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100 results found for "minimum degree" in Class 10.

Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि कोई बहुपद (x)-अक्ष को छह अलग बिंदुओं पर काटता है तो न्यूनतम संभावित घात क्या होगी?

If a polynomial cuts the (x)-axis at six distinct points, what is the minimum possible degree?

Explanation opens after your attempt
Correct Answer

C. (6)

Step 1

Concept

For six distinct real zeroes, the degree must be at least (6). Tip: the number of distinct zeroes cannot exceed the degree.

Step 2

Why this answer is correct

The correct answer is C. (6). For six distinct real zeroes, the degree must be at least (6). Tip: the number of distinct zeroes cannot exceed the degree.

Step 3

Exam Tip

छह अलग वास्तविक शून्यकों के लिए घात कम से कम (6) होनी चाहिए। टिप: अलग शून्यकों की संख्या घात से अधिक नहीं हो सकती।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि किसी बहुपद का ग्राफ (x)-अक्ष को तीन अलग बिंदुओं पर काटता है, तो बहुपद की न्यूनतम संभावित घात क्या हो सकती है?

If a polynomial graph cuts the (x)-axis at three distinct points, what can be the minimum possible degree of the polynomial?

Explanation opens after your attempt
Correct Answer

C. (3)

Step 1

Concept

For three distinct real zeroes, the degree must be at least (3). Tip: the number of distinct zeroes cannot exceed the degree.

Step 2

Why this answer is correct

The correct answer is C. (3). For three distinct real zeroes, the degree must be at least (3). Tip: the number of distinct zeroes cannot exceed the degree.

Step 3

Exam Tip

तीन अलग वास्तविक शून्यकों के लिए घात कम से कम (3) होनी चाहिए। टिप: अलग शून्यकों की संख्या घात से अधिक नहीं हो सकती।

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Question 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 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 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 Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि कोई बहुपद (x)-अक्ष को आठ अलग बिंदुओं पर काटता है, तो न्यूनतम संभावित घात क्या होगी?

If a polynomial cuts the (x)-axis at eight distinct points, what is the minimum possible degree?

Explanation opens after your attempt
Correct Answer

C. (8)

Step 1

Concept

For eight distinct real zeroes, the degree must be at least (8). Tip: the number of distinct zeroes cannot exceed the degree.

Step 2

Why this answer is correct

The correct answer is C. (8). For eight distinct real zeroes, the degree must be at least (8). Tip: the number of distinct zeroes cannot exceed the degree.

Step 3

Exam Tip

आठ अलग वास्तविक शून्यकों के लिए घात कम से कम (8) होनी चाहिए। टिप: अलग शून्यकों की संख्या घात से अधिक नहीं हो सकती।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि कोई बहुपद (x)-अक्ष को सात अलग बिंदुओं पर काटता है, तो न्यूनतम संभावित घात क्या होगी?

If a polynomial cuts the (x)-axis at seven distinct points, what is the minimum possible degree?

Explanation opens after your attempt
Correct Answer

C. (7)

Step 1

Concept

For seven distinct real zeroes, the degree must be at least (7). Tip: the number of distinct zeroes cannot exceed the degree.

Step 2

Why this answer is correct

The correct answer is C. (7). For seven distinct real zeroes, the degree must be at least (7). Tip: the number of distinct zeroes cannot exceed the degree.

Step 3

Exam Tip

सात अलग वास्तविक शून्यकों के लिए घात कम से कम (7) होनी चाहिए। टिप: अलग शून्यकों की संख्या घात से अधिक नहीं हो सकती।

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Question Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि कोई बहुपद (x)-अक्ष को चार अलग बिंदुओं पर काटता है, तो न्यूनतम संभावित घात क्या होगी?

If a polynomial cuts the (x)-axis at four distinct points, what is the minimum possible degree?

Explanation opens after your attempt
Correct Answer

C. (4)

Step 1

Concept

For four distinct real zeroes, the degree must be at least (4). Tip: the number of distinct zeroes cannot exceed the degree.

Step 2

Why this answer is correct

The correct answer is C. (4). For four distinct real zeroes, the degree must be at least (4). Tip: the number of distinct zeroes cannot exceed the degree.

Step 3

Exam Tip

चार अलग वास्तविक शून्यकों के लिए घात कम से कम (4) होनी चाहिए। टिप: अलग शून्यकों की संख्या घात से अधिक नहीं हो सकती।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

एक ग्राफ (x)-अक्ष को तीन बार काटता है। उस बहुपद की न्यूनतम संभावित डिग्री क्या हो सकती है?

A graph cuts the (x)-axis three times. What can be the minimum possible degree of that polynomial?

Explanation opens after your attempt
Correct Answer

A. (3)

Step 1

Concept

The number of real zeroes cannot exceed the degree of the polynomial. Three crossings need minimum degree (3).

Step 2

Why this answer is correct

The correct answer is A. (3). The number of real zeroes cannot exceed the degree of the polynomial. Three crossings need minimum degree (3).

Step 3

Exam Tip

किसी बहुपद के वास्तविक शून्यकों की संख्या उसकी डिग्री से अधिक नहीं हो सकती। तीन कटान के लिए न्यूनतम डिग्री (3) है।

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Question Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि किसी बहुपद का ग्राफ (x)-अक्ष को पाँच अलग बिंदुओं पर काटता है तो बहुपद की न्यूनतम घात क्या हो सकती है?

If a polynomial graph cuts the (x)-axis at five distinct points, what can be the minimum degree of the polynomial?

Explanation opens after your attempt
Correct Answer

D. (5)

Step 1

Concept

For five distinct real zeroes the degree must be at least (5). Tip: the number of zeroes cannot exceed the degree.

Step 2

Why this answer is correct

The correct answer is D. (5). For five distinct real zeroes the degree must be at least (5). Tip: the number of zeroes cannot exceed the degree.

Step 3

Exam Tip

पाँच अलग वास्तविक शून्यकों के लिए घात कम से कम (5) होनी चाहिए। टिप: शून्यकों की संख्या घात से अधिक नहीं हो सकती।

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Question Medium Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि किसी बहुपद का आलेख (x)-अक्ष को चार अलग बिंदुओं पर काटता है तो उसका न्यूनतम संभावित घात क्या हो सकता है?

If a polynomial graph cuts the (x)-axis at four distinct points, what can be its minimum possible degree?

Explanation opens after your attempt
Correct Answer

D. (4)

Step 1

Concept

For four distinct real zeroes, the degree must be at least (4). Tip: the number of zeroes cannot exceed the degree.

Step 2

Why this answer is correct

The correct answer is D. (4). For four distinct real zeroes, the degree must be at least (4). Tip: the number of zeroes cannot exceed the degree.

Step 3

Exam Tip

चार अलग वास्तविक शून्यकों के लिए घात कम से कम (4) होना चाहिए। टिप: शून्यकों की संख्या घात से अधिक नहीं हो सकती।

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Question Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x-2-2x+k) का न्यूनतम मान (3) है, तो (k) क्या है?

If the minimum value of (p(x)=x-2-2x+k) is (3), what is (k)?

Explanation opens after your attempt
Correct Answer

A. (4)

Step 1

Concept

(x-2-2x+k=(x-1)2+k-1), so the minimum value is (k-1). From (k-1=3), (k=4).

Step 2

Why this answer is correct

The correct answer is A. (4). (x-2-2x+k=(x-1)2+k-1), so the minimum value is (k-1). From (k-1=3), (k=4).

Step 3

Exam Tip

(x-2-2x+k=(x-1)2+k-1), इसलिए न्यूनतम मान (k-1) है। (k-1=3) से (k=4)।

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Question Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(p(x)=x-2+14x+53) का न्यूनतम मान क्या है?

What is the minimum value of (p(x)=x-2+14x+53)?

Explanation opens after your attempt
Correct Answer

B. (4)

Step 1

Concept

(x-2+14x+53=(x+7)2+4), so the minimum value is (4). A square term is never negative.

