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

समीकरण \(x^2-7x-18=0\) के मूलों के घनों का योग क्या है?

What is the sum of cubes of the roots of \(x^2-7x-18=0\)?

Explanation opens after your attempt

Correct Answer

A. (721)

Step 1

Concept

The sum of roots is (7) and the product is (-18). (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=343+378=721).

Step 2

Why this answer is correct

The correct answer is A. (721). The sum of roots is (7) and the product is (-18). (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=343+378=721).

Step 3

Exam Tip

मूलों का योग (7) और गुणनफल (-18) है। (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=343+378=721)।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Introduction to Quadratic Equations
Difficulty: Expert
Level: 30

Question Hindi:
समीकरण (x^2-7x-18=0) के मूलों के घनों का योग क्या है?

Question English:
What is the sum of cubes of the roots of (x^2-7x-18=0)?

Options:
A. (721)
B. (343)
C. (378)
D. (-721)

Correct Answer:
A. (721)

Explanation Hindi:
मूलों का योग (7) और गुणनफल (-18) है। (\alpha^3+\beta^3=(\alpha+\beta)^3-3\alpha\beta(\alpha+\beta)=343+378=721)।

Explanation English:
The sum of roots is (7) and the product is (-18). (\alpha^3+\beta^3=(\alpha+\beta)^3-3\alpha\beta(\alpha+\beta)=343+378=721).

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

समीकरण \(x^2-6x-16=0\) के मूलों के घनों का योग क्या है?

What is the sum of cubes of the roots of \(x^2-6x-16=0\)?

Explanation opens after your attempt

Correct Answer

A. (504)

Step 1

Concept

The sum of roots is (6) and the product is (-16). (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=216+288=504).

Step 2

Why this answer is correct

The correct answer is A. (504). The sum of roots is (6) and the product is (-16). (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=216+288=504).

Step 3

Exam Tip

मूलों का योग (6) और गुणनफल (-16) है। (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=216+288=504)।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Introduction to Quadratic Equations
Difficulty: Expert
Level: 29

Question Hindi:
समीकरण (x^2-6x-16=0) के मूलों के घनों का योग क्या है?

Question English:
What is the sum of cubes of the roots of (x^2-6x-16=0)?

Options:
A. (504)
B. (216)
C. (288)
D. (-504)

Correct Answer:
A. (504)

Explanation Hindi:
मूलों का योग (6) और गुणनफल (-16) है। (\alpha^3+\beta^3=(\alpha+\beta)^3-3\alpha\beta(\alpha+\beta)=216+288=504)।

Explanation English:
The sum of roots is (6) and the product is (-16). (\alpha^3+\beta^3=(\alpha+\beta)^3-3\alpha\beta(\alpha+\beta)=216+288=504).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
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Question Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

समीकरण \(x^2-5x-14=0\) के मूलों के घनों का योग क्या है?

What is the sum of cubes of the roots of \(x^2-5x-14=0\)?

Explanation opens after your attempt

Correct Answer

A. (335)

Step 1

Concept

The sum of roots is (5) and the product is (-14). (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=125+210=335).

Step 2

Why this answer is correct

The correct answer is A. (335). The sum of roots is (5) and the product is (-14). (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=125+210=335).

Step 3

Exam Tip

मूलों का योग (5) और गुणनफल (-14) है। (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=125+210=335)।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Introduction to Quadratic Equations
Difficulty: Expert
Level: 28

Question Hindi:
समीकरण (x^2-5x-14=0) के मूलों के घनों का योग क्या है?

Question English:
What is the sum of cubes of the roots of (x^2-5x-14=0)?

Options:
A. (335)
B. (125)
C. (210)
D. (-335)

Correct Answer:
A. (335)

Explanation Hindi:
मूलों का योग (5) और गुणनफल (-14) है। (\alpha^3+\beta^3=(\alpha+\beta)^3-3\alpha\beta(\alpha+\beta)=125+210=335)।

Explanation English:
The sum of roots is (5) and the product is (-14). (\alpha^3+\beta^3=(\alpha+\beta)^3-3\alpha\beta(\alpha+\beta)=125+210=335).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
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Question Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण \(x^2-3x-10=0\) के मूलों के घनों का योग क्या है?

What is the sum of cubes of the roots of \(x^2-3x-10=0\)?

