Class 9 Mathematics - Exploring Algebraic Identities - Factorisation Expert Quiz

Mathematics Exploring Algebraic Identities Factorisation Expert Class 9 Level 68

Level 68 • 8/50 questions • 25 seconds per question.

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Question 1/8 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

यदि वर्गाकार मॉडल में कुल क्षेत्रफल \(x^2+12x+36\) दिख रहा है तो उस वर्ग की भुजा कौन सी होगी?

If a square model shows total area \(x^2+12x+36\), what is the side of that square?

Explanation opens after your attempt
Correct Answer

B. (x+6)

Step 1

Concept

Here (36) is \(6^2\) and (12x) is \(2\cdot6\cdot x\). Exam tip: find the added width from the constant square.

Step 2

Why this answer is correct

The correct answer is B. (x+6). Here (36) is \(6^2\) and (12x) is \(2\cdot6\cdot x\). Exam tip: find the added width from the constant square.

Step 3

Exam Tip

(36) को \(6^2\) और (12x) को \(2\cdot6\cdot x\) माना जाता है। परीक्षा में स्थिर वर्ग से जोड़ी गई चौड़ाई निकालें।

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Question 2/8 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक टाइल मॉडल \(x^2+11x+30\) को आयत के रूप में व्यवस्थित करता है। यदि एक ओर (x+5) है तो दूसरी ओर कौन सी होगी?

A tile model arranges \(x^2+11x+30\) as a rectangle. If one side is (x+5), what will be the other side?

Explanation opens after your attempt
Correct Answer

B. (x+6)

Step 1

Concept

Because (5+6=11) and \(5\cdot6=30\). Exam tip: match both sum and product in a rectangle model.

Step 2

Why this answer is correct

The correct answer is B. (x+6). Because (5+6=11) and \(5\cdot6=30\). Exam tip: match both sum and product in a rectangle model.

Step 3

Exam Tip

क्योंकि (5+6=11) और \(5\cdot6=30\) है। परीक्षा में आयत मॉडल में योग और गुणनफल दोनों मिलाएं।

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Question 3/8 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक आयत को \(x^2\), (5x), (7x), (35) भागों में बांटा गया है। आयत की संभावित भुजाएं क्या हैं?

A rectangle is divided into parts \(x^2\), (5x), (7x), and (35). What are the possible sides of the rectangle?

Explanation opens after your attempt
Correct Answer

B. (x+5) और (x+7)(x+5) and (x+7)

Step 1

Concept

The parts (5x) and (7x), with corner (35), show constant sides (5) and (7). Exam tip: the corner product reveals the constant side lengths.

Step 2

Why this answer is correct

The correct answer is B. (x+5) और (x+7) / (x+5) and (x+7). The parts (5x) and (7x), with corner (35), show constant sides (5) and (7). Exam tip: the corner product reveals the constant side lengths.

Step 3

Exam Tip

भाग (5x) और (7x) तथा कोना (35) भुजाओं (5) और (7) को दिखाते हैं। परीक्षा में कोने का गुणनफल भुजाओं की स्थिर लंबाइयां बताता है।

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Question 4/8 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

यदि \(x^2+9x+20\) का टाइल मॉडल पूरा आयत बनाता है तो कौन सी व्यवस्था सही है?

If the tile model of \(x^2+9x+20\) forms a complete rectangle, which arrangement is correct?

Explanation opens after your attempt
Correct Answer

A. भुजाएं (x+4) और (x+5)Sides (x+4) and (x+5)

Step 1

Concept

Since (4+5=9) and \(4\cdot5=20\), the rectangle is complete. Exam tip: verify both conditions together.

Step 2

Why this answer is correct

The correct answer is A. भुजाएं (x+4) और (x+5) / Sides (x+4) and (x+5). Since (4+5=9) and \(4\cdot5=20\), the rectangle is complete. Exam tip: verify both conditions together.

