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identity comparison MCQ Questions for Class 9

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9 questions tagged with identity comparison.

Question 1/9 Hard Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 73

\(x^2+4x+4\) और \(x^2-4\) में क्या संबंध है?

What is the relation between \(x^2+4x+4\) and \(x^2-4\)?

Explanation opens after your attempt
Correct Answer

A. पहला पूर्ण वर्ग है और दूसरा वर्गों का अंतर हैFirst is a perfect square and second is difference of squares

Step 1

Concept

(x-2+4x+4=(x+2)2) and (x-2-4=(x-2)(x+2)). In exams, check signs and the middle term.

Step 2

Why this answer is correct

The correct answer is A. पहला पूर्ण वर्ग है और दूसरा वर्गों का अंतर है / First is a perfect square and second is difference of squares. (x-2+4x+4=(x+2)2) and (x-2-4=(x-2)(x+2)). In exams, check signs and the middle term.

Step 3

Exam Tip

(x-2+4x+4=(x+2)2) और (x-2-4=(x-2)(x+2)) है। परीक्षा में चिन्ह और मध्य पद देखें।

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Question 2/9 Medium Mathematics Exploring Algebraic Identities Quadratic expressions Class 9 Level 75

\(x^2+4x+4\) और \(x^2-4\) में मुख्य अंतर क्या है?

What is the main difference between \(x^2+4x+4\) and \(x^2-4\)?

Explanation opens after your attempt
Correct Answer

A. पहला पूर्ण वर्ग है और दूसरा दो वर्गों का अंतर हैThe first is a perfect square and the second is a difference of two squares

Step 1

Concept

(x-2+4x+4=(x+2)2) and (x-2-4=(x-2)(x+2)). Exam tip: distinguish similar-looking quadratics by identity.

Step 2

Why this answer is correct

The correct answer is A. पहला पूर्ण वर्ग है और दूसरा दो वर्गों का अंतर है / The first is a perfect square and the second is a difference of two squares. (x-2+4x+4=(x+2)2) and (x-2-4=(x-2)(x+2)). Exam tip: distinguish similar-looking quadratics by identity.

Step 3

Exam Tip

(x-2+4x+4=(x+2)2) और (x-2-4=(x-2)(x+2)) है। परीक्षा में समान दिखने वाले द्विघातों की पहचान अलग करें।

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

एक दृश्य प्रमाण में \(a^2+2ab+b^2\) और \(a^2-b^2\) दोनों दिखाई देते हैं। कौन सा कथन सही है?

In a visual proof, both \(a^2+2ab+b^2\) and \(a^2-b^2\) appear. Which statement is correct?

Explanation opens after your attempt
Correct Answer

A. पहला योग के वर्ग से और दूसरा वर्गों के अंतर से जुड़ा हैThe first is linked to square of sum and the second to difference of squares

Step 1

Concept

(a-2+2ab+b-2=(a+b)2) and (a-2-b-2=(a+b)(a-b)). Exam tip: identify the type of model.

Step 2

Why this answer is correct

The correct answer is A. पहला योग के वर्ग से और दूसरा वर्गों के अंतर से जुड़ा है / The first is linked to square of sum and the second to difference of squares. (a-2+2ab+b-2=(a+b)2) and (a-2-b-2=(a+b)(a-b)). Exam tip: identify the type of model.

Step 3

Exam Tip

(a-2+2ab+b-2=(a+b)2) और (a-2-b-2=(a+b)(a-b)) हैं। परीक्षा में मॉडल का प्रकार पहचानें।

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Question 4/9 Expert Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 66

यदि ((a+b)2-(a-b)2) को दो वर्गों के दृश्य अंतर से दिखाएं तो बचा क्षेत्रफल क्या होगा?

If ((a+b)2-(a-b)2) is shown as the visual difference of two squares, what remaining area is obtained?

Explanation opens after your attempt
Correct Answer

B. (4ab)four rectangular parts

Step 1

Concept

Subtracting the two expansions leaves (4ab). In exams the equal \(a^2\) and \(b^2\) terms cancel.

Step 2

Why this answer is correct

The correct answer is B. (4ab) / four rectangular parts. Subtracting the two expansions leaves (4ab). In exams the equal \(a^2\) and \(b^2\) terms cancel.

Step 3

Exam Tip

दोनों विस्तार घटाने पर (4ab) बचता है। परीक्षा में समान \(a^2\) और \(b^2\) पद कट जाते हैं।

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Question 5/9 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (x+3)2-(x-1)(x+7) ) का सरल रूप क्या है?