Step 2

Why this answer is correct

The correct answer is B. (4). (x-2+14x+53=(x+7)2+4), so the minimum value is (4). A square term is never negative.

Step 3

Exam Tip

(x-2+14x+53=(x+7)2+4), इसलिए न्यूनतम मान (4) है। वर्ग पद कभी ऋणात्मक नहीं होता।

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Question Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(p(x)=x-2-12x+40) का न्यूनतम मान किस (x) पर आता है?

At which (x) does (p(x)=x-2-12x+40) attain its minimum value?

Explanation opens after your attempt
Correct Answer

C. (x=6)

Step 1

Concept

(x-2-12x+40=(x-6)2+4), so the minimum occurs at (x=6). Completing the square is useful.

Step 2

Why this answer is correct

The correct answer is C. (x=6). (x-2-12x+40=(x-6)2+4), so the minimum occurs at (x=6). Completing the square is useful.

Step 3

Exam Tip

(x-2-12x+40=(x-6)2+4), इसलिए न्यूनतम (x=6) पर आता है। वर्ग पूर्ण करना उपयोगी तरीका है।

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 48

(p(x)=x-2+10x+29) का न्यूनतम मान क्या है?

What is the minimum value of (p(x)=x-2+10x+29)?

Explanation opens after your attempt
Correct Answer

B. (4)

Step 1

Concept

(x-2+10x+29=(x+5)2+4), so the minimum value is (4). A square term is never negative.

Step 2

Why this answer is correct

The correct answer is B. (4). (x-2+10x+29=(x+5)2+4), so the minimum value is (4). A square term is never negative.

Step 3

Exam Tip

(x-2+10x+29=(x+5)2+4), इसलिए न्यूनतम मान (4) है। वर्ग पद कभी ऋणात्मक नहीं होता।

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 48

(p(x)=x-2-8x+17) का न्यूनतम मान किस (x) पर आता है?

At which (x) does (p(x)=x-2-8x+17) attain its minimum value?

Explanation opens after your attempt
Correct Answer

C. (x=4)

Step 1

Concept

(x-2-8x+17=(x-4)2+1), so the minimum occurs at (x=4). Completing the square is useful.

Step 2

Why this answer is correct

The correct answer is C. (x=4). (x-2-8x+17=(x-4)2+1), so the minimum occurs at (x=4). Completing the square is useful.

Step 3

Exam Tip

(x-2-8x+17=(x-4)2+1), इसलिए न्यूनतम (x=4) पर आता है। वर्ग पूर्ण करना उपयोगी तरीका है।

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(p(x)=x-2-6x+10) का न्यूनतम मान क्या है?

What is the minimum value of (p(x)=x-2-6x+10)?

Explanation opens after your attempt
Correct Answer

A. (1)

Step 1

Concept

(x-2-6x+10=(x-3)2+1), so the minimum value is (1). A square term is never negative.

Step 2

Why this answer is correct

The correct answer is A. (1). (x-2-6x+10=(x-3)2+1), so the minimum value is (1). A square term is never negative.

Step 3

Exam Tip

(x-2-6x+10=(x-3)2+1), इसलिए न्यूनतम मान (1) है। वर्ग पद कभी ऋणात्मक नहीं होता।

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(p(x)=x-2+4x+5) का न्यूनतम मान किस (x) पर आता है?

At which (x) does (p(x)=x-2+4x+5) attain its minimum value?

Explanation opens after your attempt
Correct Answer

B. (x=-2)

Step 1

Concept

(x-2+4x+5=(x+2)2+1), so the minimum occurs at (x=-2). Completing the square is useful.

Step 2

Why this answer is correct

The correct answer is B. (x=-2). (x-2+4x+5=(x+2)2+1), so the minimum occurs at (x=-2). Completing the square is useful.

Step 3

Exam Tip

(x-2+4x+5=(x+2)2+1), इसलिए न्यूनतम (x=-2) पर आता है। वर्ग पूर्ण करना उपयोगी तरीका है।

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Question Hard Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 21

यदि \(\frac{x}{540}\) का दशमलव प्रसार सांत है, तो (x) में कम से कम कौन-सा गुणनखंड अवश्य होगा?

If \(\frac{x}{540}\) has a terminating decimal expansion, what factor must (x) contain at minimum?

Explanation opens after your attempt
Correct Answer

B. (27)

Step 1

Concept

\(540=2^2\cdot 3^3\cdot 5\).

Step 2

Why this answer is correct

For a terminating decimal, \(3^3\) must cancel completely from the denominator. So (x) must contain (27).

Step 3

Exam Tip

(2) and (5) may remain, but (3) must not. चरण 1: \(540=2^2\cdot 3^3\cdot 5\) है। चरण 2: सांत दशमलव के लिए सरलतम हर से \(3^3\) पूरी तरह कटना चाहिए। इसलिए (x) में (27) अवश्य होना चाहिए। चरण 3: (2) और (5) रह सकते हैं, पर (3) नहीं।

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Question Hard Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 20

यदि \(\frac{m}{735}\) का दशमलव प्रसार सांत है, तो (m) में कम से कम कौन-सा गुणनखंड अवश्य होना चाहिए?

If \(\frac{m}{735}\) has a terminating decimal expansion, what factor must (m) contain at minimum?

Explanation opens after your attempt
Correct Answer

C. (147)

Step 1

Concept

\(735=3\cdot 5\cdot 7^2\).

Step 2

Why this answer is correct

For a terminating decimal, (3) and \(7^2\) must not remain in the reduced denominator. So (m) must contain \(3\cdot 7^2=147\).

Step 3

Exam Tip

The factor (5) may remain, but (3) and (7) must cancel. चरण 1: \(735=3\cdot 5\cdot 7^2\) है। चरण 2: सांत दशमलव के लिए सरलतम हर में (3) और \(7^2\) नहीं बचने चाहिए। इसलिए (m) में \(3\cdot 7^2=147\) अवश्य होना चाहिए। चरण 3: (5) हर में रह सकता है, पर (3) और (7) कटने चाहिए।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 48

एक छात्र \(x^2+2x+1\) की घात (3) बताता है क्योंकि इसमें (3) पद हैं। सही घात क्या है?

A student says the degree of \(x^2+2x+1\) is (3) because it has (3) terms. What is the correct degree?

Explanation opens after your attempt
Correct Answer

B. (2)

Step 1

Concept

Degree is decided by the highest power (2), not by the number of terms. Avoid this common exam mistake.

Step 2

Why this answer is correct

The correct answer is B. (2). Degree is decided by the highest power (2), not by the number of terms. Avoid this common exam mistake.

Step 3

Exam Tip

घात पदों की संख्या से नहीं, सबसे बड़ी घात (2) से तय होती है। यह सामान्य गलती परीक्षा में न करें।

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Question 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 48

(p(x)=0x-5+7x-3-2x+1) की घात क्या है?

What is the degree of (p(x)=0x-5+7x-3-2x+1)?

Explanation opens after your attempt
Correct Answer

B. (3)

Step 1

Concept

The coefficient of \(0x^5\) is (0), so that term is not counted. The highest effective power is (3).

Step 2

Why this answer is correct

The correct answer is B. (3). The coefficient of \(0x^5\) is (0), so that term is not counted. The highest effective power is (3).

Step 3

Exam Tip

\(0x^5\) का गुणांक (0) है इसलिए वह पद नहीं गिना जाएगा। सबसे बड़ी प्रभावी घात (3) है।

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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 48

अशून्य अचर बहुपद (p(x)=-18) की घात क्या है?

What is the degree of the non-zero constant polynomial (p(x)=-18)?

Explanation opens after your attempt
Correct Answer

A. (0)

Step 1

Concept

A non-zero constant polynomial has degree (0). A constant number is linked with degree (0).

Step 2

Why this answer is correct

The correct answer is A. (0). A non-zero constant polynomial has degree (0). A constant number is linked with degree (0).

