Class 10 degree MCQ Questions

Question 1/94 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=ax^-2+bx+c) और (p(1)=p(2)=p(3)=0), तो कौन-सा निष्कर्ष सही है?

If (p(x)=ax^-2+bx+c) and (p(1)=p(2)=p(3)=0), which conclusion is correct?

Explanation opens after your attempt

Correct Answer

A. (p(x)) शून्य बहुपद है(p(x)) is the zero polynomial

Step 1

Concept

A polynomial of degree at most (2) can have three distinct zeroes only if it is the zero polynomial. A non-zero polynomial cannot have more distinct zeroes than its degree.

Step 2

Why this answer is correct

The correct answer is A. (p(x)) शून्य बहुपद है / (p(x)) is the zero polynomial. A polynomial of degree at most (2) can have three distinct zeroes only if it is the zero polynomial. A non-zero polynomial cannot have more distinct zeroes than its degree.

Step 3

Exam Tip

अधिकतम द्विघात बहुपद के तीन अलग-अलग शून्यक तभी हो सकते हैं जब वह शून्य बहुपद हो। घात से अधिक अलग शून्यक असंभव होते हैं।

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Question 2/94 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=(k-3)x^-5+2x^-3-x+9) की घात (3) है, तो (k) क्या है?

If (p(x)=(k-3)x^-5+2x^-3-x+9) has degree (3), what is (k)?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

For degree (3), the coefficient of \(x^5\) must be (0). Thus (k-3=0) and (k=3).

Step 2

Why this answer is correct

The correct answer is A. (3). For degree (3), the coefficient of \(x^5\) must be (0). Thus (k-3=0) and (k=3).

Step 3

Exam Tip

घात (3) होने के लिए \(x^5\) का गुणांक (0) होना चाहिए। इसलिए (k-3=0) और (k=3)।

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Question 3/94 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=mx^-5+(m^-4)x^-4+3x^-2+1) की घात (4) है, तो (m) क्या है?

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

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

For degree (4), the coefficient of \(x^5\) must be (0) and the coefficient of \(x^4\) must be non-zero. For (m=0), (m^-4=-4).

Step 2

Why this answer is correct

The correct answer is A. (0). For degree (4), the coefficient of \(x^5\) must be (0) and the coefficient of \(x^4\) must be non-zero. For (m=0), (m^-4=-4).

Step 3

Exam Tip

घात (4) के लिए \(x^5\) का गुणांक (0) और \(x^4\) का गुणांक अशून्य चाहिए। (m=0) पर (m^-4=-4) है।

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Question 4/94 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=ax^-5+bx^-4+cx^-3+d) में (a=0), \(b\ne0\) और \(c\ne0\), तो (p(x)) की घात क्या होगी?

If (a=0), \(b\ne0\), and \(c\ne0\) in (p(x)=ax^-5+bx^-4+cx^-3+d), what will be the degree of (p(x))?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

Since (a=0), the \(x^5\)-term vanishes, and since \(b\ne0\), the \(x^4\)-term remains. So the degree is (4).

Step 2

Why this answer is correct

The correct answer is B. (4). Since (a=0), the \(x^5\)-term vanishes, and since \(b\ne0\), the \(x^4\)-term remains. So the degree is (4).

Step 3

Exam Tip

(a=0) से \(x^5\) पद हट जाता है और \(b\ne0\) से \(x^4\) पद बचता है। इसलिए घात (4) है।

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Question 5/94 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि अशून्य बहुपद (p(x)) की घात (6) और (q(x)) की घात (3) है, तो (p(x)q(x)) की घात क्या होगी?

If non-zero polynomial (p(x)) has degree (6) and (q(x)) has degree (3), what will be the degree of (p(x)q(x))?

Explanation opens after your attempt

Correct Answer

C. (9)

Step 1

Concept

In the product of two non-zero polynomials, degrees add, so (6+3=9). In multiplication, look at the highest-power terms.

Step 2

Why this answer is correct

The correct answer is C. (9). In the product of two non-zero polynomials, degrees add, so (6+3=9). In multiplication, look at the highest-power terms.

Step 3

Exam Tip

दो अशून्य बहुपदों के गुणन में घातें जुड़ती हैं, इसलिए (6+3=9)। गुणन में उच्चतम घातों का गुणन देखें।

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Question 6/94 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(p(x)=6x^-5-4x^-2+1) और (q(x)=-6x^-5+3x^-4+x-9) के योग की घात क्या है?