Explanation opens after your attempt

Correct Answer

A. (117)

Step 1

Concept

The sum of roots is (3) and the product is (-10). (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=27+90=117).

Step 2

Why this answer is correct

The correct answer is A. (117). The sum of roots is (3) and the product is (-10). (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=27+90=117).

Step 3

Exam Tip

मूलों का योग (3) और गुणनफल (-10) है। (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=27+90=117)।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Introduction to Quadratic Equations
Difficulty: Hard
Level: 30

Question Hindi:
समीकरण (x^2-3x-10=0) के मूलों के घनों का योग क्या है?

Question English:
What is the sum of cubes of the roots of (x^2-3x-10=0)?

Options:
A. (117)
B. (27)
C. (90)
D. (-117)

Correct Answer:
A. (117)

Explanation Hindi:
मूलों का योग (3) और गुणनफल (-10) है। (\alpha^3+\beta^3=(\alpha+\beta)^3-3\alpha\beta(\alpha+\beta)=27+90=117)।

Explanation English:
The sum of roots is (3) and the product is (-10). (\alpha^3+\beta^3=(\alpha+\beta)^3-3\alpha\beta(\alpha+\beta)=27+90=117).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
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Question Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

समीकरण \(x^2-2x-3=0\) के मूलों के घनों का योग क्या है?

What is the sum of cubes of the roots of \(x^2-2x-3=0\)?

Explanation opens after your attempt

Correct Answer

A. (26)

Step 1

Concept

The sum of roots is (2) and the product is (-3). (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=8+18=26).

Step 2

Why this answer is correct

The correct answer is A. (26). The sum of roots is (2) and the product is (-3). (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=8+18=26).

Step 3

Exam Tip

मूलों का योग (2) और गुणनफल (-3) है। (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=8+18=26)।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Introduction to Quadratic Equations
Difficulty: Hard
Level: 29

Question Hindi:
समीकरण (x^2-2x-3=0) के मूलों के घनों का योग क्या है?

Question English:
What is the sum of cubes of the roots of (x^2-2x-3=0)?

Options:
A. (26)
B. (8)
C. (20)
D. (-26)

Correct Answer:
A. (26)

Explanation Hindi:
मूलों का योग (2) और गुणनफल (-3) है। (\alpha^3+\beta^3=(\alpha+\beta)^3-3\alpha\beta(\alpha+\beta)=8+18=26)।

Explanation English:
The sum of roots is (2) and the product is (-3). (\alpha^3+\beta^3=(\alpha+\beta)^3-3\alpha\beta(\alpha+\beta)=8+18=26).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
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Question Expert Mathematics Real Numbers 3: Prime factorisation Class 10 Level 7

यदि \(540=2^2\times3^3\times5\), तो (540) के ऐसे गुणनखंडों की संख्या कितनी है जो पूर्ण घन हैं?

If \(540=2^2\times3^3\times5\), how many factors of (540) are perfect cubes?

Explanation opens after your attempt

Correct Answer

A. (2)

Step 1

Concept

A cube factor must have exponents that are multiples of (3).

Step 2

Why this answer is correct

For (2), only (0); for (3), (0) or (3); for (5), only (0). Total (=2).

Step 3

Exam Tip

Remember that (0) is also a multiple of (3). चरण 1: पूर्ण घन गुणनखंड में हर अभाज्य घात (3) की गुणज होनी चाहिए। चरण 2: (2) की घात केवल (0), (3) की घात (0) या (3), और (5) की घात केवल (0) हो सकती है। कुल \(1\times2\times1=2\)। चरण 3: घन गुणनखंडों में (0) भी (3) की गुणज माना जाता है।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Real Numbers
Topic: 3: Prime factorisation
Difficulty: Expert
Level: 7

Question Hindi:
यदि (540=2^2\times3^3\times5), तो (540) के ऐसे गुणनखंडों की संख्या कितनी है जो पूर्ण घन हैं?

Question English:
If (540=2^2\times3^3\times5), how many factors of (540) are perfect cubes?