Step 3

Exam Tip

अशून्य अचर बहुपद की घात (0) होती है। अचर संख्या का अर्थ घात (0) से जुड़ा है।

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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 48

बहुपद (p(x)=11x-6-4x-3+x-9) की घात क्या है?

What is the degree of the polynomial (p(x)=11x-6-4x-3+x-9)?

Explanation opens after your attempt
Correct Answer

C. (6)

Step 1

Concept

The highest power is (6), so the degree is (6). Look at the highest power of the variable, not the coefficient.

Step 2

Why this answer is correct

The correct answer is C. (6). The highest power is (6), so the degree is (6). Look at the highest power of the variable, not the coefficient.

Step 3

Exam Tip

सबसे बड़ी घात (6) है इसलिए घात (6) होगी। गुणांक नहीं बल्कि चर की सबसे ऊंची घात देखें।

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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 47

कौन सा विकल्प \(2x^3-5x^2+x-4\) की घात और नियत पद को सही बताता है?

Which option correctly gives the degree and constant term of \(2x^3-5x^2+x-4\)?

Explanation opens after your attempt
Correct Answer

A. घात (3), नियत पद (-4)Degree (3), constant term (-4)

Step 1

Concept

The highest power is (3) and the term without (x) is (-4). So the correct pair is degree (3), constant term (-4).

Step 2

Why this answer is correct

The correct answer is A. घात (3), नियत पद (-4) / Degree (3), constant term (-4). The highest power is (3) and the term without (x) is (-4). So the correct pair is degree (3), constant term (-4).

Step 3

Exam Tip

सबसे बड़ी घात (3) है और बिना (x) वाला पद (-4) है। इसलिए सही जोड़ी घात (3), नियत पद (-4) है।

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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 47

\(x^2+1\), \(x^3+x\), (5x-2) में सबसे कम घात वाला बहुपद कौन सा है?

Among \(x^2+1\), \(x^3+x\), and (5x-2), which polynomial has the least degree?

Explanation opens after your attempt
Correct Answer

C. (5x-2)

Step 1

Concept

Their degrees are (2), (3), and (1) respectively. The least degree is (1).

Step 2

Why this answer is correct

The correct answer is C. (5x-2). Their degrees are (2), (3), and (1) respectively. The least degree is (1).

Step 3

Exam Tip

इनकी घातें क्रमशः (2), (3) और (1) हैं। सबसे कम घात (1) है।

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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि किसी गैर-शून्य नियत बहुपद की घात पूछी जाए, तो सही उत्तर क्या होगा?

If the degree of a non-zero constant polynomial is asked, what will be the correct answer?

Explanation opens after your attempt
Correct Answer

A. (0)

Step 1

Concept

The degree of a non-zero constant polynomial is (0). Keep it separate from the zero polynomial.

Step 2

Why this answer is correct

The correct answer is A. (0). The degree of a non-zero constant polynomial is (0). Keep it separate from the zero polynomial.

Step 3

Exam Tip

गैर-शून्य नियत बहुपद की घात (0) होती है। इसे शून्य बहुपद से अलग रखें।

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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 47

किस मान के लिए (p(x)=(a-2)x-3+4x-2+1) की घात (2) हो जाएगी?

For which value will (p(x)=(a-2)x-3+4x-2+1) have degree (2)?

Explanation opens after your attempt
Correct Answer

C. (a=2)

Step 1

Concept

For degree (2), the coefficient of \(x^3\) must be (0). From (a-2=0), we get (a=2).

Step 2

Why this answer is correct

The correct answer is C. (a=2). For degree (2), the coefficient of \(x^3\) must be (0). From (a-2=0), we get (a=2).

Step 3

Exam Tip

घात (2) के लिए \(x^3\) का गुणांक (0) होना चाहिए। (a-2=0) से (a=2) मिलता है।

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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=ax-2+3x+5) की घात (1) है, तो (a) का मान क्या होगा?

If (p(x)=ax-2+3x+5) has degree (1), what will be the value of (a)?

Explanation opens after your attempt
Correct Answer

A. (0)

Step 1

Concept

For degree (1), the coefficient of \(x^2\) must be (0). Therefore (a=0).

Step 2

Why this answer is correct

The correct answer is A. (0). For degree (1), the coefficient of \(x^2\) must be (0). Therefore (a=0).

Step 3

Exam Tip

घात (1) होने के लिए \(x^2\) का गुणांक (0) होना चाहिए। इसलिए (a=0) है।

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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)=(m-2)x-3+4x-2-7) की घात (2) है, तो (m) का मान क्या होगा?

If the degree of (p(x)=(m-2)x-3+4x-2-7) is (2), what will be the value of (m)?

Explanation opens after your attempt
Correct Answer

B. (2)

Step 1

Concept

For the degree to be (2), the coefficient of \(x^3\) must be (0), so (m-2=0) and (m=2). In exams, check the coefficient of the highest power first.

Step 2

Why this answer is correct

The correct answer is B. (2). For the degree to be (2), the coefficient of \(x^3\) must be (0), so (m-2=0) and (m=2). In exams, check the coefficient of the highest power first.

Step 3

Exam Tip

घात (2) होने के लिए \(x^3\) का गुणांक (0) होना चाहिए, इसलिए (m-2=0) और (m=2)। परीक्षा में सबसे ऊंची घात के गुणांक को पहले देखें।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 47

निम्न में से कौन सा (x) में बहुपद है जिसकी घात (4) है?

Which of the following is a polynomial in (x) with degree (4)?

Explanation opens after your attempt
Correct Answer

A. \(x^4-2x+7\)

Step 1

Concept

In \(x^4-2x+7\), the highest power is (4). To identify degree, check the greatest power.

Step 2

Why this answer is correct

The correct answer is A. \(x^4-2x+7\). In \(x^4-2x+7\), the highest power is (4). To identify degree, check the greatest power.

Step 3

Exam Tip

\(x^4-2x+7\) में सबसे बड़ी घात (4) है। घात पहचानने के लिए सबसे बड़ी शक्ति देखें।

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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 46

किसी रैखिक बहुपद (ax+b) में \(a\ne0\) हो तो उसकी घात क्या है?

If \(a\ne0\) in a linear polynomial (ax+b), what is its degree?

Explanation opens after your attempt
Correct Answer

B. (1)

Step 1

Concept

When \(a\ne0\) in (ax+b), the highest power of (x) is (1). So the degree is (1).

Step 2

Why this answer is correct

The correct answer is B. (1). When \(a\ne0\) in (ax+b), the highest power of (x) is (1). So the degree is (1).

Step 3

Exam Tip

(ax+b) में \(a\ne0\) होने पर (x) की सबसे बड़ी घात (1) है। इसलिए घात (1) होगी।

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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 46

\(3x^4+0x^3-2x+5\) की घात क्या है?

What is the degree of \(3x^4+0x^3-2x+5\)?

Explanation opens after your attempt
Correct Answer

C. (4)

Step 1

Concept

The term \(0x^3\) is ineffective, and the highest non-zero power is (4). Ignore terms with zero coefficient.

Step 2

Why this answer is correct

The correct answer is C. (4). The term \(0x^3\) is ineffective, and the highest non-zero power is (4). Ignore terms with zero coefficient.

Step 3

Exam Tip

\(0x^3\) पद प्रभावी नहीं है और सबसे बड़ी अशून्य घात (4) है। शून्य गुणांक वाले पद को नजरअंदाज करें।

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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 46

अशून्य अचर बहुपद (p(x)=12) की घात क्या होती है?

What is the degree of the non-zero constant polynomial (p(x)=12)?

Explanation opens after your attempt
Correct Answer

A. (0)

Step 1

Concept

A non-zero constant polynomial has degree (0). Keep it separate from the zero polynomial.

Step 2

Why this answer is correct

The correct answer is A. (0). A non-zero constant polynomial has degree (0). Keep it separate from the zero polynomial.

Step 3

Exam Tip

अशून्य अचर बहुपद की घात (0) होती है। शून्य बहुपद से इसे अलग रखें।

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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 46

बहुपद (p(x)=4x-5-3x-2+9) की घात क्या है?