Step 3

Exam Tip

(4+5=9) और \(4\cdot5=20\) है इसलिए आयत पूरा बनता है। परीक्षा में दोनों शर्तों को साथ जांचें।

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Question 5/8 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक दृश्य मॉडल में \(x^2-49\) को आयत में बदलना है। कौन सी कटाई सबसे उपयोगी होगी?

A visual model must rearrange \(x^2-49\) into a rectangle. Which cut is most useful?

Explanation opens after your attempt
Correct Answer

A. भुजा (7) वाला वर्ग हटानाRemoving a square of side (7)

Step 1

Concept

Since \(49=7^2\), a square of side (7) is removed. Exam tip: identify the square root of the constant square.

Step 2

Why this answer is correct

The correct answer is A. भुजा (7) वाला वर्ग हटाना / Removing a square of side (7). Since \(49=7^2\), a square of side (7) is removed. Exam tip: identify the square root of the constant square.

Step 3

Exam Tip

\(49=7^2\) है इसलिए भुजा (7) का वर्ग हटता है। परीक्षा में स्थिर वर्ग का वर्गमूल पहचानें।

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Question 6/8 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक टाइल मॉडल \(x^2+px+48\) का आयत बनाता है जिसकी स्थिर भुजाएं (6) और (8) हैं। (p) कितना होगा?

A tile model forms a rectangle for \(x^2+px+48\) whose constant side parts are (6) and (8). What is (p)?

Explanation opens after your attempt
Correct Answer

A. (14)

Step 1

Concept

The middle term is (6x+8x=14x), so (p=14). Exam tip: the sum of constant side parts gives the middle coefficient.

Step 2

Why this answer is correct

The correct answer is A. (14). The middle term is (6x+8x=14x), so (p=14). Exam tip: the sum of constant side parts gives the middle coefficient.

Step 3

Exam Tip

मध्य पद (6x+8x=14x) है इसलिए (p=14) होगा। परीक्षा में स्थिर भुजाओं का योग मध्य गुणांक देता है।

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Question 7/8 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

कौन सा दृश्य मॉडल \(9x^2-1\) को सही ढंग से दिखाता है?

Which visual model correctly represents \(9x^2-1\)?

Explanation opens after your attempt
Correct Answer

A. भुजा (3x) वाले वर्ग से भुजा (1) वाला वर्ग हटानाRemoving a square of side (1) from a square of side (3x)

Step 1

Concept

Here (9x-2=(3x)2) and \(1=1^2\), so it is a difference of squares. Exam tip: view both terms as perfect squares.

Step 2

Why this answer is correct

The correct answer is A. भुजा (3x) वाले वर्ग से भुजा (1) वाला वर्ग हटाना / Removing a square of side (1) from a square of side (3x). Here (9x-2=(3x)2) and \(1=1^2\), so it is a difference of squares. Exam tip: view both terms as perfect squares.

Step 3

Exam Tip

(9x-2=(3x)2) और \(1=1^2\) है इसलिए यह वर्गों का अंतर है। परीक्षा में दोनों पदों को पूर्ण वर्ग के रूप में देखें।

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Question 8/8 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक मॉडल में \(x^2+15x+56\) को आयत के रूप में दिखाया गया है। कौन सा जोड़ा रैखिक पट्टियों को सही बनाता है?

A model shows \(x^2+15x+56\) as a rectangle. Which pair correctly forms the linear strips?

Explanation opens after your attempt
Correct Answer

A. (7x) और (8x)(7x) and (8x)

Step 1

Concept

Since (7+8=15) and \(7\cdot8=56\), these strips are correct. Exam tip: match both product and sum.

Step 2

Why this answer is correct

The correct answer is A. (7x) और (8x) / (7x) and (8x). Since (7+8=15) and \(7\cdot8=56\), these strips are correct. Exam tip: match both product and sum.

Step 3

Exam Tip

(7+8=15) और \(7\cdot8=56\) है इसलिए यही पट्टियां सही हैं। परीक्षा में गुणनफल और योग दोनों मिलाएं।

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