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Mathematics Quiz - Class 9 Mathematics Hard Level 29 Quiz

Question 1/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि (p(x)=(a-2)x^-8+(a+1)x^-5-3x+7) की डिग्री (5) है, तो (a) का सही मान कौन सा है?

If the degree of (p(x)=(a-2)x^-8+(a+1)x^-5-3x+7) is (5), which value of (a) is correct?

Explanation opens after your attempt

Correct Answer

A. (a=2)

Step 1

Concept

For degree (5), the coefficient of \(x^8\) must be (0) and the coefficient of \(x^5\) must be non-zero. This condition holds at (a=2).

Step 2

Why this answer is correct

The correct answer is A. (a=2). For degree (5), the coefficient of \(x^8\) must be (0) and the coefficient of \(x^5\) must be non-zero. This condition holds at (a=2).

Step 3

Exam Tip

डिग्री (5) के लिए \(x^8\) का गुणांक (0) और \(x^5\) का गुणांक अशून्य होना चाहिए। (a=2) पर यह शर्त पूरी होती है।

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Question 2/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

सरल करने के बाद (x^-3\(x^4-2\)-x^-7+5x^-2) की डिग्री क्या है?

After simplifying (x^-3\(x^4-2\)-x^-7+5x^-2), what is the degree?

Explanation opens after your attempt

Correct Answer

C. (3)

Step 1

Concept

(x^-3\(x^4-2\)=x^-7-2x^-3), and \(x^7\) cancels. The remaining \(-2x^3+5x^2\) has degree (3).

Step 2

Why this answer is correct

The correct answer is C. (3). (x^-3\(x^4-2\)=x^-7-2x^-3), and \(x^7\) cancels. The remaining \(-2x^3+5x^2\) has degree (3).

Step 3

Exam Tip

(x^-3\(x^4-2\)=x^-7-2x^-3) और \(x^7\) कट जाता है। बचा \(-2x^3+5x^2\) है जिसकी डिग्री (3) है।

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Question 3/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि (q(x)=\(k^2-9\)x^-6+(k-3)x^-4+2x^-2) और (k=3), तो (q(x)) की डिग्री क्या है?

If (q(x)=\(k^2-9\)x^-6+(k-3)x^-4+2x^-2) and (k=3), what is the degree of (q(x))?

Explanation opens after your attempt

Correct Answer

D. (2)

Step 1

Concept

At (k=3), both \(x^6\) and \(x^4\) terms vanish. The remaining highest power is (2).

Step 2

Why this answer is correct

The correct answer is D. (2). At (k=3), both \(x^6\) and \(x^4\) terms vanish. The remaining highest power is (2).

Step 3

Exam Tip

(k=3) पर \(x^6\) और \(x^4\) दोनों पद हट जाते हैं। बची हुई सबसे बड़ी घात (2) है।

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Question 4/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

बहुपद (\(2x^3-5\)\(x^4+x^2+1\)) की डिग्री क्या है?

What is the degree of the polynomial (\(2x^3-5\)\(x^4+x^2+1\))?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

The highest term comes from \(2x^3\cdot x^4=2x^7\). Therefore the degree of the product is (7).

Step 2

Why this answer is correct

The correct answer is C. (7). The highest term comes from \(2x^3\cdot x^4=2x^7\). Therefore the degree of the product is (7).

Step 3

Exam Tip

उच्चतम पद \(2x^3\cdot x^4=2x^7\) से मिलेगा। इसलिए गुणनफल की डिग्री (7) है।

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Question 5/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि (f(x)=x^-5-3x^-5+2x^-5+4x-1), तो (f(x)) की डिग्री क्या है?

If (f(x)=x^-5-3x^-5+2x^-5+4x-1), what is the degree of (f(x))?

Explanation opens after your attempt

Correct Answer

C. (1)

Step 1

Concept

\(x^5-3x^5+2x^5=0\). The remaining (4x-1) has degree (1).

Step 2

Why this answer is correct

The correct answer is C. (1). \(x^5-3x^5+2x^5=0\). The remaining (4x-1) has degree (1).

Step 3

Exam Tip

\(x^5-3x^5+2x^5=0\) हो जाता है। बचा हुआ (4x-1) डिग्री (1) का है।

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Question 6/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

बहुपद \(4x^2y^5-3x^4y^2+7xy-9\) की कुल डिग्री क्या है?

What is the total degree of \(4x^2y^5-3x^4y^2+7xy-9\)?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

The total power of the first term is (2+5=7), and it is the highest. Therefore the total degree is (7).

Step 2

Why this answer is correct

The correct answer is B. (7). The total power of the first term is (2+5=7), and it is the highest. Therefore the total degree is (7).

Step 3

Exam Tip

पहले पद की कुल घात (2+5=7) है और यह सबसे बड़ी है। इसलिए कुल डिग्री (7) है।

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Question 7/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

(x) के संदर्भ में \(6x^3y^7-4x^5y^2+9y-1\) की डिग्री क्या है?

With respect to (x), what is the degree of \(6x^3y^7-4x^5y^2+9y-1\)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

With respect to (x), (y) is treated like a coefficient. The highest power of (x) is (5).

Step 2

Why this answer is correct

The correct answer is B. (5). With respect to (x), (y) is treated like a coefficient. The highest power of (x) is (5).