Options:
A. (2)
B. (3)
C. (4)
D. (6)

Correct Answer:
A. (2)

Explanation Hindi:
चरण 1: पूर्ण घन गुणनखंड में हर अभाज्य घात (3) की गुणज होनी चाहिए। चरण 2: (2) की घात केवल (0), (3) की घात (0) या (3), और (5) की घात केवल (0) हो सकती है। कुल (1\times2\times1=2)। चरण 3: घन गुणनखंडों में (0) भी (3) की गुणज माना जाता है।

Explanation English:
Step 1: A cube factor must have exponents that are multiples of (3). Step 2: For (2), only (0); for (3), (0) or (3); for (5), only (0). Total (=2). Step 3: Remember that (0) is also a multiple of (3).

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5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
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Question Expert Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

अनुक्रम \(1,8,27,64,\ldots\) समांतर श्रेणी है या नहीं?

Is the sequence \(1,8,27,64,\ldots\) an AP?

Explanation opens after your attempt

Correct Answer

D. नहीं, अंतर \(7,19,37,\ldots\) हैंNo, the differences are \(7,19,37,\ldots\)

Step 1

Concept

The consecutive differences are not equal, so it is not an AP. In exams, test constancy of differences, not just the visible pattern.

Step 2

Why this answer is correct

The correct answer is D. नहीं, अंतर \(7,19,37,\ldots\) हैं / No, the differences are \(7,19,37,\ldots\). The consecutive differences are not equal, so it is not an AP. In exams, test constancy of differences, not just the visible pattern.

Step 3

Exam Tip

लगातार अंतर बराबर नहीं हैं, इसलिए यह समांतर श्रेणी नहीं है। परीक्षा में नाम या पैटर्न नहीं, अंतर की स्थिरता जांचें।

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Question Page:
https://muftshiksha.com/question/is-the-sequence-1-8-27-64-ldots-an-ap

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Arithmetic Progressions (AP)
Topic: Introduction to APs and common difference.
Difficulty: Expert
Level: 63

Question Hindi:
अनुक्रम (1,8,27,64,\ldots) समांतर श्रेणी है या नहीं?

Question English:
Is the sequence (1,8,27,64,\ldots) an AP?

Options:
A. हाँ, (d=7) / Yes, (d=7)
B. नहीं, क्योंकि पद घन हैं / No, because the terms are cubes
C. हाँ, (d=19) / Yes, (d=19)
D. नहीं, अंतर (7,19,37,\ldots) हैं / No, the differences are (7,19,37,\ldots)

Correct Answer:
D. नहीं, अंतर (7,19,37,\ldots) हैं / No, the differences are (7,19,37,\ldots)

Explanation Hindi:
लगातार अंतर बराबर नहीं हैं, इसलिए यह समांतर श्रेणी नहीं है। परीक्षा में नाम या पैटर्न नहीं, अंतर की स्थिरता जांचें।

Explanation English:
The consecutive differences are not equal, so it is not an AP. In exams, test constancy of differences, not just the visible pattern.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि \(y \neq 0\), तो (\dfrac{(x+y)³-(x-y)³}{2y}) का सरल रूप क्या है?

If \(y \neq 0\), what is the simplified form of (\dfrac{(x+y)³-(x-y)³}{2y})?

Explanation opens after your attempt

Correct Answer

A. \(,3x^2+y^2,\)

Step 1

Concept

The numerator difference is (6x^-2y+2y^-3=2y\(3x^2+y^2\)), so division gives \(3x^2+y^2\). In exams, take out the common factor.

Step 2

Why this answer is correct

The correct answer is A. \(,3x^2+y^2,\). The numerator difference is (6x^-2y+2y^-3=2y\(3x^2+y^2\)), so division gives \(3x^2+y^2\). In exams, take out the common factor.

Step 3

Exam Tip

ऊपर का अंतर (6x^-2y+2y^-3=2y\(3x^2+y^2\)) है, इसलिए भाग देने पर \(3x^2+y^2\) मिलता है। परीक्षा में common factor निकालें।

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AI Video Prompt 16:9 + 9:16

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Question Page:
https://muftshiksha.com/question/if-y-neq-0-what-is-the-simplified-form-of-dfrac-x-y-3-x-y-3-2y

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Hard
Level: 44

Question Hindi:
यदि (y \neq 0), तो (\dfrac{(x+y)^3-(x-y)^3}{2y}) का सरल रूप क्या है?

Question English:
If (y \neq 0), what is the simplified form of (\dfrac{(x+y)^3-(x-y)^3}{2y})?