What is the degree of the sum of (p(x)=6x^-5-4x^-2+1) and (q(x)=-6x^-5+3x^-4+x-9)?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

The \(x^5\)-terms cancel and the highest remaining power is (4). Recheck the degree of the polynomial after addition.

Step 2

Why this answer is correct

The correct answer is C. (4). The \(x^5\)-terms cancel and the highest remaining power is (4). Recheck the degree of the polynomial after addition.

Step 3

Exam Tip

\(x^5\) के पद कट जाते हैं और सबसे बड़ी बची घात (4) है। जोड़ के बाद बहुपद की घात फिर से जांचें।

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Question 7/94 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=(a-1)x^-6+(a+2)x^-4-5x+7) की घात (4) है, तो (a) क्या होगा?

If the degree of (p(x)=(a-1)x^-6+(a+2)x^-4-5x+7) is (4), what will (a) be?

Explanation opens after your attempt

Correct Answer

B. (1)

Step 1

Concept

For degree (4), the coefficient of \(x^6\) must be (0) and the coefficient of \(x^4\) must be non-zero. Both conditions hold for (a=1).

Step 2

Why this answer is correct

The correct answer is B. (1). For degree (4), the coefficient of \(x^6\) must be (0) and the coefficient of \(x^4\) must be non-zero. Both conditions hold for (a=1).

Step 3

Exam Tip

घात (4) के लिए \(x^6\) का गुणांक (0) और \(x^4\) का गुणांक अशून्य चाहिए। (a=1) पर दोनों शर्तें पूरी होती हैं।

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Question 8/94 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 46

निम्न में से कौन-सा (x) में रेखीय बहुपद है?

Which of the following is a linear polynomial in (x)?

Explanation opens after your attempt

Correct Answer

A. (5x-9)

Step 1

Concept

A linear polynomial has degree (1), so (5x-9) is linear. Its leading coefficient must be non-zero.

Step 2

Why this answer is correct

The correct answer is A. (5x-9). A linear polynomial has degree (1), so (5x-9) is linear. Its leading coefficient must be non-zero.

Step 3

Exam Tip

रेखीय बहुपद की घात (1) होती है, इसलिए (5x-9) रेखीय है। प्रमुख गुणांक शून्य नहीं होना चाहिए।

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Question 9/94 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 46

निम्न में से कौन-सा स्थिर बहुपद है?

Which of the following is a constant polynomial?

Explanation opens after your attempt

Correct Answer

A. (7)

Step 1

Concept

A constant polynomial has no variable term, so (7) is a constant polynomial. A non-zero constant polynomial has degree (0).

Step 2

Why this answer is correct

The correct answer is A. (7). A constant polynomial has no variable term, so (7) is a constant polynomial. A non-zero constant polynomial has degree (0).

Step 3

Exam Tip

स्थिर बहुपद में चर का पद नहीं होता, इसलिए (7) स्थिर बहुपद है। अशून्य स्थिर बहुपद की घात (0) होती है।

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Question 10/94 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 46

कौन-सा कथन सही है: (p(x)=0) जहाँ (p(x)) शून्य बहुपद है?

Which statement is correct for (p(x)=0), where (p(x)) is the zero polynomial?

Explanation opens after your attempt

Correct Answer

A. इसकी घात परिभाषित नहीं होतीIts degree is not defined

Step 1

Concept

The zero polynomial has no non-zero term, so its degree is not defined. A non-zero constant polynomial has degree (0).

Step 2

Why this answer is correct

The correct answer is A. इसकी घात परिभाषित नहीं होती / Its degree is not defined. The zero polynomial has no non-zero term, so its degree is not defined. A non-zero constant polynomial has degree (0).

Step 3

Exam Tip

शून्य बहुपद में कोई अशून्य पद नहीं होता, इसलिए उसकी घात परिभाषित नहीं होती। स्थिर अशून्य बहुपद की घात (0) होती है।

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Question 11/94 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 46

किस मान के लिए (p(x)=(m^-2)x^-4+3x^-2+x+1) की घात (2) से अधिक नहीं होगी?

For which value will (p(x)=(m^-2)x^-4+3x^-2+x+1) have degree not more than (2)?