Step 3

Exam Tip

(x) के संदर्भ में (y) को गुणांक जैसा मानते हैं। (x) की सबसे बड़ी घात (5) है।

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Question 8/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

(y) के संदर्भ में \(6x^3y^7-4x^5y^2+9y-1\) की डिग्री क्या है?

With respect to (y), what is the degree of \(6x^3y^7-4x^5y^2+9y-1\)?

Explanation opens after your attempt

Correct Answer

A. (7)

Step 1

Concept

The highest power of (y) is (7). Therefore the degree with respect to (y) is (7).

Step 2

Why this answer is correct

The correct answer is A. (7). The highest power of (y) is (7). Therefore the degree with respect to (y) is (7).

Step 3

Exam Tip

(y) की सबसे बड़ी घात (7) है। इसलिए (y) के संदर्भ में डिग्री (7) है।

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Question 9/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि \(2x^n+5x^7-3\) की डिग्री (n) है और (n>7), तो निम्न में से (n) का कौन सा मान संभव है?

If the degree of \(2x^n+5x^7-3\) is (n) and (n>7), which value of (n) is possible?

Explanation opens after your attempt

Correct Answer

C. (n=8)

Step 1

Concept

When (n>7), \(x^n\) gives the highest power. Among the options, only (n=8) satisfies the condition.

Step 2

Why this answer is correct

The correct answer is C. (n=8). When (n>7), \(x^n\) gives the highest power. Among the options, only (n=8) satisfies the condition.

Step 3

Exam Tip

जब (n>7) है, तो \(x^n\) सबसे बड़ी घात देगा। दिए गए विकल्पों में (n=8) ही शर्त पूरी करता है।

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Question 10/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि \(3x^m+4x^6-1\) की डिग्री (6) है और (m<6), तो (m) का संभावित मान कौन सा है?

If the degree of \(3x^m+4x^6-1\) is (6) and (m<6), which value of (m) is possible?

Explanation opens after your attempt

Correct Answer

D. (m=4)

Step 1

Concept

The \(x^6\) term is already present and (m<6) is required. At (m=4), the highest power remains (6).

Step 2

Why this answer is correct

The correct answer is D. (m=4). The \(x^6\) term is already present and (m<6) is required. At (m=4), the highest power remains (6).

Step 3

Exam Tip

\(x^6\) पद पहले से है और (m<6) चाहिए। (m=4) पर सबसे बड़ी घात (6) ही रहती है।

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Question 11/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

बहुपद (\(x^2-1\)³) की डिग्री क्या है?

What is the degree of the polynomial (\(x^2-1\)³)?

Explanation opens after your attempt

Correct Answer

D. (6)

Step 1

Concept

The highest term will be (\(x^2\)³=x^-6). Therefore the degree is (6).

Step 2

Why this answer is correct

The correct answer is D. (6). The highest term will be (\(x^2\)³=x^-6). Therefore the degree is (6).

Step 3

Exam Tip

उच्चतम पद (\(x^2\)³=x^-6) बनेगा। इसलिए डिग्री (6) है।

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Question 12/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

बहुपद (\(x^3+2\)²-\(x^6+4x^3\)) की डिग्री क्या है?

What is the degree of (\(x^3+2\)²-\(x^6+4x^3\))?

Explanation opens after your attempt

Correct Answer

C. (0)

Step 1

Concept

(\(x^3+2\)²=x^-6+4x^-3+4). After subtraction, only (4) remains, whose degree is (0).

Step 2

Why this answer is correct

The correct answer is C. (0). (\(x^3+2\)²=x^-6+4x^-3+4). After subtraction, only (4) remains, whose degree is (0).

Step 3

Exam Tip

(\(x^3+2\)²=x^-6+4x^-3+4) होता है। घटाने पर केवल (4) बचता है जिसकी डिग्री (0) है।

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Question 13/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि \(a\neq1\), तो ((a-1)x^{10}+7x^-4-8) की डिग्री क्या होगी?

If \(a\neq1\), what will be the degree of ((a-1)x^{10}+7x^-4-8)?

Explanation opens after your attempt

Correct Answer

C. (10)

Step 1

Concept

When \(a\neq1\), the coefficient of \(x^{10}\) is not zero. Therefore the highest power remains (10).

Step 2

Why this answer is correct

The correct answer is C. (10). When \(a\neq1\), the coefficient of \(x^{10}\) is not zero. Therefore the highest power remains (10).

Step 3

Exam Tip

\(a\neq1\) होने पर \(x^{10}\) का गुणांक शून्य नहीं है। इसलिए सबसे बड़ी घात (10) रहेगी।

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Question 14/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि (a=1), तो ((a-1)x^{10}+7x^-4-8) की डिग्री क्या होगी?

If (a=1), what will be the degree of ((a-1)x^{10}+7x^-4-8)?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

When (a=1), the \(x^{10}\) term disappears. The remaining highest power is (4).

Step 2

Why this answer is correct

The correct answer is C. (4). When (a=1), the \(x^{10}\) term disappears. The remaining highest power is (4).

Step 3

Exam Tip

(a=1) होने पर \(x^{10}\) पद हट जाता है। बची हुई सबसे बड़ी घात (4) है।

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Question 15/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

बहुपद (\(x^2+x+1\)\(x^4-x^2+1\)) की डिग्री क्या है?

