Class 9 Mathematics Expert Quiz

Mathematics Expert Class 9 Level 68

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Question 1/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक वर्ग का दृश्य मॉडल पहले भुजा (a) वाला था। उसमें दाईं ओर चौड़ाई (b) की पट्टी और नीचे चौड़ाई (b) की पट्टी जोड़कर कोने में छोटा वर्ग बनाया गया। कुल क्षेत्रफल किस पहचान को दिखाता है?

A square visual model first has side (a). A strip of width (b) is added on the right and another strip of width (b) at the bottom with a small corner square. Which identity does the total area show?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

The two equal rectangles have area (ab) and the small square has area \(b^2\). Exam tip: split the big square into smaller regions before writing the identity.

Step 2

Why this answer is correct

The correct answer is A. (a-2+2ab+b-2=(a+b)2). The two equal rectangles have area (ab) and the small square has area \(b^2\). Exam tip: split the big square into smaller regions before writing the identity.

Step 3

Exam Tip

दो समान आयतों का क्षेत्रफल (ab) और छोटे वर्ग का क्षेत्रफल \(b^2\) है। परीक्षा में बड़े वर्ग को छोटे भागों में बांटकर पहचान लिखें।

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Question 2/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

भुजा (p) वाले बड़े वर्ग से ऊपर और दाईं ओर चौड़ाई (q) की दो पट्टियां हटाई जाती हैं। कोने का वर्ग \(q^2\) दो बार हटने से वापस जोड़ा जाता है। शेष क्षेत्रफल क्या होगा?

From a large square of side (p), two strips of width (q) are removed from the top and the right. The corner square \(q^2\) is added back because it was removed twice. What is the remaining area?

Explanation opens after your attempt
Correct Answer

A. \(p^2-2pq+q^2\)

Step 1

Concept

After subtracting two strips the common corner must be added back. Exam tip: check overlap when subtracting areas.

Step 2

Why this answer is correct

The correct answer is A. \(p^2-2pq+q^2\). After subtracting two strips the common corner must be added back. Exam tip: check overlap when subtracting areas.

Step 3

Exam Tip

दो पट्टियां घटाने के बाद साझा कोना फिर जोड़ना पड़ता है। परीक्षा में घटाए गए भागों की पुनरावृत्ति जांचें।

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Question 3/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक आयत की लंबाई (x+7) और चौड़ाई (x+3) है। इसे \(x^2\) वर्ग टाइलों और रैखिक पट्टियों में बांटने पर मध्य पद का गुणांक कितना बनेगा?

A rectangle has length (x+7) and width (x+3). When it is split into \(x^2\) square tiles and linear strips, what will be the coefficient of the middle term?

Explanation opens after your attempt
Correct Answer

A. (10)

Step 1

Concept

The total strip area is (7x+3x=10x). Exam tip: in ((x+a)(x+b)), the middle coefficient is (a+b).

Step 2

Why this answer is correct

The correct answer is A. (10). The total strip area is (7x+3x=10x). Exam tip: in ((x+a)(x+b)), the middle coefficient is (a+b).

Step 3

Exam Tip

पट्टियों का कुल क्षेत्रफल (7x+3x=10x) है। परीक्षा में ((x+a)(x+b)) में मध्य गुणांक (a+b) लें।

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Question 4/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

भुजा (m+n) वाले वर्ग को चार भागों में बांटा गया है। दो भागों के क्षेत्रफल \(m^2\) और \(n^2\) हैं। बाकी दो समान आयतों का संयुक्त क्षेत्रफल कौन सा है?

A square of side (m+n) is divided into four parts. Two parts have areas \(m^2\) and \(n^2\). What is the combined area of the remaining two equal rectangles?

Explanation opens after your attempt
Correct Answer

B. (2mn)

Step 1

Concept

Each rectangle has area (mn), so together they give (2mn). Exam tip: do not forget the number of equal rectangles.

Step 2

Why this answer is correct

The correct answer is B. (2mn). Each rectangle has area (mn), so together they give (2mn). Exam tip: do not forget the number of equal rectangles.

Step 3

Exam Tip

दोनों आयतों में प्रत्येक का क्षेत्रफल (mn) है इसलिए कुल (2mn) होगा। परीक्षा में समान आयतों की संख्या न भूलें।

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Question 5/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

दृश्य मॉडल में \(r^2\) क्षेत्रफल वाले वर्ग से \(s^2\) क्षेत्रफल वाला छोटा वर्ग हटाया गया। बचे हुए एल आकार को काटकर एक आयत बनाया गया। उस आयत की भुजाएं क्या होंगी?

In a visual model, a small square of area \(s^2\) is removed from a square of area \(r^2\). The remaining L-shape is cut and rearranged into a rectangle. What will be the sides of that rectangle?