Explanation opens after your attempt

Correct Answer

A. (m=2)

Step 1

Concept

To make the degree not more than (2), the coefficient of \(x^4\) must be (0), so (m^-2=0). Degree reduces only when the highest term vanishes.

Step 2

Why this answer is correct

The correct answer is A. (m=2). To make the degree not more than (2), the coefficient of \(x^4\) must be (0), so (m^-2=0). Degree reduces only when the highest term vanishes.

Step 3

Exam Tip

घात (2) से अधिक न हो इसके लिए \(x^4\) का गुणांक (0) चाहिए, अतः (m^-2=0)। उच्चतम पद हटाकर ही घात घटती है।

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Question 12/94 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि बहुपद (p(x)=kx^-3+2x^-2-3x+1) वास्तव में द्विघात बहुपद है, तो (k) का मान क्या होगा?

If (p(x)=kx^-3+2x^-2-3x+1) is actually a quadratic polynomial, what must be the value of (k)?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

For it to be quadratic, the coefficient of \(x^3\) must be (0), while the coefficient of \(x^2\) is non-zero. Focus on the leading non-zero term.

Step 2

Why this answer is correct

The correct answer is A. (0). For it to be quadratic, the coefficient of \(x^3\) must be (0), while the coefficient of \(x^2\) is non-zero. Focus on the leading non-zero term.

Step 3

Exam Tip

द्विघात होने के लिए \(x^3\) का गुणांक (0) होना चाहिए और \(x^2\) का गुणांक अशून्य है। घात पहचानते समय प्रमुख पद पर ध्यान दें।

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Question 13/94 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)=x^-4-5x^-2+4) है, तो (p(x)) का घात कितना है?

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

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

The highest power is \(x^4\), so the degree is (4). Terms with zero coefficients do not affect the degree.

Step 2

Why this answer is correct

The correct answer is A. (4). The highest power is \(x^4\), so the degree is (4). Terms with zero coefficients do not affect the degree.

Step 3

Exam Tip

सबसे बड़ी घात \(x^4\) है, इसलिए घात (4) है। शून्य गुणांक वाले पदों को घात तय करने में नहीं गिनते।

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Question 14/94 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=mx^-4+(m+2)x^-3+5x+1) की घात (3) है, तो (m) क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (0)

Step 1

Concept

For degree (3), the coefficient of \(x^4\) must be (0) and the coefficient of \(x^3\) must be non-zero. For (m=0), (m+2=2).

Step 2

Why this answer is correct

The correct answer is B. (0). For degree (3), the coefficient of \(x^4\) must be (0) and the coefficient of \(x^3\) must be non-zero. For (m=0), (m+2=2).

Step 3

Exam Tip

घात (3) के लिए \(x^4\) का गुणांक (0) चाहिए और \(x^3\) का गुणांक अशून्य चाहिए। (m=0) पर (m+2=2) है।

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Question 15/94 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=ax^-4+bx^-3+cx^-2+d) में (a=0), (b=0) और \(c\ne0\), तो (p(x)) की घात क्या होगी?

If (a=0), (b=0), and \(c\ne0\) in (p(x)=ax^-4+bx^-3+cx^-2+d), what will be the degree of (p(x))?

Explanation opens after your attempt

Correct Answer

C. (2)

Step 1

Concept

The \(x^4\)- and \(x^3\)-terms vanish, but \(c\ne0\) keeps the \(x^2\)-term. So the degree is (2).

Step 2

Why this answer is correct

The correct answer is C. (2). The \(x^4\)- and \(x^3\)-terms vanish, but \(c\ne0\) keeps the \(x^2\)-term. So the degree is (2).

Step 3

Exam Tip

\(x^4\) और \(x^3\) के पद हट जाते हैं, लेकिन \(c\ne0\) से \(x^2\) पद बचता है। इसलिए घात (2) है।

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Question 16/94 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)) की घात (5) और (q(x)) की घात (2) है, तो अशून्य (p(x)q(x)) की घात क्या होगी?

If the degree of (p(x)) is (5) and the degree of (q(x)) is (2), what is the degree of non-zero (p(x)q(x))?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

In the product of two non-zero polynomials, degrees add, so (5+2=7). Remember degree addition in multiplication.

Step 2

Why this answer is correct

The correct answer is C. (7). In the product of two non-zero polynomials, degrees add, so (5+2=7). Remember degree addition in multiplication.