What is the degree of (\(x^2+x+1\)\(x^4-x^2+1\))?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

The highest term comes from \(x^2\cdot x^4=x^6\). Therefore the degree is (6).

Step 2

Why this answer is correct

The correct answer is C. (6). The highest term comes from \(x^2\cdot x^4=x^6\). Therefore the degree is (6).

Step 3

Exam Tip

उच्चतम पद \(x^2\cdot x^4=x^6\) से मिलेगा। इसलिए डिग्री (6) है।

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Question 16/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

सरल करने के बाद (2x^-4\(x^3-1\)-2x^-7+9x^-5) की डिग्री क्या है?

After simplifying (2x^-4\(x^3-1\)-2x^-7+9x^-5), what is the degree?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

(2x^-4\(x^3-1\)=2x^-7-2x^-4), and \(2x^7\) cancels. The remaining \(9x^5-2x^4\) has degree (5).

Step 2

Why this answer is correct

The correct answer is B. (5). (2x^-4\(x^3-1\)=2x^-7-2x^-4), and \(2x^7\) cancels. The remaining \(9x^5-2x^4\) has degree (5).

Step 3

Exam Tip

(2x^-4\(x^3-1\)=2x^-7-2x^-4) और \(2x^7\) कटता है। बचा \(9x^5-2x^4\) है जिसकी डिग्री (5) है।

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Question 17/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

बहुपद \(0x^{12}+0x^9+0x^2-17\) की डिग्री क्या है?

What is the degree of \(0x^{12}+0x^9+0x^2-17\)?

Explanation opens after your attempt

Correct Answer

D. (0)

Step 1

Concept

Terms with zero coefficients disappear and (-17) remains. It is a non-zero constant polynomial of degree (0).

Step 2

Why this answer is correct

The correct answer is D. (0). Terms with zero coefficients disappear and (-17) remains. It is a non-zero constant polynomial of degree (0).

Step 3

Exam Tip

शून्य गुणांक वाले पद हट जाते हैं और (-17) बचता है। यह अशून्य नियतांक बहुपद है जिसकी डिग्री (0) है।

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Question 18/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

किस विकल्प में बहुपद की डिग्री (7) है और \(x^6\) का गुणांक (0) है?

Which option has degree (7) and coefficient of \(x^6\) equal to (0)?

Explanation opens after your attempt

Correct Answer

A. \(3x^7-2x^5+1\)

Step 1

Concept

The first polynomial has degree (7), and the \(x^6\) term is absent. So the coefficient of \(x^6\) is (0).

Step 2

Why this answer is correct

The correct answer is A. \(3x^7-2x^5+1\). The first polynomial has degree (7), and the \(x^6\) term is absent. So the coefficient of \(x^6\) is (0).

Step 3

Exam Tip

पहले बहुपद की डिग्री (7) है और \(x^6\) पद अनुपस्थित है। इसलिए \(x^6\) का गुणांक (0) है।

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Question 19/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि (g(x)=0), तो (g(x)) की डिग्री क्या है?

If (g(x)=0), what is the degree of (g(x))?

Explanation opens after your attempt

Correct Answer

C. परिभाषित नहींNot defined

Step 1

Concept

(g(x)=0) is the zero polynomial. The degree of the zero polynomial is not defined.

Step 2

Why this answer is correct

The correct answer is C. परिभाषित नहीं / Not defined. (g(x)=0) is the zero polynomial. The degree of the zero polynomial is not defined.

Step 3

Exam Tip

(g(x)=0) शून्य बहुपद है। शून्य बहुपद की डिग्री परिभाषित नहीं होती।

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Question 20/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि (p(x)=x^-2\(x^2-1\)-x^-4+x^-2+5), तो (p(x)) की डिग्री क्या है?

If (p(x)=x^-2\(x^2-1\)-x^-4+x^-2+5), what is the degree of (p(x))?

Explanation opens after your attempt

Correct Answer

D. (0)

Step 1

Concept

(x^-2\(x^2-1\)=x^-4-x^-2). All variable terms cancel and (5) remains, whose degree is (0).

Step 2

Why this answer is correct

The correct answer is D. (0). (x^-2\(x^2-1\)=x^-4-x^-2). All variable terms cancel and (5) remains, whose degree is (0).

Step 3

Exam Tip

(x^-2\(x^2-1\)=x^-4-x^-2) है। सभी चर पद कट जाते हैं और (5) बचता है जिसकी डिग्री (0) है।

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Question 21/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

बहुपद (\(x^2+2x\)\(x^3-x\)-x^-5) की डिग्री क्या है?

What is the degree of (\(x^2+2x\)\(x^3-x\)-x^-5)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

Multiplication gives \(x^5+2x^4-x^3-2x^2\), and \(x^5\) cancels. The remaining highest power is (4).

Step 2

Why this answer is correct

The correct answer is B. (4). Multiplication gives \(x^5+2x^4-x^3-2x^2\), and \(x^5\) cancels. The remaining highest power is (4).

Step 3

Exam Tip

गुणन से \(x^5+2x^4-x^3-2x^2\) मिलता है और \(x^5\) कटता है। बची सबसे बड़ी घात (4) है।

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Question 22/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि ((c+2)x^-5+\(c^2-4\)x^-3+9) की डिग्री (0) है, तो (c) का मान क्या है?