Explanation opens after your attempt
Correct Answer

A. (r-s) और (r+s)(r-s) and (r+s)

Step 1

Concept

Rearranging the difference of squares forms the rectangle ((r-s)(r+s)). Exam tip: identify \(r^2-s^2\) as a difference of squares.

Step 2

Why this answer is correct

The correct answer is A. (r-s) और (r+s) / (r-s) and (r+s). Rearranging the difference of squares forms the rectangle ((r-s)(r+s)). Exam tip: identify \(r^2-s^2\) as a difference of squares.

Step 3

Exam Tip

वर्गों के अंतर को पुनर्व्यवस्थित करने पर आयत ((r-s)(r+s)) बनता है। परीक्षा में \(r^2-s^2\) को अंतर के रूप में पहचानें।

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Question 6/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक (x) by (x) वर्ग के साथ चार (x) by (2) पट्टियां और चार (2) by (2) छोटे वर्ग मिलाकर एक बड़ा वर्ग बनता है। बड़े वर्ग की भुजा क्या होगी?

A square (x) by (x), four strips (x) by (2), and four small squares (2) by (2) form one larger square. What is the side of the larger square?

Explanation opens after your attempt
Correct Answer

B. (x+4)

Step 1

Concept

The four small width parts show an increase of (4) along each side. Exam tip: observe the total added width on the edge.

Step 2

Why this answer is correct

The correct answer is B. (x+4). The four small width parts show an increase of (4) along each side. Exam tip: observe the total added width on the edge.

Step 3

Exam Tip

चार छोटी (2) इकाई चौड़ाइयां मिलकर हर दिशा में (4) की वृद्धि दिखाती हैं। परीक्षा में किनारे पर लगी कुल चौड़ाई देखें।

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Question 7/50 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 8/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक वर्ग मॉडल में दो समान आयतों का कुल क्षेत्रफल (18xy) है और कोने का छोटा वर्ग \(81y^2\) है। यदि मुख्य वर्ग \(x^2\) है तो पूर्ण वर्ग क्षेत्रफल क्या है?

In a square model, the combined area of two equal rectangles is (18xy) and the small corner square is \(81y^2\). If the main square is \(x^2\), what is the complete square area?

Explanation opens after your attempt
Correct Answer

A. \(x^2+18xy+81y^2\)

Step 1

Concept

The small square has side (9y) and the two rectangles together give (18xy). Exam tip: the sum of the two rectangles directly gives the middle term.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+18xy+81y^2\). The small square has side (9y) and the two rectangles together give (18xy). Exam tip: the sum of the two rectangles directly gives the middle term.

Step 3

Exam Tip

छोटे वर्ग की भुजा (9y) है और दो आयतों का कुल क्षेत्रफल (18xy) है। परीक्षा में दो आयतों का योग सीधे मध्य पद देता है।

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Question 9/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक दृश्य प्रमाण में (a+b+c) भुजा वाले वर्ग को नौ भागों में बांटा गया है। तीन वर्गों के क्षेत्रफल \(a^2\), \(b^2\), \(c^2\) हैं। आयताकार भागों का कुल क्षेत्रफल कौन सा है?

In a visual proof, a square of side (a+b+c) is divided into nine parts. Three square parts have areas \(a^2\), \(b^2\), and \(c^2\). What is the total area of the rectangular parts?

Explanation opens after your attempt
Correct Answer

B. (2ab+2bc+2ca)

Step 1

Concept

Each pair forms two equal rectangles, so the total is (2ab+2bc+2ca). Exam tip: count pairwise rectangles twice in a trinomial square.

Step 2

Why this answer is correct

The correct answer is B. (2ab+2bc+2ca). Each pair forms two equal rectangles, so the total is (2ab+2bc+2ca). Exam tip: count pairwise rectangles twice in a trinomial square.

Step 3

Exam Tip

हर जोड़ी के दो समान आयत बनते हैं इसलिए कुल (2ab+2bc+2ca) होता है। परीक्षा में तीन पदों के वर्ग में जोड़ीदार आयतों को दो बार गिनें।

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Question 10/50 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 11/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक बड़े वर्ग से (4x) और (4x) क्षेत्रफल वाली दो पट्टियां हटाकर (16) क्षेत्रफल का कोना वापस जोड़ा गया। यदि मूल वर्ग \(x^2\) था तो बना क्षेत्रफल किसके बराबर है?

Two strips of areas (4x) and (4x) are removed from a large square and a corner of area (16) is added back. If the original square was \(x^2\), the resulting area equals what?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

Two (4x) strips are subtracted and the common corner (16) is added back. Exam tip: recognize the ((x-4)2) model.

Step 2

Why this answer is correct

The correct answer is B. \(x^2-8x+16\). Two (4x) strips are subtracted and the common corner (16) is added back. Exam tip: recognize the ((x-4)2) model.