What is the degree of the polynomial (p(x)=4x-5-3x-2+9)?

Explanation opens after your attempt
Correct Answer

C. (5)

Step 1

Concept

The highest power is (5), so the degree is (5). Always check the highest exponent.

Step 2

Why this answer is correct

The correct answer is C. (5). The highest power is (5), so the degree is (5). Always check the highest exponent.

Step 3

Exam Tip

सबसे बड़ी घात (5) है इसलिए बहुपद की घात (5) है। हमेशा सबसे ऊंची घात देखें।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 47

\(x^5+1\) की घात क्या है?

What is the degree of \(x^5+1\)?

Explanation opens after your attempt
Correct Answer

C. (5)

Step 1

Concept

The highest power is (5), so the degree is (5). The constant term does not increase the degree.

Step 2

Why this answer is correct

The correct answer is C. (5). The highest power is (5), so the degree is (5). The constant term does not increase the degree.

Step 3

Exam Tip

सबसे बड़ी घात (5) है इसलिए बहुपद की घात (5) है। नियत पद घात को नहीं बढ़ाता।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 47

निम्न में से किस बहुपद की घात (2) है?

Which polynomial has degree (2)?

Explanation opens after your attempt
Correct Answer

A. \(x^2+4x\)

Step 1

Concept

The highest power in \(x^2+4x\) is (2). Therefore its degree is (2).

Step 2

Why this answer is correct

The correct answer is A. \(x^2+4x\). The highest power in \(x^2+4x\) is (2). Therefore its degree is (2).

Step 3

Exam Tip

\(x^2+4x\) में सबसे बड़ी घात (2) है। इसलिए इसकी घात (2) है।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 47

निम्न में से किस बहुपद की घात (1) है?

Which polynomial has degree (1)?

Explanation opens after your attempt
Correct Answer

B. (9x-3)

Step 1

Concept

In (9x-3), the highest power of (x) is (1). So it is a polynomial of degree (1).

Step 2

Why this answer is correct

The correct answer is B. (9x-3). In (9x-3), the highest power of (x) is (1). So it is a polynomial of degree (1).

Step 3

Exam Tip

(9x-3) में (x) की सबसे बड़ी घात (1) है। इसलिए यह घात (1) का बहुपद है।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 47

शून्य बहुपद (0) की घात के बारे में सही कथन कौन सा है?

Which statement about the degree of the zero polynomial (0) is correct?

Explanation opens after your attempt
Correct Answer

C. घात परिभाषित नहीं हैDegree is not defined

Step 1

Concept

The degree of the zero polynomial is not defined. Remember it separately from a non-zero constant polynomial.

Step 2

Why this answer is correct

The correct answer is C. घात परिभाषित नहीं है / Degree is not defined. The degree of the zero polynomial is not defined. Remember it separately from a non-zero constant polynomial.

Step 3

Exam Tip

शून्य बहुपद की घात परिभाषित नहीं होती। इसे गैर-शून्य नियत बहुपद से अलग याद रखें।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 47

\(6x^4-2x^2+x-8\) की घात क्या है?

What is the degree of \(6x^4-2x^2+x-8\)?

Explanation opens after your attempt
Correct Answer

C. (4)

Step 1

Concept

The highest power is (4), so the degree is (4). The degree depends on the highest power, not on the number of terms.

Step 2

Why this answer is correct

The correct answer is C. (4). The highest power is (4), so the degree is (4). The degree depends on the highest power, not on the number of terms.

Step 3

Exam Tip

सबसे बड़ी घात (4) है इसलिए घात (4) है। पदों की संख्या नहीं, सबसे बड़ी घात महत्वपूर्ण है।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 47

बहुपद \(7x^3-4x+9\) की घात क्या है?

What is the degree of the polynomial \(7x^3-4x+9\)?

Explanation opens after your attempt
Correct Answer

C. (3)

Step 1

Concept

The highest power is (3), so the degree is (3). Always check the highest power of the variable.

Step 2

Why this answer is correct

The correct answer is C. (3). The highest power is (3), so the degree is (3). Always check the highest power of the variable.

Step 3

Exam Tip

सबसे बड़ी घात (3) है इसलिए बहुपद की घात (3) है। हमेशा चर की सबसे बड़ी घात देखें।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि किसी बहुपद की घात (3) है, तो उसे क्या कहते हैं?

If a polynomial has degree (3), what is it called?

Explanation opens after your attempt
Correct Answer

A. घन बहुपदCubic polynomial

Step 1

Concept

A degree (3) polynomial is called a cubic polynomial. The highest power decides the name.

Step 2

Why this answer is correct

The correct answer is A. घन बहुपद / Cubic polynomial. A degree (3) polynomial is called a cubic polynomial. The highest power decides the name.

Step 3

Exam Tip

घात (3) वाला बहुपद घन बहुपद कहलाता है। सबसे बड़ी घात ही नाम तय करती है।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि किसी बहुपद की घात (2) है, तो उसे क्या कहते हैं?

If a polynomial has degree (2), what is it called?

Explanation opens after your attempt
Correct Answer

B. द्विघात बहुपदQuadratic polynomial

Step 1

Concept

A degree (2) polynomial is called quadratic. A non-zero \(x^2\)-term must be present.

Step 2

Why this answer is correct

The correct answer is B. द्विघात बहुपद / Quadratic polynomial. A degree (2) polynomial is called quadratic. A non-zero \(x^2\)-term must be present.

Step 3

Exam Tip

घात (2) वाला बहुपद द्विघात कहलाता है। \(x^2\) का अशून्य पद होना जरूरी है।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि किसी बहुपद की घात (1) है, तो उसे क्या कहते हैं?

If a polynomial has degree (1), what is it called?

Explanation opens after your attempt
Correct Answer

B. रैखिक बहुपदLinear polynomial

Step 1

Concept

A polynomial of degree (1) is called a linear polynomial. Link the name with the degree.

Step 2

Why this answer is correct

The correct answer is B. रैखिक बहुपद / Linear polynomial. A polynomial of degree (1) is called a linear polynomial. Link the name with the degree.

Step 3

Exam Tip

घात (1) वाले बहुपद को रैखिक बहुपद कहते हैं। नाम हमेशा घात से जोड़कर याद करें।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 48

(p(x)=ax+b) में यदि \(a\ne0\) है, तो इसकी घात क्या होती है?

In (p(x)=ax+b), if \(a\ne0\), what is its degree?

Explanation opens after your attempt
Correct Answer

B. (1)

Step 1

Concept

When \(a\ne0\), the (x)-term exists, so the degree is (1). This is the form of a linear polynomial.

Step 2

Why this answer is correct

The correct answer is B. (1). When \(a\ne0\), the (x)-term exists, so the degree is (1). This is the form of a linear polynomial.

Step 3

Exam Tip

\(a\ne0\) होने पर (x) वाला पद मौजूद है, इसलिए घात (1) है। यही रैखिक बहुपद का रूप है।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 48

बहुपद \(11x^5-3x^2+8\) की घात क्या है?

What is the degree of \(11x^5-3x^2+8\)?

Explanation opens after your attempt
Correct Answer

C. (5)

Step 1

Concept

The highest power is (5), so the degree is (5). Look at the greatest power, not the number of terms.

Step 2

Why this answer is correct

The correct answer is C. (5). The highest power is (5), so the degree is (5). Look at the greatest power, not the number of terms.

Step 3

Exam Tip

सबसे बड़ी घात (5) है इसलिए घात (5) होगी। पदों की संख्या नहीं बल्कि सबसे बड़ी घात देखें।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 48

बहुपद (5) की घात क्या है?

What is the degree of the polynomial (5)?

Explanation opens after your attempt
Correct Answer

A. (0)

Step 1

Concept

A non-zero constant polynomial has degree (0). Remember \(5=5x^0\) may be considered.