If the degree of ((c+2)x^-5+\(c^2-4\)x^-3+9) is (0), what is the value of (c)?

Explanation opens after your attempt

Correct Answer

B. (c=-2)

Step 1

Concept

For degree (0), both \(x^5\) and \(x^3\) terms must vanish. At (c=-2), both coefficients become (0).

Step 2

Why this answer is correct

The correct answer is B. (c=-2). For degree (0), both \(x^5\) and \(x^3\) terms must vanish. At (c=-2), both coefficients become (0).

Step 3

Exam Tip

डिग्री (0) के लिए \(x^5\) और \(x^3\) दोनों पद हटने चाहिए। (c=-2) पर दोनों गुणांक (0) हो जाते हैं।

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Question 23/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

किस मान पर ((d-1)x^-4+(d+3)x^-2+6) की डिग्री (2) होगी?

For which value will the degree of ((d-1)x^-4+(d+3)x^-2+6) be (2)?

Explanation opens after your attempt

Correct Answer

A. (d=1)

Step 1

Concept

For degree (2), the \(x^4\) term must vanish and the \(x^2\) term must remain. This is true at (d=1).

Step 2

Why this answer is correct

The correct answer is A. (d=1). For degree (2), the \(x^4\) term must vanish and the \(x^2\) term must remain. This is true at (d=1).

Step 3

Exam Tip

डिग्री (2) के लिए \(x^4\) पद हटना चाहिए और \(x^2\) पद बचना चाहिए। (d=1) पर यह सही होता है।

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Question 24/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

बहुपद \(x^2y^3z^4+3xy^2z-5\) की कुल डिग्री क्या है?

What is the total degree of \(x^2y^3z^4+3xy^2z-5\)?

Explanation opens after your attempt

Correct Answer

C. (9)

Step 1

Concept

The total power of the first term is (2+3+4=9). This is the highest total power.

Step 2

Why this answer is correct

The correct answer is C. (9). The total power of the first term is (2+3+4=9). This is the highest total power.

Step 3

Exam Tip

पहले पद की कुल घात (2+3+4=9) है। यही सबसे बड़ी कुल घात है।

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Question 25/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

(z) के संदर्भ में \(4x^2z^5-3xz^3+8x-1\) की डिग्री क्या है?

With respect to (z), what is the degree of \(4x^2z^5-3xz^3+8x-1\)?

Explanation opens after your attempt

Correct Answer

C. (5)

Step 1

Concept

The highest power of (z) is (5). Other variables are treated like coefficients with respect to (z).

Step 2

Why this answer is correct

The correct answer is C. (5). The highest power of (z) is (5). Other variables are treated like coefficients with respect to (z).

Step 3

Exam Tip

(z) की सबसे बड़ी घात (5) है। बाकी चर (z) के संदर्भ में गुणांक जैसे माने जाते हैं।

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Question 26/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि (h(x)=\(x^2+x\)²-x^-4-2x^-3), तो (h(x)) की डिग्री क्या है?

If (h(x)=\(x^2+x\)²-x^-4-2x^-3), what is the degree of (h(x))?

Explanation opens after your attempt

Correct Answer

C. (2)

Step 1

Concept

(\(x^2+x\)²=x^-4+2x^-3+x^-2). After subtraction, \(x^2\) remains, whose degree is (2).

Step 2

Why this answer is correct

The correct answer is C. (2). (\(x^2+x\)²=x^-4+2x^-3+x^-2). After subtraction, \(x^2\) remains, whose degree is (2).

Step 3

Exam Tip

(\(x^2+x\)²=x^-4+2x^-3+x^-2) है। घटाने पर \(x^2\) बचता है जिसकी डिग्री (2) है।

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Question 27/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

बहुपद (\(x^3-1\)\(x^3+1\)) की डिग्री क्या है?

What is the degree of (\(x^3-1\)\(x^3+1\))?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

The product is \(x^6-1\). Its highest power is (6).

Step 2

Why this answer is correct

The correct answer is C. (6). The product is \(x^6-1\). Its highest power is (6).

Step 3

Exam Tip

गुणनफल \(x^6-1\) है। इसमें सबसे बड़ी घात (6) है।

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Question 28/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि (n) अऋणात्मक पूर्णांक है और \(x^{n+2}+x^5+1\) की डिग्री (5) है, तो (n) के लिए कौन सी शर्त सही है?

If (n) is a non-negative integer and the degree of \(x^{n+2}+x^5+1\) is (5), which condition is correct for (n)?

Explanation opens after your attempt

Correct Answer

A. \(n\le3\)

Step 1

Concept

For degree (5), \(n+2\le5\) must hold. Therefore \(n\le3\) is the correct condition.

Step 2

Why this answer is correct

The correct answer is A. \(n\le3\). For degree (5), \(n+2\le5\) must hold. Therefore \(n\le3\) is the correct condition.

Step 3

Exam Tip

डिग्री (5) के लिए \(n+2\le5\) होना चाहिए। इसलिए \(n\le3\) सही शर्त है।

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Question 29/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि (p(x)=\(x^4-2x^2+1\)-\(x^4-x^2\)), तो (p(x)) की डिग्री क्या है?

If (p(x)=\(x^4-2x^2+1\)-\(x^4-x^2\)), what is the degree of (p(x))?