Step 3

Exam Tip

दो अशून्य बहुपदों के गुणन में घातें जुड़ती हैं, इसलिए (5+2=7)। गुणन में घातों का योग याद रखें।

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Question 17/94 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 48

(p(x)=5x^-4-2x^-2+1) और (q(x)=-5x^-4+3x^-3+x-6) के योग की घात क्या है?

What is the degree of the sum of (p(x)=5x^-4-2x^-2+1) and (q(x)=-5x^-4+3x^-3+x-6)?

Explanation opens after your attempt

Correct Answer

C. (3)

Step 1

Concept

The \(x^4\)-terms cancel and the highest remaining power is (3). Recheck the degree after addition.

Step 2

Why this answer is correct

The correct answer is C. (3). The \(x^4\)-terms cancel and the highest remaining power is (3). Recheck the degree after addition.

Step 3

Exam Tip

\(x^4\) के पद कट जाते हैं और सबसे बड़ी बची घात (3) है। जोड़ के बाद घात दोबारा जांचना जरूरी है।

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Question 18/94 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=(m+2)x^-5+(m^-3)x^-4+6x-1) की घात (4) है, तो (m) क्या होगा?

If the degree of (p(x)=(m+2)x^-5+(m^-3)x^-4+6x-1) is (4), what is (m)?

Explanation opens after your attempt

Correct Answer

A. (-2)

Step 1

Concept

For degree (4), the coefficient of \(x^5\) must be (0) and the coefficient of \(x^4\) must be non-zero. Both conditions hold for (m=-2).

Step 2

Why this answer is correct

The correct answer is A. (-2). For degree (4), the coefficient of \(x^5\) must be (0) and the coefficient of \(x^4\) must be non-zero. Both conditions hold for (m=-2).

Step 3

Exam Tip

घात (4) के लिए \(x^5\) का गुणांक (0) और \(x^4\) का गुणांक अशून्य चाहिए। (m=-2) पर दोनों शर्तें पूरी होती हैं।

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Question 19/94 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

\(x^4-1\) के रैखिक गुणनखंडों में से कौन सा गलत है?

Which one is not a linear factor of \(x^4-1\)?

Explanation opens after your attempt

Correct Answer

C. \(x^2+1\)

Step 1

Concept

\(x^2+1\) is not linear because its degree is (2). Over real numbers, it is not a linear factor.

Step 2

Why this answer is correct

The correct answer is C. \(x^2+1\). \(x^2+1\) is not linear because its degree is (2). Over real numbers, it is not a linear factor.

Step 3

Exam Tip

\(x^2+1\) रैखिक नहीं है क्योंकि उसकी घात (2) है। वास्तविक संख्याओं में इसे रैखिक गुणनखंड नहीं माना जाता।

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Question 20/94 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

किस बहुपद की घात (4) है?

Which polynomial has degree (4)?

Explanation opens after your attempt

Correct Answer

A. \(7x^4+0x^5-3x+1\)

Step 1

Concept

The term \(0x^5\) does not affect degree because its coefficient is (0). The highest non-zero power is (4).

Step 2

Why this answer is correct

The correct answer is A. \(7x^4+0x^5-3x+1\). The term \(0x^5\) does not affect degree because its coefficient is (0). The highest non-zero power is (4).

Step 3

Exam Tip

\(0x^5\) पद घात नहीं बढ़ाता क्योंकि उसका गुणांक (0) है। सबसे बड़ा शून्येतर घात (4) है।

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Question 21/94 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

बहुपद (p(x)=ax^-3+bx^-2+cx+d) में \(a\ne0\) है। यदि (p(x)) को रैखिक बहुपद कहा जाए, तो यह कथन क्यों गलत है?

In the polynomial (p(x)=ax^-3+bx^-2+cx+d), \(a\ne0\). Why is it wrong to call (p(x)) a linear polynomial?

Explanation opens after your attempt

Correct Answer

C. क्योंकि घात (3) हैBecause degree is (3)

Step 1

Concept

The highest power is (3), so the polynomial is cubic. In exams, always check the highest non-zero exponent.

Step 2

Why this answer is correct

The correct answer is C. क्योंकि घात (3) है / Because degree is (3). The highest power is (3), so the polynomial is cubic. In exams, always check the highest non-zero exponent.