Step 2

Why this answer is correct

The correct answer is A. (0). A non-zero constant polynomial has degree (0). Remember \(5=5x^0\) may be considered.

Step 3

Exam Tip

अशून्य नियत बहुपद की घात (0) होती है। याद रखें \(5=5x^0\) माना जा सकता है।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 48

बहुपद \(7x^3-2x+9\) की घात क्या है?

What is the degree of the polynomial \(7x^3-2x+9\)?

Explanation opens after your attempt
Correct Answer

C. (3)

Step 1

Concept

The highest power is (3), so the degree is (3). In exams identify the greatest exponent.

Step 2

Why this answer is correct

The correct answer is C. (3). The highest power is (3), so the degree is (3). In exams identify the greatest exponent.

Step 3

Exam Tip

सबसे बड़ी घात (3) है इसलिए बहुपद की घात (3) होगी। परीक्षा में सबसे बड़े घातांक को पहचानें।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)=ax+b) और \(a\neq0\), तो (p(x)) की घात क्या है?

If (p(x)=ax+b) and \(a\neq0\), what is the degree of (p(x))?

Explanation opens after your attempt
Correct Answer

B. (1)

Step 1

Concept

Since \(a\neq0\), the (x)-term is present. Therefore the degree of the polynomial is (1).

Step 2

Why this answer is correct

The correct answer is B. (1). Since \(a\neq0\), the (x)-term is present. Therefore the degree of the polynomial is (1).

Step 3

Exam Tip

\(a\neq0\) होने से (x) वाला पद मौजूद है। इसलिए बहुपद की घात (1) है।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 46

बहुपद \(4x^3-2x^3+x+5\) को सरल करने पर घात क्या होगी?

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

Explanation opens after your attempt
Correct Answer

C. (3)

Step 1

Concept

Combining like terms gives \(2x^3+x+5\). The highest power is (3).

Step 2

Why this answer is correct

The correct answer is C. (3). Combining like terms gives \(2x^3+x+5\). The highest power is (3).

Step 3

Exam Tip

समान पद मिलाकर \(2x^3+x+5\) मिलता है। सबसे बड़ी घात (3) है।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 46

बहुपद \(3x^3+0x^2-2x+5\) की घात क्या है?

What is the degree of \(3x^3+0x^2-2x+5\)?

Explanation opens after your attempt
Correct Answer

C. (3)

Step 1

Concept

The highest non-zero power term is \(3x^3\). So the degree is (3).

Step 2

Why this answer is correct

The correct answer is C. (3). The highest non-zero power term is \(3x^3\). So the degree is (3).

Step 3

Exam Tip

सबसे बड़ी शून्य से भिन्न घात वाला पद \(3x^3\) है। इसलिए घात (3) है।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 46

शून्य बहुपद (p(x)=0) की घात के बारे में सही कथन कौन-सा है?

Which statement is correct about the degree of the zero polynomial (p(x)=0)?

Explanation opens after your attempt
Correct Answer

C. घात परिभाषित नहीं हैDegree is undefined

Step 1

Concept

The degree of the zero polynomial is undefined. In exams, keep it separate from a non-zero constant polynomial.

Step 2

Why this answer is correct

The correct answer is C. घात परिभाषित नहीं है / Degree is undefined. The degree of the zero polynomial is undefined. In exams, keep it separate from a non-zero constant polynomial.

Step 3

Exam Tip

शून्य बहुपद की घात परिभाषित नहीं होती। परीक्षा में इसे स्थिर शून्य से भिन्न बहुपद से अलग रखें।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 46

स्थिर बहुपद (p(x)=9) की घात क्या है?

What is the degree of the constant polynomial (p(x)=9)?

Explanation opens after your attempt
Correct Answer

A. (0)

Step 1

Concept

A non-zero constant polynomial has degree (0). The number (9) may be written as \(9x^0\).

Step 2

Why this answer is correct

The correct answer is A. (0). A non-zero constant polynomial has degree (0). The number (9) may be written as \(9x^0\).

Step 3

Exam Tip

शून्य से भिन्न स्थिर बहुपद की घात (0) होती है। (9) को \(9x^0\) माना जा सकता है।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 46

बहुपद (p(x)=4x-3-2x+9) की घात क्या है?

What is the degree of the polynomial (p(x)=4x-3-2x+9)?

Explanation opens after your attempt
Correct Answer

A. (3)

Step 1

Concept

The highest power is (3), so the degree of the polynomial is (3). In exams, look at the highest power of the variable.

Step 2

Why this answer is correct

The correct answer is A. (3). The highest power is (3), so the degree of the polynomial is (3). In exams, look at the highest power of the variable.

Step 3

Exam Tip

सबसे बड़ी घात (3) है इसलिए बहुपद की घात (3) है। परीक्षा में सबसे बड़ी चर घात देखें।

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Question Easy Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण \(x^2+1=0\) की घात क्या है?

What is the degree of \(x^2+1=0\)?

Explanation opens after your attempt
Correct Answer

B. (2)

Step 1

Concept

The highest power of (x) is (2). The constant term does not change the degree.

Step 2

Why this answer is correct

The correct answer is B. (2). The highest power of (x) is (2). The constant term does not change the degree.

Step 3

Exam Tip

इसमें (x) की सबसे बड़ी घात (2) है। स्थिर पद घात को नहीं बदलता।

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Question Easy Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण \(7x^2-4x+9=0\) की घात क्या है?

What is the degree of the equation \(7x^2-4x+9=0\)?

Explanation opens after your attempt
Correct Answer

B. (2)

Step 1

Concept

The highest power of (x) in this equation is (2). Degree is decided by the greatest power of the variable.

Step 2

Why this answer is correct

The correct answer is B. (2). The highest power of (x) in this equation is (2). Degree is decided by the greatest power of the variable.

Step 3

Exam Tip

इस समीकरण में (x) की सबसे बड़ी घात (2) है। घात हमेशा चर की सबसे बड़ी शक्ति से तय होती है।

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Question Easy Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

\(6x^2-5x+2=0\) की घात क्या है?

What is the degree of \(6x^2-5x+2=0\)?

Explanation opens after your attempt
Correct Answer

C. (2)

Step 1

Concept

The highest power is (2). Therefore it is a quadratic equation.

Step 2

Why this answer is correct

The correct answer is C. (2). The highest power is (2). Therefore it is a quadratic equation.

Step 3

Exam Tip

सबसे बड़ी घात (2) है। इसलिए यह द्विघात समीकरण है।

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Question Easy Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

\(5x^2+2x-1=0\) की घात क्या है?

What is the degree of \(5x^2+2x-1=0\)?

Explanation opens after your attempt
Correct Answer

C. (2)

Step 1

Concept

The highest power is (2). Therefore the equation is quadratic.

Step 2

Why this answer is correct

The correct answer is C. (2). The highest power is (2). Therefore the equation is quadratic.

Step 3

Exam Tip

सबसे बड़ी घात (2) है। इसलिए समीकरण द्विघात है।

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Question Easy Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

यदि किसी समीकरण की घात (2) है और वह (x) में है तो उसे क्या कहते हैं?

If an equation in (x) has degree (2), what is it called?

Explanation opens after your attempt
Correct Answer

B. द्विघात समीकरणQuadratic equation

Step 1

Concept

An equation of degree (2) is called a quadratic equation. Remember that quadratic means degree (2).

Step 2

Why this answer is correct

The correct answer is B. द्विघात समीकरण / Quadratic equation. An equation of degree (2) is called a quadratic equation. Remember that quadratic means degree (2).

Step 3

Exam Tip

घात (2) वाले समीकरण को द्विघात समीकरण कहते हैं। नाम याद रखने के लिए द्वि का अर्थ (2) समझें।

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Question Expert Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 21

यदि \(\frac{a}{2^6\cdot 3\cdot 5^4\cdot 7\cdot 13}\) का दशमलव सांत हो तो (a) में कम से कम कौन-सा गुणनखंड होना चाहिए?