Step 3

Exam Tip

दो (4x) पट्टियां घटती हैं और साझा कोना (16) वापस जुड़ता है। परीक्षा में ((x-4)2) मॉडल को पहचानें।

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Question 12/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

भुजा (u+v) वाले वर्ग में \(u^2+v^2\) क्षेत्रफल अलग रंग से दिखाया गया है। शेष दो समान आयतों का क्षेत्रफल जोड़कर कौन सा पद मिलेगा?

In a square of side (u+v), the areas \(u^2+v^2\) are shown in a different color. What term is obtained by adding the areas of the remaining two equal rectangles?

Explanation opens after your attempt
Correct Answer

C. (2uv)

Step 1

Concept

Both remaining rectangles are (u) by (v), so their sum is (2uv). Exam tip: add colored and uncolored parts separately.

Step 2

Why this answer is correct

The correct answer is C. (2uv). Both remaining rectangles are (u) by (v), so their sum is (2uv). Exam tip: add colored and uncolored parts separately.

Step 3

Exam Tip

शेष दोनों आयत (u) by (v) हैं इसलिए योग (2uv) है। परीक्षा में रंगीन भागों और शेष भागों को अलग अलग जोड़ें।

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Question 13/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक आयत मॉडल में लंबाई (2x+3) और चौड़ाई (2x-3) है। यह कौन सा क्षेत्रफल पहचान दिखाता है?

In a rectangle model, the length is (2x+3) and the width is (2x-3). Which area identity does it show?

Explanation opens after your attempt
Correct Answer

B. \(4x^2-9\)

Step 1

Concept

This is ((2x+3)(2x-3)), which gives \(4x^2-9\). Exam tip: connect product of sum and difference with difference of squares.

Step 2

Why this answer is correct

The correct answer is B. \(4x^2-9\). This is ((2x+3)(2x-3)), which gives \(4x^2-9\). Exam tip: connect product of sum and difference with difference of squares.

Step 3

Exam Tip

यह ((2x+3)(2x-3)) है जो \(4x^2-9\) देता है। परीक्षा में योग और अंतर के गुणन को वर्गों के अंतर से जोड़ें।

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Question 14/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक वर्गीय टाइल मॉडल में केंद्रीय वर्ग \(9a^2\), दो समान पट्टियों का कुल क्षेत्रफल (30ab), और छोटा वर्ग \(25b^2\) है। पूरे वर्ग की भुजा क्या है?

In a square tile model, the central square is \(9a^2\), the combined area of two equal strips is (30ab), and the small square is \(25b^2\). What is the side of the whole square?

Explanation opens after your attempt
Correct Answer

A. (3a+5b)

Step 1

Concept

The main square side is (3a) and the small square side is (5b). Exam tip: identify sides using square roots.

Step 2

Why this answer is correct

The correct answer is A. (3a+5b). The main square side is (3a) and the small square side is (5b). Exam tip: identify sides using square roots.

Step 3

Exam Tip

मुख्य वर्ग की भुजा (3a) और छोटे वर्ग की भुजा (5b) है। परीक्षा में वर्गमूल से भुजाएं पहचानें।

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Question 15/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक मॉडल में \(x^2\) वर्ग के दोनों ओर कुल (14x) क्षेत्रफल की पट्टियां जोड़ी गई हैं। वर्ग पूरा करने के लिए कोने में कितना क्षेत्रफल जोड़ना होगा?

In a model, strips of total area (14x) are added on two sides of an \(x^2\) square. How much corner area must be added to complete the square?

Explanation opens after your attempt
Correct Answer

A. (49)

Step 1

Concept

The two strips show width (7) on each side, so the corner is \(7^2=49\). Exam tip: halve the middle coefficient and square it.

Step 2

Why this answer is correct

The correct answer is A. (49). The two strips show width (7) on each side, so the corner is \(7^2=49\). Exam tip: halve the middle coefficient and square it.

Step 3

Exam Tip

दोनों पट्टियों से हर ओर (7) की चौड़ाई मिलती है इसलिए कोना \(7^2=49\) होगा। परीक्षा में मध्य पद को आधा करके वर्ग लें।

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Question 16/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

किस दृश्य व्यवस्था से \(y^2-6y+9\) का वर्ग मॉडल सबसे ठीक बनता है?

Which visual arrangement best forms the square model for \(y^2-6y+9\)?

Explanation opens after your attempt
Correct Answer

A. भुजा (y) वाले वर्ग से दो (3y) पट्टियां हटाकर (9) कोना जोड़नाRemoving two (3y) strips from a square of side (y) and adding the (9) corner

Step 1

Concept

The negative middle term comes from the two removed strips. Exam tip: use the sign to decide addition or subtraction model.

Step 2

Why this answer is correct

The correct answer is A. भुजा (y) वाले वर्ग से दो (3y) पट्टियां हटाकर (9) कोना जोड़ना / Removing two (3y) strips from a square of side (y) and adding the (9) corner. The negative middle term comes from the two removed strips. Exam tip: use the sign to decide addition or subtraction model.