Step 3

Exam Tip

सबसे बड़ी घात (3) है इसलिए बहुपद घन है। परीक्षा में हमेशा सबसे बड़े शून्येतर घातांक को देखें।

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Question 22/94 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=mx^-3+(m^-1)x^-2+2x+1) की घात (2) है, तो (m) क्या है?

If the degree of (p(x)=mx^-3+(m^-1)x^-2+2x+1) is (2), what is (m)?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

For degree (2), the coefficient of \(x^3\) must be (0) and the coefficient of \(x^2\) must be non-zero. Both conditions hold when (m=0).

Step 2

Why this answer is correct

The correct answer is A. (0). For degree (2), the coefficient of \(x^3\) must be (0) and the coefficient of \(x^2\) must be non-zero. Both conditions hold when (m=0).

Step 3

Exam Tip

घात (2) के लिए \(x^3\) का गुणांक (0) चाहिए और \(x^2\) का गुणांक अशून्य चाहिए। (m=0) पर ये दोनों शर्तें पूरी होती हैं।

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Question 23/94 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=ax^-3+bx^-2+cx+d) में (a=0) और \(b\ne0\), तो (p(x)) की घात क्या होगी?

If (a=0) and \(b\ne0\) in (p(x)=ax^-3+bx^-2+cx+d), what will be the degree of (p(x))?

Explanation opens after your attempt

Correct Answer

C. (2)

Step 1

Concept

Since (a=0), the \(x^3\)-term vanishes, and since \(b\ne0\), the \(x^2\)-term remains. So the degree is (2).

Step 2

Why this answer is correct

The correct answer is C. (2). Since (a=0), the \(x^3\)-term vanishes, and since \(b\ne0\), the \(x^2\)-term remains. So the degree is (2).

Step 3

Exam Tip

(a=0) होने से \(x^3\) पद हट जाता है और \(b\ne0\) होने से \(x^2\) पद बचता है। इसलिए घात (2) है।

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Question 24/94 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)) की घात (4) और (q(x)) की घात (3) है, तो सामान्यतः (p(x)q(x)) की घात 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

B. (7)

Step 1

Concept

In the product of two non-zero polynomials, degrees add, so (4+3=7). Remember degree addition in multiplication.

Step 2

Why this answer is correct

The correct answer is B. (7). In the product of two non-zero polynomials, degrees add, so (4+3=7). Remember degree addition in multiplication.

Step 3

Exam Tip

दो अशून्य बहुपदों के गुणन में घातें जुड़ती हैं, इसलिए (4+3=7)। गुणन में घातों का योग याद रखें।

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Question 25/94 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(p(x)=4x^-4-3x^-2+2) और (q(x)=-4x^-4+5x^-3+x-8) के योग की घात क्या है?

What is the degree of the sum of (p(x)=4x^-4-3x^-2+2) and (q(x)=-4x^-4+5x^-3+x-8)?

Explanation opens after your attempt

Correct Answer

C. (3)

Step 1

Concept

The \(x^4\)-terms cancel and the highest remaining power is (3). Recheck the degree after addition.

Step 2

Why this answer is correct

The correct answer is C. (3). The \(x^4\)-terms cancel and the highest remaining power is (3). Recheck the degree after addition.

Step 3

Exam Tip

\(x^4\) के पद कट जाते हैं और सबसे बड़ी बची घात (3) है। जोड़ के बाद घात फिर से जांचें।

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Question 26/94 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=(a-5)x^-5+2x^-3-7x+4) की घात (3) है, तो (a) क्या होगा?

If the degree of (p(x)=(a-5)x^-5+2x^-3-7x+4) is (3), what is (a)?

Explanation opens after your attempt

Correct Answer

C. (5)

Step 1

Concept

For the degree to be (3), the coefficient of \(x^5\) must be (0), so (a-5=0). First make the highest-degree term vanish.

Step 2

Why this answer is correct

The correct answer is C. (5). For the degree to be (3), the coefficient of \(x^5\) must be (0), so (a-5=0). First make the highest-degree term vanish.

Step 3

Exam Tip

घात (3) होने के लिए \(x^5\) का गुणांक (0) होना चाहिए, इसलिए (a-5=0)। उच्चतम घात वाले पद को पहले शून्य करें।

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Question 27/94 Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=(k-4)x^-4+3x^-2-5x+2) की घात (2) है, तो (k) का मान क्या होगा?