If \(\frac{a}{2^6\cdot 3\cdot 5^4\cdot 7\cdot 13}\) is to have a terminating decimal, what factor must (a) contain at minimum?

Explanation opens after your attempt
Correct Answer

B. (273)

Step 1

Concept

The factors (3), (7), and (13) must be removed from the reduced denominator, so the minimum factor is \(3\cdot 7\cdot 13=273\). Factors (2) and (5) may remain.

Step 2

Why this answer is correct

The correct answer is B. (273). The factors (3), (7), and (13) must be removed from the reduced denominator, so the minimum factor is \(3\cdot 7\cdot 13=273\). Factors (2) and (5) may remain.

Step 3

Exam Tip

सरलतम हर से (3), (7) और (13) हटने चाहिए इसलिए न्यूनतम गुणनखंड \(3\cdot 7\cdot 13=273\) है। (2) और (5) हर में रह सकते हैं।

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Question Expert Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 21

यदि \(\frac{a}{2^5\cdot 3^4\cdot 5^2\cdot 19}\) का दशमलव सांत हो तो (a) में कम से कम कौन-सा गुणनखंड होना चाहिए?

If \(\frac{a}{2^5\cdot 3^4\cdot 5^2\cdot 19}\) is to have a terminating decimal, what factor must (a) contain at minimum?

Explanation opens after your attempt
Correct Answer

B. (1539)

Step 1

Concept

The factors \(3^4\) and (19) must be removed from the reduced denominator, so the minimum factor is \(81\cdot 19=1539\). Factors (2) and (5) may remain.

Step 2

Why this answer is correct

The correct answer is B. (1539). The factors \(3^4\) and (19) must be removed from the reduced denominator, so the minimum factor is \(81\cdot 19=1539\). Factors (2) and (5) may remain.

Step 3

Exam Tip

सरलतम हर से \(3^4\) और (19) हटने चाहिए इसलिए न्यूनतम गुणनखंड \(81\cdot 19=1539\) है। (2) और (5) हर में रह सकते हैं।

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Question Expert Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 20

यदि \(\frac{a}{2^4\cdot 3^3\cdot 5^2\cdot 23}\) का दशमलव सांत हो तो (a) में कम से कम कौन-सा गुणनखंड होना चाहिए?

If \(\frac{a}{2^4\cdot 3^3\cdot 5^2\cdot 23}\) is to have a terminating decimal, what factor must (a) contain at minimum?

Explanation opens after your attempt
Correct Answer

B. (621)

Step 1

Concept

The factors \(3^3\) and (23) must be removed from the reduced denominator, so the minimum factor is \(27\cdot 23=621\). Factors (2) and (5) may remain.

Step 2

Why this answer is correct

The correct answer is B. (621). The factors \(3^3\) and (23) must be removed from the reduced denominator, so the minimum factor is \(27\cdot 23=621\). Factors (2) and (5) may remain.

Step 3

Exam Tip

सरलतम हर से \(3^3\) और (23) हटने चाहिए इसलिए न्यूनतम गुणनखंड \(27\cdot 23=621\) है। (2) और (5) हर में रह सकते हैं।

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Question Expert Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 19

यदि \(q=2^r5^s\) और \(\frac{p}{q}\) सरलतम रूप में है, तो दशमलव को \(\frac{N}{10^k}\) के रूप में लिखने के लिए न्यूनतम (k) क्या होगा?

If \(q=2^r5^s\) and \(\frac{p}{q}\) is in lowest form, what is the minimum (k) to write the decimal as \(\frac{N}{10^k}\)?

Explanation opens after your attempt
Correct Answer

B. (\max(r,s))

Step 1

Concept

To form \(10^k=2^k5^k\), both powers must reach at least the larger exponent. Therefore the minimum (k=\max(r,s)).

Step 2

Why this answer is correct

The correct answer is B. (\max(r,s)). To form \(10^k=2^k5^k\), both powers must reach at least the larger exponent. Therefore the minimum (k=\max(r,s)).

Step 3

Exam Tip

\(10^k=2^k5^k\) बनाने के लिए दोनों घातें कम से कम बड़ी घात तक पहुँचनी चाहिए। इसलिए न्यूनतम (k=\max(r,s)) है।

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Question Expert Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 19

यदि \(\frac{a}{2^3\cdot 3^2\cdot 5^4\cdot 17}\) का दशमलव सांत हो, तो (a) में कम से कम कौन-सा गुणनखंड होना चाहिए?

If \(\frac{a}{2^3\cdot 3^2\cdot 5^4\cdot 17}\) is to have a terminating decimal, what factor must (a) contain at minimum?

Explanation opens after your attempt
Correct Answer

A. (153)

Step 1

Concept

The factors \(3^2\) and (17) must be removed from the reduced denominator, so the minimum factor is \(3^2\cdot 17=153\). Factors (2) and (5) may remain.

Step 2

Why this answer is correct

The correct answer is A. (153). The factors \(3^2\) and (17) must be removed from the reduced denominator, so the minimum factor is \(3^2\cdot 17=153\). Factors (2) and (5) may remain.

Step 3

Exam Tip

सरलतम हर से \(3^2\) और (17) हटने चाहिए, इसलिए न्यूनतम गुणनखंड \(3^2\cdot 17=153\) है। (2) और (5) हर में रह सकते हैं।

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Question Hard Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 21

यदि \(\frac{a}{2^2\cdot 3\cdot 5\cdot 19}\) का दशमलव सांत हो, तो (a) में कम से कम कौन-सा गुणनखंड होना चाहिए?

If \(\frac{a}{2^2\cdot 3\cdot 5\cdot 19}\) is to have a terminating decimal, what factor must (a) contain at minimum?

Explanation opens after your attempt
Correct Answer

B. (57)

Step 1

Concept

The denominator contains (2), (5), (3), and (19).

Step 2

Why this answer is correct

For a terminating decimal, (3) and (19) must cancel. So the minimum factor is \(3\cdot 19=57\).

Step 3

Exam Tip

Only (2) and (5) may remain in the denominator. चरण 1: हर में (2), (5), (3), और (19) हैं। चरण 2: सांत दशमलव के लिए (3) और (19) कटने चाहिए। इसलिए न्यूनतम गुणनखंड \(3\cdot 19=57\) है। चरण 3: केवल (2) और (5) हर में रह सकते हैं।

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Question Hard Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 20

\(\frac{a}{2310}\) का दशमलव प्रसार सांत हो, इसके लिए (a) में कम से कम कौन-सा गुणनखंड होना चाहिए?

For \(\frac{a}{2310}\) to have a terminating decimal expansion, what factor must (a) contain at minimum?

Explanation opens after your attempt
Correct Answer

C. (231)

Step 1

Concept

\(2310=2\cdot 3\cdot 5\cdot 7\cdot 11\).

Step 2

Why this answer is correct

For a terminating decimal, (3), (7), and (11) must cancel from the denominator. So the minimum factor is \(3\cdot 7\cdot 11=231\).

Step 3

Exam Tip

(2) and (5) may remain, but other prime factors must not. चरण 1: \(2310=2\cdot 3\cdot 5\cdot 7\cdot 11\) है। चरण 2: सांत दशमलव के लिए (3), (7), और (11) हर से कटने चाहिए। इसलिए न्यूनतम गुणनखंड \(3\cdot 7\cdot 11=231\) है। चरण 3: (2) और (5) रह सकते हैं, पर अन्य अभाज्य गुणनखंड नहीं।

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Question Hard Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 19

\(\frac{41}{2^2\cdot 5^3}\) के दशमलव प्रसार को \(10^k\) हर वाली भिन्न में बदलने के लिए (k) का न्यूनतम मान क्या होगा?

For \(\frac{41}{2^2\cdot 5^3}\), what is the minimum value of (k) to convert the denominator into \(10^k\)?

Explanation opens after your attempt
Correct Answer

B. (3)

Step 1

Concept

The denominator is \(2^2\cdot 5^3\).

Step 2

Why this answer is correct

Since \(10^k=2^k\cdot 5^k\), the powers must become equal. The larger power is (3), so (k=3).