Explanation opens after your attempt

Correct Answer

B. (2)

Step 1

Concept

On simplifying, we get \(-x^2+1\). Its highest power is (2).

Step 2

Why this answer is correct

The correct answer is B. (2). On simplifying, we get \(-x^2+1\). Its highest power is (2).

Step 3

Exam Tip

सरल करने पर \(-x^2+1\) मिलता है। इसकी सबसे बड़ी घात (2) है।

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Question 30/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

बहुपद (x^-4\(x^2+1\)-x^-2\(x^4-3\)) की डिग्री क्या है?

What is the degree of (x^-4\(x^2+1\)-x^-2\(x^4-3\))?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

The simplified form is \(x^6+x^4-x^6+3x^2=x^4+3x^2\). Its degree is (4).

Step 2

Why this answer is correct

The correct answer is B. (4). The simplified form is \(x^6+x^4-x^6+3x^2=x^4+3x^2\). Its degree is (4).

Step 3

Exam Tip

सरल रूप \(x^6+x^4-x^6+3x^2=x^4+3x^2\) है। इसकी डिग्री (4) है।

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Question 31/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि (e=0), तो (ex^-9+(e-2)x^-7+5x^-2-1) की डिग्री क्या है?

If (e=0), what is the degree of (ex^-9+(e-2)x^-7+5x^-2-1)?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

At (e=0), the \(x^9\) term vanishes but the coefficient of \(x^7\) remains (-2). Therefore the degree is (7).

Step 2

Why this answer is correct

The correct answer is B. (7). At (e=0), the \(x^9\) term vanishes but the coefficient of \(x^7\) remains (-2). Therefore the degree is (7).

Step 3

Exam Tip

(e=0) पर \(x^9\) पद हटता है लेकिन \(x^7\) का गुणांक (-2) रहता है। इसलिए डिग्री (7) है।

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Question 32/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि (p(x)=0x^-5+0x^-3+0x+0), तो (p(x)) की डिग्री क्या है?

If (p(x)=0x^-5+0x^-3+0x+0), what is the degree of (p(x))?

Explanation opens after your attempt

Correct Answer

D. परिभाषित नहींNot defined

Step 1

Concept

All terms have coefficient (0), so it is the zero polynomial. Its degree is not defined.

Step 2

Why this answer is correct

The correct answer is D. परिभाषित नहीं / Not defined. All terms have coefficient (0), so it is the zero polynomial. Its degree is not defined.

Step 3

Exam Tip

सभी पदों के गुणांक (0) हैं इसलिए यह शून्य बहुपद है। इसकी डिग्री परिभाषित नहीं होती।

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Question 33/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

बहुपद (x\(x^2-1\)\(x^3+2\)) की डिग्री क्या है?

What is the degree of (x\(x^2-1\)\(x^3+2\))?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

The highest power comes from \(x\cdot x^2\cdot x^3=x^6\). Therefore the degree is (6).

Step 2

Why this answer is correct

The correct answer is C. (6). The highest power comes from \(x\cdot x^2\cdot x^3=x^6\). Therefore the degree is (6).

Step 3

Exam Tip

उच्चतम घात \(x\cdot x^2\cdot x^3=x^6\) से आती है। इसलिए डिग्री (6) है।

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Question 34/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

किस विकल्प में कुल डिग्री (6) वाला बहुपद है?

Which option has a polynomial of total degree (6)?

Explanation opens after your attempt

Correct Answer

B. \(x^3y^3+2x\)

Step 1

Concept

The total power of \(x^3y^3\) is (3+3=6). Therefore the total degree is (6).

Step 2

Why this answer is correct

The correct answer is B. \(x^3y^3+2x\). The total power of \(x^3y^3\) is (3+3=6). Therefore the total degree is (6).

Step 3

Exam Tip

\(x^3y^3\) की कुल घात (3+3=6) है। इसलिए कुल डिग्री (6) है।

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Question 35/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि \(t\neq0\), तो \(tx^{11}+0x^{12}+3x^5-1\) की डिग्री क्या है?

If \(t\neq0\), what is the degree of \(tx^{11}+0x^{12}+3x^5-1\)?

Explanation opens after your attempt

Correct Answer

B. (11)

Step 1

Concept

\(0x^{12}\) is a zero term, and \(t\neq0\) keeps the \(x^{11}\) term. Therefore the degree is (11).

Step 2

Why this answer is correct

The correct answer is B. (11). \(0x^{12}\) is a zero term, and \(t\neq0\) keeps the \(x^{11}\) term. Therefore the degree is (11).

Step 3

Exam Tip

\(0x^{12}\) शून्य पद है और \(t\neq0\) से \(x^{11}\) पद बचता है। इसलिए डिग्री (11) है।

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Question 36/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

बहुपद (\(x^4+x^2+1\)-\(x^4+x^2\)) की डिग्री क्या है?

What is the degree of (\(x^4+x^2+1\)-\(x^4+x^2\))?

Explanation opens after your attempt

Correct Answer

C. (0)

Step 1

Concept

On simplifying, (1) remains. (1) is a non-zero constant polynomial with degree (0).

Step 2

Why this answer is correct

The correct answer is C. (0). On simplifying, (1) remains. (1) is a non-zero constant polynomial with degree (0).