What is the simplified form of ( (x+3)2-(x-1)(x+7) )?

Explanation opens after your attempt
Correct Answer

B. (4)

Step 1

Concept

The first is \(x^2+6x+9\) and the second is \(x^2+6x-7\). Subtracting gives (9-(-7)=16), so the correct option should be (16).

Step 2

Why this answer is correct

The correct answer is B. (4). The first is \(x^2+6x+9\) and the second is \(x^2+6x-7\). Subtracting gives (9-(-7)=16), so the correct option should be (16).

Step 3

Exam Tip

पहला \(x^2+6x+9\) और दूसरा \(x^2+6x-7\) है। घटाने पर (16) नहीं बल्कि (9-(-7)=16) होगा इसलिए सही विकल्प (16) होना चाहिए।

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Question 6/9 Expert Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 63

( (a+b)2-\(a^2-b^2\) ) का सरल रूप क्या है?

What is the simplified form of ( (a+b)2-\(a^2-b^2\) )?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

\(a^2+2ab+b^2-a^2+b^2=2ab+2b^2\). Exam tip: apply the minus sign to the whole second expression.

Step 2

Why this answer is correct

The correct answer is A. \(2ab+2b^2\). \(a^2+2ab+b^2-a^2+b^2=2ab+2b^2\). Exam tip: apply the minus sign to the whole second expression.

Step 3

Exam Tip

\(a^2+2ab+b^2-a^2+b^2=2ab+2b^2\)। परीक्षा में ऋण चिन्ह को पूरे दूसरे पद पर लगाएँ।

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Question 7/9 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (x+5)(x-5) ) और ( (x-5)2 ) में क्या मुख्य अंतर है?

What is the main difference between ( (x+5)(x-5) ) and ( (x-5)2 )?

Explanation opens after your attempt
Correct Answer

A. पहला \(x^2-25\) है और दूसरा \(x^2-10x+25\) हैThe first is \(x^2-25\) and the second is \(x^2-10x+25\)

Step 1

Concept

In opposite-sign product mixed terms cancel but in a square the middle term remains. Exam tip: do not mix the two forms.

Step 2

Why this answer is correct

The correct answer is A. पहला \(x^2-25\) है और दूसरा \(x^2-10x+25\) है / The first is \(x^2-25\) and the second is \(x^2-10x+25\). In opposite-sign product mixed terms cancel but in a square the middle term remains. Exam tip: do not mix the two forms.

Step 3

Exam Tip

विपरीत चिन्ह वाले गुणन में मिश्र पद कटता है पर वर्ग में मध्य पद रहता है। परीक्षा में दोनों रूपों को न मिलाएँ।

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Question 8/9 Medium Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 64

( (a-b)2 ) और \(a^2-b^2\) का अंतर क्या है?

What is the difference between ( (a-b)2 ) and \(a^2-b^2\)?

Explanation opens after your attempt
Correct Answer

A. \(2b^2-2ab\)

Step 1

Concept

( (a-b)2=a-2-2ab+b-2 ), so subtracting \(a^2-b^2\) gives \(2b^2-2ab\). Exam tip: keep both identities separate.

Step 2

Why this answer is correct

The correct answer is A. \(2b^2-2ab\). ( (a-b)2=a-2-2ab+b-2 ), so subtracting \(a^2-b^2\) gives \(2b^2-2ab\). Exam tip: keep both identities separate.

Step 3

Exam Tip

( (a-b)2=a-2-2ab+b-2 ) है इसलिए \(a^2-b^2\) घटाने पर \(2b^2-2ab\) मिलता है। परीक्षा में दोनों पहचान अलग रखें।

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Question 9/9 Easy Mathematics Exploring Algebraic Identities Algebraic identities Class 9 Level 65

( (a+b)2-(a-b)2 ) का सरल रूप क्या है?

What is the simplified form of ( (a+b)2-(a-b)2 )?

Explanation opens after your attempt
Correct Answer

B. (4ab)

Step 1

Concept

After subtracting both expansions, (4ab) remains. Exam tip: expand first and cancel like terms.

Step 2

Why this answer is correct

The correct answer is B. (4ab). After subtracting both expansions, (4ab) remains. Exam tip: expand first and cancel like terms.

Step 3

Exam Tip

दोनों विस्तार घटाने पर (4ab) बचता है। परीक्षा में पहले विस्तार करके समान पद काटें।

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