Step 3

Exam Tip

ऋण मध्य पद घटाई गई दो पट्टियों से आता है। परीक्षा में संकेत देखकर जोड़ने या घटाने का मॉडल चुनें।

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Question 17/50 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 18/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

यदि टाइल मॉडल में \(a^2-b^2\) क्षेत्र को आयत में बदलते समय लंबाई (a+b) बनती है तो चौड़ाई क्या होगी?

If the region \(a^2-b^2\) in a tile model is rearranged into a rectangle and its length becomes (a+b), what is its width?

Explanation opens after your attempt
Correct Answer

C. (a-b)

Step 1

Concept

The area is (a-2-b-2=(a+b)(a-b)). Exam tip: get the other side by dividing area by the given side.

Step 2

Why this answer is correct

The correct answer is C. (a-b). The area is (a-2-b-2=(a+b)(a-b)). Exam tip: get the other side by dividing area by the given side.

Step 3

Exam Tip

क्षेत्रफल (a-2-b-2=(a+b)(a-b)) होता है। परीक्षा में आयत की दूसरी भुजा क्षेत्रफल को दी गई भुजा से भाग देकर मिलती है।

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Question 19/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक मॉडल में ((a+b)2) और ((a-b)2) के क्षेत्रफलों का अंतर दिखाया गया है। यह अंतर किसके बराबर होगा?

A model shows the difference between the areas of ((a+b)2) and ((a-b)2). What will this difference equal?

Explanation opens after your attempt
Correct Answer

B. (4ab)

Step 1

Concept

Subtracting the two expansions leaves (4ab). Exam tip: match visual difference with algebraic subtraction.

Step 2

Why this answer is correct

The correct answer is B. (4ab). Subtracting the two expansions leaves (4ab). Exam tip: match visual difference with algebraic subtraction.

Step 3

Exam Tip

दोनों विस्तारों को घटाने पर (4ab) बचता है। परीक्षा में दृश्य अंतर को बीजगणितीय घटाव से मिलाएं।

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Question 20/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक वर्ग मॉडल में ((2x+5)2) दिखाना है। चार भागों के क्षेत्रफल कौन से होंगे?

A square model is to show ((2x+5)2). What will be the areas of the four parts?

Explanation opens after your attempt
Correct Answer

A. \(4x^2\), (10x), (10x), (25)

Step 1

Concept

The side parts are (2x) and (5), so each rectangle is (10x). Exam tip: find each part as length times width.

Step 2

Why this answer is correct

The correct answer is A. \(4x^2\), (10x), (10x), (25). The side parts are (2x) and (5), so each rectangle is (10x). Exam tip: find each part as length times width.

Step 3

Exam Tip

भुजाएं (2x) और (5) हैं इसलिए दो आयतों में प्रत्येक (10x) है। परीक्षा में हर भाग को लंबाई गुणा चौड़ाई से निकालें।

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Question 21/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक दृश्य मॉडल में \(x^2+bx+24\) आयत के रूप में बना है जिसकी भुजाएं (x+3) और (x+8) हैं। (b) का मान क्या होगा?

A visual model forms \(x^2+bx+24\) as a rectangle with sides (x+3) and (x+8). What is the value of (b)?

Explanation opens after your attempt
Correct Answer

A. (11)

Step 1

Concept

The middle term is (3x+8x=11x), so (b=11). Exam tip: add both linear strip areas.

Step 2

Why this answer is correct

The correct answer is A. (11). The middle term is (3x+8x=11x), so (b=11). Exam tip: add both linear strip areas.

Step 3

Exam Tip

मध्य पद (3x+8x=11x) है इसलिए (b=11) होगा। परीक्षा में दोनों रैखिक पट्टियों का योग लें।

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Question 22/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

भुजा (a+b) के वर्ग में विकर्ण जैसी रेखा नहीं बल्कि दो लंबवत कट लगाए गए हैं। यदि कट (a) और (b) भाग बनाते हैं तो क्षेत्रफल का सही दृश्य योग क्या है?

In a square of side (a+b), two perpendicular cuts, not a diagonal, divide the side into parts (a) and (b). What is the correct visual sum of areas?

Explanation opens after your attempt
Correct Answer

B. \(a^2+2ab+b^2\)

Step 1

Concept

Perpendicular cuts form four parts, including two rectangles of area (ab). Exam tip: add all regions made by the cuts.

Step 2

Why this answer is correct

The correct answer is B. \(a^2+2ab+b^2\). Perpendicular cuts form four parts, including two rectangles of area (ab). Exam tip: add all regions made by the cuts.