Step 3

Exam Tip

सरल करने पर (1) बचता है। (1) अशून्य नियतांक बहुपद है जिसकी डिग्री (0) है।

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Question 37/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

किस मान पर (\(s^2-1\)x^-8+(s+1)x^-6+5) की डिग्री (0) होगी?

For which value will (\(s^2-1\)x^-8+(s+1)x^-6+5) have degree (0)?

Explanation opens after your attempt

Correct Answer

B. (s=-1)

Step 1

Concept

For degree (0), both \(x^8\) and \(x^6\) terms must vanish. At (s=-1), both coefficients become (0).

Step 2

Why this answer is correct

The correct answer is B. (s=-1). For degree (0), both \(x^8\) and \(x^6\) terms must vanish. At (s=-1), both coefficients become (0).

Step 3

Exam Tip

डिग्री (0) के लिए \(x^8\) और \(x^6\) दोनों पद हटने चाहिए। (s=-1) पर दोनों गुणांक (0) हो जाते हैं।

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Question 38/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि (A(x)=x^-6+2x^-3+1) और (B(x)=x^-6+2x^-3), तो (A(x)-B(x)) की डिग्री क्या है?

If (A(x)=x^-6+2x^-3+1) and (B(x)=x^-6+2x^-3), what is the degree of (A(x)-B(x))?

Explanation opens after your attempt

Correct Answer

D. (0)

Step 1

Concept

On subtracting, (A(x)-B(x)=1). A non-zero constant polynomial has degree (0).

Step 2

Why this answer is correct

The correct answer is D. (0). On subtracting, (A(x)-B(x)=1). A non-zero constant polynomial has degree (0).

Step 3

Exam Tip

घटाने पर (A(x)-B(x)=1) मिलता है। अशून्य नियतांक बहुपद की डिग्री (0) होती है।

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Question 39/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि (A(x)=x^-5+4) और (B(x)=-x^-5+3x^-2), तो (A(x)+B(x)) की डिग्री क्या है?

If (A(x)=x^-5+4) and (B(x)=-x^-5+3x^-2), what is the degree of (A(x)+B(x))?

Explanation opens after your attempt

Correct Answer

C. (2)

Step 1

Concept

On adding, the \(x^5\) terms cancel and \(3x^2+4\) remains. Its degree is (2).

Step 2

Why this answer is correct

The correct answer is C. (2). On adding, the \(x^5\) terms cancel and \(3x^2+4\) remains. Its degree is (2).

Step 3

Exam Tip

जोड़ने पर \(x^5\) पद कटते हैं और \(3x^2+4\) बचता है। इसकी डिग्री (2) है।

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Question 40/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि (P(x)=\(x^2-3\)\(x^2+3\)-x^-4), तो (P(x)) की डिग्री क्या है?

If (P(x)=\(x^2-3\)\(x^2+3\)-x^-4), what is the degree of (P(x))?

Explanation opens after your attempt

Correct Answer

C. (0)

Step 1

Concept

(\(x^2-3\)\(x^2+3\)=x^-4-9). Subtracting \(x^4\) leaves (-9), whose degree is (0).

Step 2

Why this answer is correct

The correct answer is C. (0). (\(x^2-3\)\(x^2+3\)=x^-4-9). Subtracting \(x^4\) leaves (-9), whose degree is (0).

Step 3

Exam Tip

(\(x^2-3\)\(x^2+3\)=x^-4-9) होता है। \(x^4\) घटाने पर (-9) बचता है जिसकी डिग्री (0) है।

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Question 41/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

बहुपद \(2x^a+3x^b+1\) में (a=4) और (b=9) हो, तो डिग्री क्या है?

If (a=4) and (b=9) in \(2x^a+3x^b+1\), what is the degree?

Explanation opens after your attempt

Correct Answer

C. (9)

Step 1

Concept

Putting (a=4) and (b=9), the powers are (4), (9), and (0). The highest power is (9).

Step 2

Why this answer is correct

The correct answer is C. (9). Putting (a=4) and (b=9), the powers are (4), (9), and (0). The highest power is (9).

Step 3

Exam Tip

(a=4) और (b=9) रखने पर घातें (4), (9), और (0) हैं। सबसे बड़ी घात (9) है।

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Question 42/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

किस विकल्प में डिग्री (4) नहीं है?

Which option does not have degree (4)?

Explanation opens after your attempt

Correct Answer

D. \(x^4-x^4+7x\)

Step 1

Concept

The last option simplifies to (7x). Therefore its degree is (1), not (4).

Step 2

Why this answer is correct

The correct answer is D. \(x^4-x^4+7x\). The last option simplifies to (7x). Therefore its degree is (1), not (4).

Step 3

Exam Tip

अंतिम विकल्प सरल होकर (7x) बनता है। इसलिए उसकी डिग्री (1) है, (4) नहीं।

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Question 43/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि (p(x)=x^-2\(x^3+x\)-x^-5-x^-3+6), तो (p(x)) की डिग्री क्या है?

If (p(x)=x^-2\(x^3+x\)-x^-5-x^-3+6), what is the degree of (p(x))?

Explanation opens after your attempt

Correct Answer

C. (0)

Step 1

Concept

(x^-2\(x^3+x\)=x^-5+x^-3), and both variable terms cancel. The remaining (6) has degree (0).

Step 2

Why this answer is correct

The correct answer is C. (0). (x^-2\(x^3+x\)=x^-5+x^-3), and both variable terms cancel. The remaining (6) has degree (0).

