Answer

A. (ac) और (bc)(ac) and (bc)

Step 1

Concept

(c(a+b)=ac+bc). Exam tip: split one side into two parts and add areas.

Step 2

Why this answer is correct

The correct answer is A. (ac) और (bc) / (ac) and (bc). (c(a+b)=ac+bc). Exam tip: split one side into two parts and add areas.

Step 3

Exam Tip

(c(a+b)=ac+bc) होता है। परीक्षा में एक भुजा को दो भागों में बाँटकर क्षेत्रफल जोड़ें।

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Question 28/37 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 69

आयत मॉडल में लंबाई (x+6) और चौड़ाई (x) है। क्षेत्रफल कौन सा होगा?

In a rectangle model, the length is (x+6) and the breadth is (x). What is the area?

Explanation opens after your attempt
Correct Answer

D. \(x^2+6x\)

Step 1

Concept

The area is (x(x+6)=x-2+6x). Exam tip: use length times breadth for rectangle area.

Step 2

Why this answer is correct

The correct answer is D. \(x^2+6x\). The area is (x(x+6)=x-2+6x). Exam tip: use length times breadth for rectangle area.

Step 3

Exam Tip

क्षेत्रफल (x(x+6)=x-2+6x) है। परीक्षा में आयत का क्षेत्रफल लंबाई गुणा चौड़ाई लें।

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Question 29/37 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 69

आयत मॉडल में ((p+2)(p+5)) के कोने वाले छोटे आयत का क्षेत्रफल क्या है?

In the rectangle model of ((p+2)(p+5)), what is the area of the small corner rectangle?

Explanation opens after your attempt
Correct Answer

B. (10)

Step 1

Concept

The small corner area is \(2\cdot 5=10\). Exam tip: multiply the numerical parts.

Step 2

Why this answer is correct

The correct answer is B. (10). The small corner area is \(2\cdot 5=10\). Exam tip: multiply the numerical parts.

Step 3

Exam Tip

छोटे कोने का क्षेत्रफल \(2\cdot 5=10\) है। परीक्षा में संख्यात्मक भागों का गुणन करें।

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Question 30/37 Easy Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 69

एक क्षेत्रफल चित्र में बड़े वर्ग से (b) चौड़ाई की पट्टी हटाई गई है। यह कौन सी पहचान दिखाता है?

In an area diagram, a strip of width (b) is removed from a big square. Which identity does this show?

Explanation opens after your attempt
Correct Answer

C. ((a-b)2=a-2-2ab+b-2)

Step 1

Concept

In a removal model, the remaining side is (a-b). Exam tip: connect the subtraction square with ((a-b)2).

Step 2

Why this answer is correct

The correct answer is C. ((a-b)2=a-2-2ab+b-2). In a removal model, the remaining side is (a-b). Exam tip: connect the subtraction square with ((a-b)2).

Step 3

Exam Tip

हटाने वाले मॉडल में बची भुजा (a-b) होती है। परीक्षा में घटाव वाले वर्ग को ((a-b)2) से जोड़ें।

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