Step 3

Exam Tip

लंबवत कट चार भाग बनाते हैं जिनमें दो आयत (ab) के होते हैं। परीक्षा में कटों से बने सभी भाग जोड़ें।

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Question 23/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

\(x^2+2xy+y^2\) के मॉडल में यदि (y) बहुत छोटा दिखाया गया है तो कौन सा निष्कर्ष फिर भी सही रहेगा?

In the model of \(x^2+2xy+y^2\), if (y) is drawn very small, which conclusion still remains correct?

Explanation opens after your attempt
Correct Answer

B. दोनों (xy) आयत अभी भी मौजूद हैंThe two (xy) rectangles still exist

Step 1

Concept

The drawing scale may change but the structure of parts does not. Exam tip: focus on area relation, not visual proportion.

Step 2

Why this answer is correct

The correct answer is B. दोनों (xy) आयत अभी भी मौजूद हैं / The two (xy) rectangles still exist. The drawing scale may change but the structure of parts does not. Exam tip: focus on area relation, not visual proportion.

Step 3

Exam Tip

चित्र का आकार बदल सकता है पर भागों की संरचना नहीं बदलती। परीक्षा में अनुपात नहीं बल्कि क्षेत्रफल संबंध देखें।

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Question 24/50 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 25/50 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 26/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक दृश्य मॉडल में \(a^2+2ab+b^2\) को ((a+b)2) और \(a^2+b^2\) से तुलना की गई। कौन सा क्षेत्रफल केवल क्रॉस आयतों का है?

A visual model compares \(a^2+2ab+b^2\) with \(a^2+b^2\). Which area belongs only to the cross rectangles?

Explanation opens after your attempt
Correct Answer

C. (2ab)

Step 1

Concept

There are two cross rectangles and each has area (ab). Exam tip: treat (2ab) as the combined area of two rectangles.

Step 2

Why this answer is correct

The correct answer is C. (2ab). There are two cross rectangles and each has area (ab). Exam tip: treat (2ab) as the combined area of two rectangles.

Step 3

Exam Tip

क्रॉस आयत दो हैं और प्रत्येक का क्षेत्रफल (ab) है। परीक्षा में (2ab) को दो आयतों का संयुक्त क्षेत्रफल मानें।

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Question 27/50 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 28/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक वर्ग मॉडल में ((3x-2y)2) के लिए दो घटाई गई पट्टियों का संयुक्त क्षेत्रफल कितना होगा?

In a square model for ((3x-2y)2), what will be the combined area of the two removed strips?

Explanation opens after your attempt
Correct Answer

B. (12xy)

Step 1

Concept

Both strips are (3x) by (2y), so (12xy) is subtracted. Exam tip: understand the negative middle term through two strips.

Step 2

Why this answer is correct

The correct answer is B. (12xy). Both strips are (3x) by (2y), so (12xy) is subtracted. Exam tip: understand the negative middle term through two strips.

Step 3

Exam Tip

दोनों पट्टियां (3x) by (2y) की हैं इसलिए कुल (12xy) घटता है। परीक्षा में ऋण मध्य पद को दो पट्टियों से समझें।

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Question 29/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

किस मॉडल से ((a+b)(a-b)=a-2-b-2) की दृश्य व्याख्या सबसे सीधी मिलती है?

Which model gives the most direct visual explanation of ((a+b)(a-b)=a-2-b-2)?

Explanation opens after your attempt
Correct Answer

A. भुजा (a) के वर्ग से भुजा (b) का वर्ग हटाकर शेष को आयत बनानाRemoving a square of side (b) from a square of side (a) and rearranging the remainder into a rectangle

Step 1

Concept

The remaining part of the difference of squares becomes the rectangle ((a+b)(a-b)). Exam tip: remember the cut-and-rearrange idea.

Step 2

Why this answer is correct

The correct answer is A. भुजा (a) के वर्ग से भुजा (b) का वर्ग हटाकर शेष को आयत बनाना / Removing a square of side (b) from a square of side (a) and rearranging the remainder into a rectangle. The remaining part of the difference of squares becomes the rectangle ((a+b)(a-b)). Exam tip: remember the cut-and-rearrange idea.

Step 3

Exam Tip

वर्गों के अंतर का शेष भाग आयत ((a+b)(a-b)) में बदलता है। परीक्षा में काटकर पुनर्व्यवस्था का विचार याद रखें।

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Question 30/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक मॉडल में \(x^2+2xk+k^2\) पूर्ण वर्ग है। यदि रैखिक पट्टियों का कुल क्षेत्रफल (16x) है तो कोने का क्षेत्रफल क्या होगा?

In a model, \(x^2+2xk+k^2\) is a perfect square. If the total area of the linear strips is (16x), what is the corner area?

Explanation opens after your attempt
Correct Answer

B. (64)

Step 1

Concept

From (2xk=16x), (k=8), so the corner is \(k^2=64\). Exam tip: get the half-width from the total strip area.