Step 3

Exam Tip

(x^-2\(x^3+x\)=x^-5+x^-3) है और दोनों चर पद कट जाते हैं। बचा (6) है जिसकी डिग्री (0) है।

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Question 44/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

बहुपद (x^-2(x-1)²) की डिग्री क्या है?

What is the degree of (x^-2(x-1)²)?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

((x-1)²) has degree (2), and there is \(x^2\) outside. The total highest power is (2+2=4).

Step 2

Why this answer is correct

The correct answer is C. (4). ((x-1)²) has degree (2), and there is \(x^2\) outside. The total highest power is (2+2=4).

Step 3

Exam Tip

((x-1)²) की डिग्री (2) है और बाहर \(x^2\) है। कुल उच्चतम घात (2+2=4) होगी।

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Question 45/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि ((r-2)x^-7+(r-2)x^-3+8) की डिग्री (0) है, तो (r) का मान क्या है?

If the degree of ((r-2)x^-7+(r-2)x^-3+8) is (0), what is the value of (r)?

Explanation opens after your attempt

Correct Answer

A. (r=2)

Step 1

Concept

For degree (0), both variable terms must vanish. From (r-2=0), we get (r=2).

Step 2

Why this answer is correct

The correct answer is A. (r=2). For degree (0), both variable terms must vanish. From (r-2=0), we get (r=2).

Step 3

Exam Tip

डिग्री (0) के लिए दोनों चर पद हटने चाहिए। (r-2=0) से (r=2) मिलता है।

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Question 46/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि (p(x)) की डिग्री (4) और (q(x)) की डिग्री (3) है, तो (p(x)q(x)) की डिग्री सामान्यतः क्या होगी?

If the degree of (p(x)) is (4) and the degree of (q(x)) is (3), what will generally be the degree of (p(x)q(x))?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

For the product of non-zero polynomials, degrees generally add. Therefore (4+3=7).

Step 2

Why this answer is correct

The correct answer is C. (7). For the product of non-zero polynomials, degrees generally add. Therefore (4+3=7).

Step 3

Exam Tip

अशून्य बहुपदों के गुणन में डिग्री सामान्यतः जुड़ती है। इसलिए (4+3=7) होगा।

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Question 47/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

बहुपद \(x^3y^2+x^2y^4+xy\) की कुल डिग्री क्या है?

What is the total degree of \(x^3y^2+x^2y^4+xy\)?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

The total power of \(x^2y^4\) is (2+4=6). This is the highest total power.

Step 2

Why this answer is correct

The correct answer is C. (6). The total power of \(x^2y^4\) is (2+4=6). This is the highest total power.

Step 3

Exam Tip

\(x^2y^4\) की कुल घात (2+4=6) है। यह सबसे बड़ी कुल घात है।

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Question 48/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

किस मान पर (\(u^2-25\)x^-9+(u-5)x^-4+3) की डिग्री (0) होगी?

For which value will (\(u^2-25\)x^-9+(u-5)x^-4+3) have degree (0)?

Explanation opens after your attempt

Correct Answer

A. (u=5)

Step 1

Concept

For degree (0), both \(x^9\) and \(x^4\) terms must vanish. At (u=5), both coefficients are (0).

Step 2

Why this answer is correct

The correct answer is A. (u=5). For degree (0), both \(x^9\) and \(x^4\) terms must vanish. At (u=5), both coefficients are (0).

Step 3

Exam Tip

डिग्री (0) के लिए \(x^9\) और \(x^4\) दोनों पद हटने चाहिए। (u=5) पर दोनों गुणांक (0) हैं।

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Question 49/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि (F(x)=2x^-8-2x^-8+5x^-4-5x^-4+9x-1), तो (F(x)) की डिग्री क्या है?

If (F(x)=2x^-8-2x^-8+5x^-4-5x^-4+9x-1), what is the degree of (F(x))?

Explanation opens after your attempt

Correct Answer

C. (1)

Step 1

Concept

The \(x^8\) and \(x^4\) terms cancel. The remaining (9x-1) has degree (1).

Step 2

Why this answer is correct

The correct answer is C. (1). The \(x^8\) and \(x^4\) terms cancel. The remaining (9x-1) has degree (1).

Step 3

Exam Tip

\(x^8\) और \(x^4\) के पद कट जाते हैं। बचा (9x-1) है जिसकी डिग्री (1) है।

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Question 50/50 Hard Mathematics Introduction to Polynomials Degree of polynomial Class 9 Level 29

यदि (M(x)=\(x^3-2\)²-\(x^6-4x^3\)+7x^-2), तो (M(x)) की डिग्री क्या है?

If (M(x)=\(x^3-2\)²-\(x^6-4x^3\)+7x^-2), what is the degree of (M(x))?

Explanation opens after your attempt

Correct Answer

C. (2)

Step 1

Concept

(\(x^3-2\)²=x^-6-4x^-3+4), and after subtraction the higher variable terms cancel. The remaining \(7x^2+4\) has degree (2).

Step 2

Why this answer is correct

The correct answer is C. (2). (\(x^3-2\)²=x^-6-4x^-3+4), and after subtraction the higher variable terms cancel. The remaining \(7x^2+4\) has degree (2).