Step 3

Exam Tip

To form \(10^k\), make the powers of (2) and (5) equal. चरण 1: हर \(2^2\cdot 5^3\) है। चरण 2: \(10^k=2^k\cdot 5^k\) बनाने के लिए दोनों घात बराबर करनी होती हैं। बड़ी घात (3) है, इसलिए (k=3)। चरण 3: \(10^k\) बनाते समय दोनों अभाज्य घातों को समान करने का विचार रखें।

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Question Hard Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 19

यदि \(\frac{n}{180}\) का दशमलव प्रसार सांत है और \(\frac{n}{180}\) सरलतम रूप में नहीं दिया गया है, तो (n) में कम से कम कौन-सा गुणनखंड अवश्य होना चाहिए?

If \(\frac{n}{180}\) has a terminating decimal expansion and the fraction is not necessarily in lowest form, what factor must (n) contain at minimum?

Explanation opens after your attempt
Correct Answer

A. \(3^2\)

Step 1

Concept

\(180=2^2\cdot 3^2\cdot 5\).

Step 2

Why this answer is correct

For a terminating decimal, \(3^2\) must cancel completely from the denominator. So (n) must contain \(3^2\).

Step 3

Exam Tip

Focus on removing denominator primes other than (2) and (5). चरण 1: \(180=2^2\cdot 3^2\cdot 5\) है। चरण 2: सांत दशमलव के लिए सरलतम रूप में हर से \(3^2\) पूरी तरह कटना चाहिए। इसलिए (n) में \(3^2\) अवश्य होना चाहिए। चरण 3: हर के (2) और (5) नहीं, बल्कि अन्य अभाज्य गुणनखंडों को हटाना जरूरी होता है।

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

यदि किसी बहुपद का ग्राफ (x)-अक्ष को (x=-2), (x=0) और (x=3) पर काटता है, तो सबसे कम घात का मोनिक बहुपद कौन-सा है?

If the graph of a polynomial cuts the (x)-axis at (x=-2), (x=0), and (x=3), which is the monic polynomial of least degree?

Explanation opens after your attempt
Correct Answer

A. \(x^3-x^2-6x\)

Step 1

Concept

The zeroes are (-2,0,3), so the polynomial is (x(x+2)(x-3)=x-3-x-2-6x). Intersections with the (x)-axis give zeroes.

Step 2

Why this answer is correct

The correct answer is A. \(x^3-x^2-6x\). The zeroes are (-2,0,3), so the polynomial is (x(x+2)(x-3)=x-3-x-2-6x). Intersections with the (x)-axis give zeroes.

Step 3

Exam Tip

शून्यक (-2,0,3) हैं, इसलिए बहुपद (x(x+2)(x-3)=x-3-x-2-6x) है। (x)-अक्ष काटने के बिंदु शून्यक बताते हैं।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 46

कौन-सा बहुपद (x) में (0) घात का है?

Which polynomial in (x) has degree (0)?

Explanation opens after your attempt
Correct Answer

A. (12)

Step 1

Concept

The number (12) is a non-zero constant polynomial and its degree is (0). The degree of the zero polynomial is undefined.

Step 2

Why this answer is correct

The correct answer is A. (12). The number (12) is a non-zero constant polynomial and its degree is (0). The degree of the zero polynomial is undefined.

Step 3

Exam Tip

(12) शून्य से भिन्न स्थिर बहुपद है और इसकी घात (0) है। (0) बहुपद की घात परिभाषित नहीं होती।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 46

कौन-सा बहुपद (x) में (4) घात का है?

Which polynomial in (x) has degree (4)?

Explanation opens after your attempt
Correct Answer

A. \(x^4+x^2+1\)

Step 1

Concept

The highest power in \(x^4+x^2+1\) is (4). So its degree is (4).

Step 2

Why this answer is correct

The correct answer is A. \(x^4+x^2+1\). The highest power in \(x^4+x^2+1\) is (4). So its degree is (4).

Step 3

Exam Tip

\(x^4+x^2+1\) में सबसे बड़ी घात (4) है। इसलिए इसकी घात (4) है।

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Question Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि बहुपद का ग्राफ (x)-अक्ष को चार अलग बिंदुओं पर काटता है तो डिग्री के बारे में कौन सा कथन सही है?

If the graph of a polynomial cuts the (x)-axis at four distinct points, which statement about its degree is correct?

Explanation opens after your attempt
Correct Answer

A. डिग्री कम से कम (4) होगीThe degree is at least (4)

Step 1

Concept

Four distinct real zeroes need degree at least four. The number of zeroes cannot exceed the degree.

Step 2

Why this answer is correct

The correct answer is A. डिग्री कम से कम (4) होगी / The degree is at least (4). Four distinct real zeroes need degree at least four. The number of zeroes cannot exceed the degree.

Step 3

Exam Tip

चार अलग वास्तविक शून्यक के लिए डिग्री कम से कम चार चाहिए। शून्यकों की संख्या डिग्री से अधिक नहीं होती।

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Question Expert Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 21

यदि (n) सबसे छोटा धनात्मक पूर्णांक है जिससे \(\frac{n}{2^4\cdot 5\cdot 7^3\cdot 11}\) का दशमलव सांत हो तो (n) क्या होगा?

If (n) is the smallest positive integer for which \(\frac{n}{2^4\cdot 5\cdot 7^3\cdot 11}\) has a terminating decimal, what is (n)?

Explanation opens after your attempt
Correct Answer

A. (3773)

Step 1

Concept

The factors \(7^3\) and (11) must be removed from the reduced denominator, so \(n=7^3\cdot 11=3773\). For the least value, do not cancel (2) and (5).

Step 2

Why this answer is correct

The correct answer is A. (3773). The factors \(7^3\) and (11) must be removed from the reduced denominator, so \(n=7^3\cdot 11=3773\). For the least value, do not cancel (2) and (5).

Step 3

Exam Tip

सरलतम हर से \(7^3\) और (11) हटने चाहिए इसलिए \(n=7^3\cdot 11=3773\) होगा। न्यूनतम मान में (2) और (5) को काटना जरूरी नहीं है।

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Question Expert Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 21

यदि (n) सबसे छोटा धनात्मक पूर्णांक है जिससे \(\frac{n}{2^3\cdot 3^2\cdot 5^4\cdot 17^2}\) का दशमलव सांत हो तो (n) क्या होगा?

If (n) is the smallest positive integer for which \(\frac{n}{2^3\cdot 3^2\cdot 5^4\cdot 17^2}\) has a terminating decimal, what is (n)?

Explanation opens after your attempt
Correct Answer

C. (2601)

Step 1

Concept

For termination, \(3^2\) and \(17^2\) must cancel completely, so (n=2601). For the least value, cancel only the factors other than (2) and (5).

Step 2

Why this answer is correct

The correct answer is C. (2601). For termination, \(3^2\) and \(17^2\) must cancel completely, so (n=2601). For the least value, cancel only the factors other than (2) and (5).

Step 3

Exam Tip

सांत दशमलव के लिए \(3^2\) और \(17^2\) पूरी तरह कटने चाहिए इसलिए (n=2601) होगा। न्यूनतम मान में केवल (2) और (5) के अलावा गुणनखंड काटें।

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Question Expert Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 20

यदि (n) सबसे छोटा धनात्मक पूर्णांक है जिससे \(\frac{n}{2^5\cdot 3^2\cdot 5^3\cdot 7^2}\) का दशमलव सांत हो तो (n) क्या होगा?

If (n) is the smallest positive integer for which \(\frac{n}{2^5\cdot 3^2\cdot 5^3\cdot 7^2}\) has a terminating decimal, what is (n)?

Explanation opens after your attempt
Correct Answer

C. (441)

Step 1

Concept

For termination, \(3^2\) and \(7^2\) must cancel completely, so (n=441). For the least value, cancel only the factors other than (2) and (5).