If the degree of (p(x)=(k-4)x^-4+3x^-2-5x+2) is (2), what will be the value of (k)?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

For the degree to be (2), the coefficient of \(x^4\) must be (0), so (k-4=0) and (k=4). Check the coefficient of the highest power first.

Step 2

Why this answer is correct

The correct answer is C. (4). For the degree to be (2), the coefficient of \(x^4\) must be (0), so (k-4=0) and (k=4). Check the coefficient of the highest power first.

Step 3

Exam Tip

घात (2) होने के लिए \(x^4\) का गुणांक (0) होना चाहिए, इसलिए (k-4=0) और (k=4)। सबसे बड़ी घात वाले पद का गुणांक पहले जांचें।

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Question 28/94 Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 48

कौन सा कथन (p(x)=x^-3+1) के बारे में सही है?

Which statement about (p(x)=x^-3+1) is correct?

Explanation opens after your attempt

Correct Answer

C. यह घन बहुपद हैIt is a cubic polynomial

Step 1

Concept

In (p(x)=x^-3+1), the highest power is (3), so it is a cubic polynomial. Decide the type of a polynomial by its degree.

Step 2

Why this answer is correct

The correct answer is C. यह घन बहुपद है / It is a cubic polynomial. In (p(x)=x^-3+1), the highest power is (3), so it is a cubic polynomial. Decide the type of a polynomial by its degree.

Step 3

Exam Tip

(p(x)=x^-3+1) में सबसे बड़ी घात (3) है इसलिए यह घन बहुपद है। बहुपद का प्रकार उसकी घात से तय करें।

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Question 29/94 Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 48

बहुपद (p(z)=-6z^-5+4z^-4-z+8) का अग्र गुणांक क्या है?

What is the leading coefficient of (p(z)=-6z^-5+4z^-4-z+8)?

Explanation opens after your attempt

Correct Answer

A. (-6)

Step 1

Concept

The coefficient of the highest power term \(z^5\) is (-6). The leading coefficient is written with its sign.

Step 2

Why this answer is correct

The correct answer is A. (-6). The coefficient of the highest power term \(z^5\) is (-6). The leading coefficient is written with its sign.

Step 3

Exam Tip

सबसे बड़ी घात \(z^5\) के पद का गुणांक (-6) है। अग्र गुणांक संकेत सहित लिखा जाता है।

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Question 30/94 Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 48

किसी रैखिक बहुपद (mx+n) में \(m\ne0\) हो तो उसकी घात क्या है?

If \(m\ne0\) in a linear polynomial (mx+n), what is its degree?

Explanation opens after your attempt

Correct Answer

B. (1)

Step 1

Concept

When \(m\ne0\), the term (mx) exists and the highest power is (1). So the degree is (1).

Step 2

Why this answer is correct

The correct answer is B. (1). When \(m\ne0\), the term (mx) exists and the highest power is (1). So the degree is (1).

Step 3

Exam Tip

\(m\ne0\) होने पर (mx) पद मौजूद रहता है और सबसे बड़ी घात (1) होती है। इसलिए घात (1) है।

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degree MCQ Questions for Class 10

Practice Questions

यदि (p(x)=ax-2+bx+c) और (p(1)=p(2)=p(3)=0), तो कौन-सा निष्कर्ष सही है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=(k-3)x-5+2x-3-x+9) की घात (3) है, तो (k) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=mx-5+(m-4)x-4+3x-2+1) की घात (4) है, तो (m) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=ax-5+bx-4+cx-3+d) में (a=0), \(b\ne0\) और \(c\ne0\), तो (p(x)) की घात क्या होगी?

Concept

Why this answer is correct

Exam Tip

यदि अशून्य बहुपद (p(x)) की घात (6) और (q(x)) की घात (3) है, तो (p(x)q(x)) की घात क्या होगी?

Concept

Why this answer is correct

Exam Tip

(p(x)=6x-5-4x-2+1) और (q(x)=-6x-5+3x-4+x-9) के योग की घात क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=(a-1)x-6+(a+2)x-4-5x+7) की घात (4) है, तो (a) क्या होगा?

Concept

Why this answer is correct

Exam Tip

निम्न में से कौन-सा (x) में रेखीय बहुपद है?

Concept

Why this answer is correct

Exam Tip

निम्न में से कौन-सा स्थिर बहुपद है?