Step 3

Exam Tip

(\(x^3-2\)²=x^-6-4x^-3+4) होता है और घटाने पर चर के बड़े पद कट जाते हैं। बचा \(7x^2+4\) है जिसकी डिग्री (2) है।

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Class 9 Mathematics Hard Quiz

यदि (p(x)=(a-2)x-8+(a+1)x-5-3x+7) की डिग्री (5) है, तो (a) का सही मान कौन सा है?

Concept

Why this answer is correct

Exam Tip

सरल करने के बाद (x-3\(x^4-2\)-x-7+5x-2) की डिग्री क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (q(x)=\(k^2-9\)x-6+(k-3)x-4+2x-2) और (k=3), तो (q(x)) की डिग्री क्या है?

Concept

Why this answer is correct

Exam Tip

बहुपद (\(2x^3-5\)\(x^4+x^2+1\)) की डिग्री क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (f(x)=x-5-3x-5+2x-5+4x-1), तो (f(x)) की डिग्री क्या है?

Concept

Why this answer is correct

Exam Tip

बहुपद \(4x^2y^5-3x^4y^2+7xy-9\) की कुल डिग्री क्या है?

Concept

Why this answer is correct

Exam Tip

(x) के संदर्भ में \(6x^3y^7-4x^5y^2+9y-1\) की डिग्री क्या है?

Concept

Why this answer is correct

Exam Tip

(y) के संदर्भ में \(6x^3y^7-4x^5y^2+9y-1\) की डिग्री क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(2x^n+5x^7-3\) की डिग्री (n) है और (n>7), तो निम्न में से (n) का कौन सा मान संभव है?

Concept

Why this answer is correct

Exam Tip

यदि \(3x^m+4x^6-1\) की डिग्री (6) है और (m<6), तो (m) का संभावित मान कौन सा है?

Concept

Why this answer is correct

Exam Tip

बहुपद (\(x^2-1\)3) की डिग्री क्या है?

Concept

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बहुपद (\(x^3+2\)2-\(x^6+4x^3\)) की डिग्री क्या है?

Concept

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यदि \(a\neq1\), तो ((a-1)x^{10}+7x-4-8) की डिग्री क्या होगी?

Concept

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Exam Tip

यदि (a=1), तो ((a-1)x^{10}+7x-4-8) की डिग्री क्या होगी?

Concept

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बहुपद (\(x^2+x+1\)\(x^4-x^2+1\)) की डिग्री क्या है?

Concept

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Exam Tip

सरल करने के बाद (2x-4\(x^3-1\)-2x-7+9x-5) की डिग्री क्या है?

Concept

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बहुपद \(0x^{12}+0x^9+0x^2-17\) की डिग्री क्या है?

Concept

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किस विकल्प में बहुपद की डिग्री (7) है और \(x^6\) का गुणांक (0) है?

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यदि (g(x)=0), तो (g(x)) की डिग्री क्या है?

Concept

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Exam Tip

यदि (p(x)=x-2\(x^2-1\)-x-4+x-2+5), तो (p(x)) की डिग्री क्या है?

Concept

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यदि (p(x)=(a-2)x^-8+(a+1)x^-5-3x+7) की डिग्री (5) है, तो (a) का सही मान कौन सा है?

सरल करने के बाद (x^-3\(x^4-2\)-x^-7+5x^-2) की डिग्री क्या है?

यदि (q(x)=\(k^2-9\)x^-6+(k-3)x^-4+2x^-2) और (k=3), तो (q(x)) की डिग्री क्या है?

यदि (f(x)=x^-5-3x^-5+2x^-5+4x-1), तो (f(x)) की डिग्री क्या है?

बहुपद (\(x^2-1\)³) की डिग्री क्या है?

बहुपद (\(x^3+2\)²-\(x^6+4x^3\)) की डिग्री क्या है?

यदि \(a\neq1\), तो ((a-1)x^{10}+7x^-4-8) की डिग्री क्या होगी?

यदि (a=1), तो ((a-1)x^{10}+7x^-4-8) की डिग्री क्या होगी?

सरल करने के बाद (2x^-4\(x^3-1\)-2x^-7+9x^-5) की डिग्री क्या है?

यदि (p(x)=x^-2\(x^2-1\)-x^-4+x^-2+5), तो (p(x)) की डिग्री क्या है?

बहुपद (\(x^2+2x\)\(x^3-x\)-x^-5) की डिग्री क्या है?

यदि ((c+2)x^-5+\(c^2-4\)x^-3+9) की डिग्री (0) है, तो (c) का मान क्या है?

किस मान पर ((d-1)x^-4+(d+3)x^-2+6) की डिग्री (2) होगी?

यदि (h(x)=\(x^2+x\)²-x^-4-2x^-3), तो (h(x)) की डिग्री क्या है?

बहुपद (x^-4\(x^2+1\)-x^-2\(x^4-3\)) की डिग्री क्या है?

यदि (e=0), तो (ex^-9+(e-2)x^-7+5x^-2-1) की डिग्री क्या है?

यदि (p(x)=0x^-5+0x^-3+0x+0), तो (p(x)) की डिग्री क्या है?

किस मान पर (\(s^2-1\)x^-8+(s+1)x^-6+5) की डिग्री (0) होगी?

यदि (A(x)=x^-6+2x^-3+1) और (B(x)=x^-6+2x^-3), तो (A(x)-B(x)) की डिग्री क्या है?