Step 2

Why this answer is correct

The correct answer is C. (441). For termination, \(3^2\) and \(7^2\) must cancel completely, so (n=441). For the least value, cancel only the factors other than (2) and (5).

Step 3

Exam Tip

सांत दशमलव के लिए \(3^2\) और \(7^2\) पूरी तरह कटने चाहिए इसलिए (n=441) होगा। न्यूनतम मान में केवल (2) और (5) के अलावा गुणनखंड काटें।

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Question Expert Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 19

यदि (n) सबसे छोटा धनात्मक पूर्णांक है जिससे \(\frac{n}{2^2\cdot 3^4\cdot 5\cdot 13}\) का दशमलव सांत हो, तो (n) क्या होगा?

If (n) is the smallest positive integer for which \(\frac{n}{2^2\cdot 3^4\cdot 5\cdot 13}\) has a terminating decimal, what is (n)?

Explanation opens after your attempt
Correct Answer

C. (1053)

Step 1

Concept

For a terminating decimal, \(3^4\) and (13) must cancel completely, so \(n=3^4\cdot 13=1053\). For the least value, cancel only the unwanted prime factors.

Step 2

Why this answer is correct

The correct answer is C. (1053). For a terminating decimal, \(3^4\) and (13) must cancel completely, so \(n=3^4\cdot 13=1053\). For the least value, cancel only the unwanted prime factors.

Step 3

Exam Tip

सांत दशमलव के लिए \(3^4\) और (13) पूरी तरह कटने चाहिए, इसलिए \(n=3^4\cdot 13=1053\)। न्यूनतम मान में केवल अनचाहे अभाज्य गुणनखंड काटें।

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Question Hard Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 21

यदि (n) सबसे छोटा धनात्मक पूर्णांक है जिससे \(\frac{n}{2^4\cdot 3^3\cdot 5^2\cdot 11}\) का दशमलव प्रसार सांत हो, तो (n) क्या होगा?

If (n) is the smallest positive integer for which \(\frac{n}{2^4\cdot 3^3\cdot 5^2\cdot 11}\) has a terminating decimal expansion, what is (n)?

Explanation opens after your attempt
Correct Answer

C. (297)

Step 1

Concept

For a terminating decimal, the reduced denominator must contain only (2) and (5).

Step 2

Why this answer is correct

The factors \(3^3\) and (11) must be cancelled, so the least (n) is \(3^3\cdot 11=297\).

Step 3

Exam Tip

For the smallest value, cancel only the unwanted prime factors. चरण 1: सांत दशमलव के लिए सरलतम हर में केवल (2) और (5) रहने चाहिए। चरण 2: हर में \(3^3\) और (11) हटाने होंगे, इसलिए \(n=3^3\cdot 11=297\) न्यूनतम है। चरण 3: सबसे छोटा मान पूछे तो केवल अनचाहे अभाज्य गुणनखंड काटिए।

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Question Hard Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 20

यदि (n) सबसे छोटा धनात्मक पूर्णांक है जिसके लिए \(\frac{n}{2^3\cdot 3^2\cdot 5\cdot 7}\) का दशमलव प्रसार सांत हो जाता है, तो (n) का मान क्या होगा?

If (n) is the smallest positive integer for which the decimal expansion of \(\frac{n}{2^3\cdot 3^2\cdot 5\cdot 7}\) becomes terminating, what is the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (63)

Step 1

Concept

For a terminating decimal, the reduced denominator must contain only (2) and (5).

Step 2

Why this answer is correct

The denominator has extra prime factors \(3^2\) and (7), so (n) must contain \(3^2\cdot 7=63\).

Step 3

Exam Tip

When the smallest value is asked, cancel only the unwanted prime factors. चरण 1: सांत दशमलव के लिए सरलतम हर में केवल (2) और (5) बचने चाहिए। चरण 2: हर में \(3^2\) और (7) अतिरिक्त अभाज्य गुणनखंड हैं, इसलिए (n) में \(3^2\cdot 7=63\) अवश्य होना चाहिए। चरण 3: सबसे छोटा मान पूछे जाने पर केवल अनचाहे अभाज्य गुणनखंडों को काटिए।

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Question Hard Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 19

\(\frac{a}{2^3\cdot 5^2\cdot 13}\) का दशमलव सांत हो, इसके लिए (a) में कम से कम कौन-सा गुणनखंड होना चाहिए?

For \(\frac{a}{2^3\cdot 5^2\cdot 13}\) to have a terminating decimal, what factor must (a) contain at minimum?

Explanation opens after your attempt
Correct Answer

C. (13)

Step 1

Concept

The denominator contains (2), (5), and (13).

Step 2

Why this answer is correct

For a terminating decimal, (13) must not remain in the reduced denominator. So (a) must contain the factor (13).

Step 3

Exam Tip

Powers of (2) and (5) may remain, but other prime factors must cancel. चरण 1: हर में (2), (5), और (13) हैं। चरण 2: सांत दशमलव के लिए सरलतम हर में (13) नहीं बचना चाहिए। इसलिए (a) में (13) का गुणनखंड अवश्य होना चाहिए। चरण 3: (2) और (5) रह सकते हैं, पर अन्य अभाज्य गुणनखंड कटने चाहिए।

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Question Expert Mathematics Real Numbers Euclid’s Division Lemma Class 10 Level 3

यदि किसी संख्या को 143 से भाग देने पर भागफल 23 है, तो उस संख्या का सबसे छोटा संभव मान क्या होगा?

If a number gives quotient 23 when divided by 143, what is the least possible value of that number?

Explanation opens after your attempt
Correct Answer

A. 3289

Step 1

Concept

The number is \(143\times23+r\).

Step 2

Why this answer is correct

For the least value, the remainder is 0, so the number is \(143\times23=3289\).

Step 3

Exam Tip

In least-value questions, taking the remainder as zero is the clearest method. चरण 1: संख्या \(143\times23+r\) होगी। चरण 2: सबसे छोटे मान के लिए शेषफल 0 होगा, इसलिए संख्या \(143\times23=3289\) है। चरण 3: न्यूनतम मान वाले प्रश्न में शेषफल शून्य लेना सबसे साफ तरीका है।

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Question Expert Mathematics Real Numbers Euclid’s Division Lemma Class 10 Level 2

यदि किसी संख्या को 118 से भाग देने पर भागफल 19 है, तो उस संख्या का सबसे छोटा संभव मान क्या होगा?

If a number gives quotient 19 when divided by 118, what is the least possible value of that number?

Explanation opens after your attempt
Correct Answer

B. 2242

Step 1

Concept

The number is \(118\times19+r\).

Step 2

Why this answer is correct

For the least value, take remainder 0, so the number is \(118\times19=2242\).

Step 3

Exam Tip

For least value questions, using remainder zero is the most direct method. चरण 1: संख्या \(118\times19+r\) होगी। चरण 2: सबसे छोटे मान के लिए शेषफल 0 लें, इसलिए संख्या \(118\times19=2242\) है। चरण 3: न्यूनतम मान के प्रश्न में शेषफल शून्य रखना सबसे सीधा तरीका है।

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Question Expert Mathematics Real Numbers Euclid’s Division Lemma Class 10 Level 1

यदि किसी संख्या को 91 से भाग देने पर भागफल 28 है, तो उस संख्या का सबसे छोटा संभव मान क्या होगा?

If a number gives quotient 28 when divided by 91, what is the least possible value of that number?

Explanation opens after your attempt
Correct Answer

A. 2548

Step 1

Concept

The number is \(91\times28+r\).

Step 2

Why this answer is correct

For the least value, the remainder is 0, so the number is \(91\times28=2548\).

Step 3

Exam Tip

In minimum value questions, taking remainder zero gives the answer quickly. चरण 1: संख्या \(91\times28+r\) होगी। चरण 2: सबसे छोटे मान के लिए शेषफल 0 होगा, इसलिए संख्या \(91\times28=2548\) है। चरण 3: न्यूनतम मान वाले प्रश्न में शेषफल शून्य लेने से उत्तर तुरंत मिलता है।

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