Step 2

Why this answer is correct

The correct answer is B. (64). From (2xk=16x), (k=8), so the corner is \(k^2=64\). Exam tip: get the half-width from the total strip area.

Step 3

Exam Tip

(2xk=16x) से (k=8) और कोना \(k^2=64\) होगा। परीक्षा में कुल पट्टी क्षेत्रफल से आधी चौड़ाई निकालें।

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Question 31/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक आयत मॉडल में \(x^2-2x-15\) को फैक्टर टाइलों से दिखाया गया है। कौन सी भुजाएं संभव हैं?

In a rectangle model, \(x^2-2x-15\) is shown using factor tiles. Which sides are possible?

Explanation opens after your attempt
Correct Answer

A. (x-5) और (x+3)(x-5) and (x+3)

Step 1

Concept

Since (-5+3=-2) and \(-5\cdot3=-15\). Exam tip: interpret factors with signs in the visual model.

Step 2

Why this answer is correct

The correct answer is A. (x-5) और (x+3) / (x-5) and (x+3). Since (-5+3=-2) and \(-5\cdot3=-15\). Exam tip: interpret factors with signs in the visual model.

Step 3

Exam Tip

(-5+3=-2) और \(-5\cdot3=-15\) है। परीक्षा में संकेतों सहित गुणनखंडों का दृश्य अर्थ समझें।

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Question 32/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

भुजा (2a+b) वाले वर्ग का दृश्य मॉडल बनाया गया। दो समान आयतों का कुल क्षेत्रफल क्या होगा?

A visual model is made for a square of side (2a+b). What will be the combined area of the two equal rectangles?

Explanation opens after your attempt
Correct Answer

B. (4ab)

Step 1

Concept

Each rectangle is (2a) by (b), so the total is (4ab). Exam tip: handle the changed side (2a) carefully.

Step 2

Why this answer is correct

The correct answer is B. (4ab). Each rectangle is (2a) by (b), so the total is (4ab). Exam tip: handle the changed side (2a) carefully.

Step 3

Exam Tip

प्रत्येक आयत (2a) by (b) है इसलिए कुल (4ab) होगा। परीक्षा में बदली हुई भुजा (2a) को ध्यान से लें।

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Question 33/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

यदि एक वर्ग का क्षेत्रफल मॉडल \(25x^2+20xy+4y^2\) है तो कौन सा कथन सही है?

If a square area model is \(25x^2+20xy+4y^2\), which statement is correct?

Explanation opens after your attempt
Correct Answer

A. पूरे वर्ग की भुजा (5x+2y) हैThe side of the whole square is (5x+2y)

Step 1

Concept

The square roots of \(25x^2\) and \(4y^2\) are (5x) and (2y), and the middle term (20xy) fits. Exam tip: confirm using the (2ab) term.

Step 2

Why this answer is correct

The correct answer is A. पूरे वर्ग की भुजा (5x+2y) है / The side of the whole square is (5x+2y). The square roots of \(25x^2\) and \(4y^2\) are (5x) and (2y), and the middle term (20xy) fits. Exam tip: confirm using the (2ab) term.

Step 3

Exam Tip

\(25x^2\) और \(4y^2\) के वर्गमूल (5x) और (2y) हैं और मध्य पद (20xy) सही है। परीक्षा में मध्य पद (2ab) से पुष्टि करें।

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Question 34/50 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 35/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक वर्ग (x+4) भुजा का है और अंदर (x-4) भुजा का वर्ग दिखाया गया है। दोनों क्षेत्रों का अंतर किसके बराबर है?

A square has side (x+4), and inside it a square of side (x-4) is shown. What is the difference of their areas?

Explanation opens after your attempt
Correct Answer

B. (16x)

Step 1

Concept

((x+4)2-(x-4)2=16x). Exam tip: use (4ab) for the difference of two such squares.

Step 2

Why this answer is correct

The correct answer is B. (16x). ((x+4)2-(x-4)2=16x). Exam tip: use (4ab) for the difference of two such squares.

Step 3

Exam Tip

((x+4)2-(x-4)2=16x) होता है। परीक्षा में दो वर्गों के अंतर में (4ab) का प्रयोग करें।

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Question 36/50 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 37/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक मॉडल में \(a^2+2ab+b^2\) का बड़ा वर्ग और \(a^2-2ab+b^2\) का छोटा वर्ग साथ दिखाया गया। दोनों का योग किसके बराबर होगा?

A model shows the big square \(a^2+2ab+b^2\) and the small square \(a^2-2ab+b^2\) together. What is their sum equal to?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

The middle terms (+2ab) and (-2ab) cancel. Exam tip: watch opposite like terms while adding.

Step 2

Why this answer is correct

The correct answer is A. \(2a^2+2b^2\). The middle terms (+2ab) and (-2ab) cancel. Exam tip: watch opposite like terms while adding.