Concept

Why this answer is correct

Exam Tip

कौन-सा कथन सही है: (p(x)=0) जहाँ (p(x)) शून्य बहुपद है?

Concept

Why this answer is correct

Exam Tip

किस मान के लिए (p(x)=(m-2)x-4+3x-2+x+1) की घात (2) से अधिक नहीं होगी?

Concept

Why this answer is correct

Exam Tip

यदि बहुपद (p(x)=kx-3+2x-2-3x+1) वास्तव में द्विघात बहुपद है, तो (k) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-4-5x-2+4) है, तो (p(x)) का घात कितना है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=mx-4+(m+2)x-3+5x+1) की घात (3) है, तो (m) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=ax-4+bx-3+cx-2+d) में (a=0), (b=0) और \(c\ne0\), तो (p(x)) की घात क्या होगी?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)) की घात (5) और (q(x)) की घात (2) है, तो अशून्य (p(x)q(x)) की घात क्या होगी?

Concept

Why this answer is correct

Exam Tip

(p(x)=5x-4-2x-2+1) और (q(x)=-5x-4+3x-3+x-6) के योग की घात क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=(m+2)x-5+(m-3)x-4+6x-1) की घात (4) है, तो (m) क्या होगा?

Concept

Why this answer is correct

Exam Tip

\(x^4-1\) के रैखिक गुणनखंडों में से कौन सा गलत है?

Concept

Why this answer is correct

Exam Tip

किस बहुपद की घात (4) है?

Concept

यदि (p(x)=ax^-2+bx+c) और (p(1)=p(2)=p(3)=0), तो कौन-सा निष्कर्ष सही है?

यदि (p(x)=(k-3)x^-5+2x^-3-x+9) की घात (3) है, तो (k) क्या है?

यदि (p(x)=mx^-5+(m^-4)x^-4+3x^-2+1) की घात (4) है, तो (m) क्या है?

यदि (p(x)=ax^-5+bx^-4+cx^-3+d) में (a=0), \(b\ne0\) और \(c\ne0\), तो (p(x)) की घात क्या होगी?

(p(x)=6x^-5-4x^-2+1) और (q(x)=-6x^-5+3x^-4+x-9) के योग की घात क्या है?

यदि (p(x)=(a-1)x^-6+(a+2)x^-4-5x+7) की घात (4) है, तो (a) क्या होगा?

किस मान के लिए (p(x)=(m^-2)x^-4+3x^-2+x+1) की घात (2) से अधिक नहीं होगी?

यदि बहुपद (p(x)=kx^-3+2x^-2-3x+1) वास्तव में द्विघात बहुपद है, तो (k) का मान क्या होगा?

यदि (p(x)=x^-4-5x^-2+4) है, तो (p(x)) का घात कितना है?

यदि (p(x)=mx^-4+(m+2)x^-3+5x+1) की घात (3) है, तो (m) क्या है?

यदि (p(x)=ax^-4+bx^-3+cx^-2+d) में (a=0), (b=0) और \(c\ne0\), तो (p(x)) की घात क्या होगी?

(p(x)=5x^-4-2x^-2+1) और (q(x)=-5x^-4+3x^-3+x-6) के योग की घात क्या है?

यदि (p(x)=(m+2)x^-5+(m^-3)x^-4+6x-1) की घात (4) है, तो (m) क्या होगा?

बहुपद (p(x)=ax^-3+bx^-2+cx+d) में \(a\ne0\) है। यदि (p(x)) को रैखिक बहुपद कहा जाए, तो यह कथन क्यों गलत है?

यदि (p(x)=mx^-3+(m^-1)x^-2+2x+1) की घात (2) है, तो (m) क्या है?

यदि (p(x)=ax^-3+bx^-2+cx+d) में (a=0) और \(b\ne0\), तो (p(x)) की घात क्या होगी?

(p(x)=4x^-4-3x^-2+2) और (q(x)=-4x^-4+5x^-3+x-8) के योग की घात क्या है?

यदि (p(x)=(a-5)x^-5+2x^-3-7x+4) की घात (3) है, तो (a) क्या होगा?

यदि (p(x)=(k-4)x^-4+3x^-2-5x+2) की घात (2) है, तो (k) का मान क्या होगा?

कौन सा कथन (p(x)=x^-3+1) के बारे में सही है?

बहुपद (p(z)=-6z^-5+4z^-4-z+8) का अग्र गुणांक क्या है?