Step 3

Exam Tip

मध्य पद (+2ab) और (-2ab) कट जाते हैं। परीक्षा में जोड़ते समय समान विपरीत पदों को देखें।

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Question 38/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

भुजा (x+y+z) वाले वर्ग के मॉडल में \(x^2\), \(y^2\), \(z^2\), (2xy), (2yz) दिखते हैं। कौन सा भाग छूटा है?

In the model of a square of side (x+y+z), the parts \(x^2\), \(y^2\), \(z^2\), (2xy), and (2yz) are shown. Which part is missing?

Explanation opens after your attempt
Correct Answer

B. (2xz)

Step 1

Concept

In a trinomial square, twice the product of every pair appears. Exam tip: count the pair (x) and (z) too.

Step 2

Why this answer is correct

The correct answer is B. (2xz). In a trinomial square, twice the product of every pair appears. Exam tip: count the pair (x) and (z) too.

Step 3

Exam Tip

तीन पदों के वर्ग में हर जोड़ी का दुगुना गुणनफल आता है। परीक्षा में (x) और (z) की जोड़ी भी गिनें।

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Question 39/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक वर्ग मॉडल \(x^2+mx+100\) को पूर्ण वर्ग दिखाता है। यदि कोने की भुजा (10) है तो (m) क्या होगा?

A square model \(x^2+mx+100\) shows a perfect square. If the corner side is (10), what is (m)?

Explanation opens after your attempt
Correct Answer

B. (20)

Step 1

Concept

The two linear strips give (10x) and (10x), so (m=20). Exam tip: add the two equal strips.

Step 2

Why this answer is correct

The correct answer is B. (20). The two linear strips give (10x) and (10x), so (m=20). Exam tip: add the two equal strips.

Step 3

Exam Tip

दो रैखिक पट्टियां (10x) और (10x) देती हैं इसलिए (m=20) है। परीक्षा में दो बराबर पट्टियों का योग लें।

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Question 40/50 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 41/50 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 42/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक मॉडल में \(4x^2+12x+9\) को वर्ग में सजाया गया है। मध्य की दो पट्टियों में प्रत्येक का क्षेत्रफल कितना है?

In a model, \(4x^2+12x+9\) is arranged as a square. What is the area of each of the two middle strips?

Explanation opens after your attempt
Correct Answer

B. (6x)

Step 1

Concept

The total middle term is (12x), and there are two equal strips, so each is (6x). Exam tip: divide the middle term into two equal parts.

Step 2

Why this answer is correct

The correct answer is B. (6x). The total middle term is (12x), and there are two equal strips, so each is (6x). Exam tip: divide the middle term into two equal parts.

Step 3

Exam Tip

कुल मध्य पद (12x) है और दो समान पट्टियां हैं इसलिए प्रत्येक (6x) है। परीक्षा में कुल मध्य पद को दो बराबर भागों में बांटें।

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Question 43/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

यदि \(x^2-10x+25\) का क्षेत्रफल मॉडल बनाया जाए तो कोने के वर्ग की भुजा क्या होगी?

If an area model is made for \(x^2-10x+25\), what will be the side of the corner square?

Explanation opens after your attempt
Correct Answer

C. (5)

Step 1

Concept

Since \(25=5^2\), and the middle term matches \(2\cdot5\cdot x\). Exam tip: take the square root of the constant term.

Step 2

Why this answer is correct

The correct answer is C. (5). Since \(25=5^2\), and the middle term matches \(2\cdot5\cdot x\). Exam tip: take the square root of the constant term.

Step 3

Exam Tip

\(25=5^2\) है और मध्य पद \(2\cdot5\cdot x\) से मेल खाता है। परीक्षा में स्थिर पद का वर्गमूल लें।

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Question 44/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक दृश्य मॉडल में आयत की भुजाएं (x+a) और (x-a) हैं। मध्य रैखिक भागों का क्या प्रभाव होगा?

In a visual model, the rectangle sides are (x+a) and (x-a). What will be the effect of the middle linear parts?

Explanation opens after your attempt
Correct Answer

B. वे कटकर शून्य हो जाएंगेThey cancel to zero

Step 1

Concept

The parts (ax) and (-ax) are opposite linear parts, so they cancel. Exam tip: the middle term is zero in product of sum and difference.

Step 2

Why this answer is correct

The correct answer is B. वे कटकर शून्य हो जाएंगे / They cancel to zero. The parts (ax) and (-ax) are opposite linear parts, so they cancel. Exam tip: the middle term is zero in product of sum and difference.

Step 3

Exam Tip

(ax) और (-ax) विपरीत रैखिक भाग हैं इसलिए कट जाते हैं। परीक्षा में योग और अंतर के गुणन में मध्य पद शून्य होता है।

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Question 45/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक वर्ग मॉडल में \(x^2+2xy+y^2\) के चार भागों को जोड़ने की जगह केवल बाहरी परिमाप देखा गया। यह तरीका क्यों गलत है?

In a square model of \(x^2+2xy+y^2\), only the outer perimeter is observed instead of adding the four areas. Why is this method wrong?

Explanation opens after your attempt
Correct Answer

A. क्योंकि पहचान क्षेत्रफल पर आधारित हैBecause the identity is based on area

Step 1

Concept

The visual identity is formed by adding areas of parts, not by perimeter. Exam tip: keep area and perimeter separate.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि पहचान क्षेत्रफल पर आधारित है / Because the identity is based on area. The visual identity is formed by adding areas of parts, not by perimeter. Exam tip: keep area and perimeter separate.

Step 3

Exam Tip

दृश्य पहचान भागों के क्षेत्रफल जोड़कर बनती है परिमाप से नहीं। परीक्षा में क्षेत्रफल और परिमाप को अलग रखें।

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Question 46/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक (x+2) भुजा वाले वर्ग और (x-2) भुजा वाले वर्ग के क्षेत्रफलों का अंतर दृश्य रूप से चार पट्टियों में दिखता है। कुल अंतर क्या होगा?

The difference of areas of squares with sides (x+2) and (x-2) is shown visually by four strips. What is the total difference?

Explanation opens after your attempt
Correct Answer

B. (8x)

Step 1

Concept

((x+2)2-(x-2)2=8x). Exam tip: use ((a+b)2-(a-b)2=4ab).

Step 2

Why this answer is correct

The correct answer is B. (8x). ((x+2)2-(x-2)2=8x). Exam tip: use ((a+b)2-(a-b)2=4ab).

Step 3

Exam Tip

((x+2)2-(x-2)2=8x) होता है। परीक्षा में ((a+b)2-(a-b)2=4ab) लगाएं।

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Question 47/50 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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Question 48/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

यदि \(4a^2-b^2\) का दृश्य मॉडल बनाया जाए तो पुनर्व्यवस्थित आयत की भुजाएं क्या होंगी?

If a visual model is made for \(4a^2-b^2\), what will be the sides of the rearranged rectangle?

Explanation opens after your attempt
Correct Answer

A. (2a-b) और (2a+b)(2a-b) and (2a+b)

Step 1

Concept

Since (4a-2=(2a)2), the difference becomes ((2a-b)(2a+b)). Exam tip: identify the side of the larger square first.

Step 2

Why this answer is correct

The correct answer is A. (2a-b) और (2a+b) / (2a-b) and (2a+b). Since (4a-2=(2a)2), the difference becomes ((2a-b)(2a+b)). Exam tip: identify the side of the larger square first.

Step 3

Exam Tip

(4a-2=(2a)2) है इसलिए अंतर ((2a-b)(2a+b)) बनेगा। परीक्षा में पहले बड़े वर्ग की भुजा पहचानें।

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Question 49/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक वर्ग मॉडल में कुल क्षेत्रफल \(x^2+18x+81\) है। यदि बीच की पट्टियां हटाकर केवल दो वर्ग बचे तो उनका कुल क्षेत्रफल क्या होगा?

A square model has total area \(x^2+18x+81\). If the middle strips are removed and only the two squares remain, what is their total area?

Explanation opens after your attempt
Correct Answer

A. \(x^2+81\)

Step 1

Concept

The two squares are \(x^2\) and (81), while (18x) is the strip area. Exam tip: separate square parts from rectangular parts.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+81\). The two squares are \(x^2\) and (81), while (18x) is the strip area. Exam tip: separate square parts from rectangular parts.

Step 3

Exam Tip

दो वर्ग \(x^2\) और (81) हैं जबकि (18x) पट्टियों का क्षेत्रफल है। परीक्षा में वर्ग भागों और आयत भागों को अलग करें।

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Question 50/50 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 68

एक दृश्य मॉडल में \(x^2+2xy+y^2\) को गलत तरीके से \(x^2+y^2\) माना गया। कौन सा दृश्य भाग अनदेखा किया गया?

In a visual model, \(x^2+2xy+y^2\) is incorrectly treated as \(x^2+y^2\). Which visual part has been ignored?

Explanation opens after your attempt
Correct Answer

A. दो (xy) आयतTwo (xy) rectangles

Step 1

Concept

The mistake ignores the two cross rectangles of total area (2xy). Exam tip: never write ((x+y)2) as \(x^2+y^2\).

Step 2

Why this answer is correct

The correct answer is A. दो (xy) आयत / Two (xy) rectangles. The mistake ignores the two cross rectangles of total area (2xy). Exam tip: never write ((x+y)2) as \(x^2+y^2\).

Step 3

Exam Tip

गलती में दोनों क्रॉस आयतों का क्षेत्रफल (2xy) छोड़ दिया गया। परीक्षा में ((x+y)2) को कभी \(x^2+y^2\) न लिखें।

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