Options:
A. (,3x^2+y^2,)
B. (,x^2+3y^2,)
C. (,3x^2-y^2,)
D. (,x^2-y^2,)

Correct Answer:
A. (,3x^2+y^2,)

Explanation Hindi:
ऊपर का अंतर (6x^2y+2y^3=2y(3x^2+y^2)) है, इसलिए भाग देने पर (3x^2+y^2) मिलता है। परीक्षा में common factor निकालें।

Explanation English:
The numerator difference is (6x^2y+2y^3=2y(3x^2+y^2)), so division gives (3x^2+y^2). In exams, take out the common factor.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((x+1)³-(x-1)³) का सरल रूप क्या है?

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

Explanation opens after your attempt

Correct Answer

A. \(,6x^2+2,\)

Step 1

Concept

On expansion, ((x+1)³=x^-3+3x^-2+3x+1) and ((x-1)³=x^-3-3x^-2+3x-1), so the difference is \(6x^2+2\). In exams, expand cubes carefully.

Step 2

Why this answer is correct

The correct answer is A. \(,6x^2+2,\). On expansion, ((x+1)³=x^-3+3x^-2+3x+1) and ((x-1)³=x^-3-3x^-2+3x-1), so the difference is \(6x^2+2\). In exams, expand cubes carefully.

Step 3

Exam Tip

विस्तार करने पर ((x+1)³=x^-3+3x^-2+3x+1) और ((x-1)³=x^-3-3x^-2+3x-1), इसलिए अंतर \(6x^2+2\) है। परीक्षा में cube expansion ध्यान से करें।

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AI Video Prompt 16:9 + 9:16

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Question Page:
https://muftshiksha.com/question/what-is-the-simplified-form-of-x-1-3-x-1-3

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Hard
Level: 44

Question Hindi:
((x+1)^3-(x-1)^3) का सरल रूप क्या है?

Question English:
What is the simplified form of ((x+1)^3-(x-1)^3)?

Options:
A. (,6x^2+2,)
B. (,6x^2-2,)
C. (,2x^3+2,)
D. (,3x^2+1,)

Correct Answer:
A. (,6x^2+2,)

Explanation Hindi:
विस्तार करने पर ((x+1)^3=x^3+3x^2+3x+1) और ((x-1)^3=x^3-3x^2+3x-1), इसलिए अंतर (6x^2+2) है। परीक्षा में cube expansion ध्यान से करें।

Explanation English:
On expansion, ((x+1)^3=x^3+3x^2+3x+1) and ((x-1)^3=x^3-3x^2+3x-1), so the difference is (6x^2+2). In exams, expand cubes carefully.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\(8x^3+1\)) को ((2x+1)) से भाग देने पर भागफल क्या है?

What is the quotient when (\(8x^3+1\)) is divided by ((2x+1))?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

Because (8x^-3+1=(2x)³+1³=(2x+1)\(4x^2-2x+1\)). In exams, remember the identity for sum of cubes.

Step 2

Why this answer is correct

The correct answer is A. \(,4x^2-2x+1,\). Because (8x^-3+1=(2x)³+1³=(2x+1)\(4x^2-2x+1\)). In exams, remember the identity for sum of cubes.

Step 3

Exam Tip

क्योंकि (8x^-3+1=(2x)³+1³=(2x+1)\(4x^2-2x+1\))। परीक्षा में sum of cubes की identity याद रखें।

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AI Video Prompt 16:9 + 9:16

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Create a premium AI MCQ quiz video for Muft Shiksha in BOTH formats: 16:9 landscape and 9:16 vertical short.

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Question Page:
https://muftshiksha.com/question/what-is-the-quotient-when-8x-3-1-is-divided-by-2x-1

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Hard
Level: 44

Question Hindi:
((8x^3+1)) को ((2x+1)) से भाग देने पर भागफल क्या है?

Question English:
What is the quotient when ((8x^3+1)) is divided by ((2x+1))?

Options:
A. (,4x^2-2x+1,)
B. (,4x^2+2x+1,)
C. (,4x^2-1,)
D. (,2x^2-2x+1,)

Correct Answer:
A. (,4x^2-2x+1,)

Explanation Hindi:
क्योंकि (8x^3+1=(2x)^3+1^3=(2x+1)(4x^2-2x+1))। परीक्षा में sum of cubes की identity याद रखें।

Explanation English:
Because (8x^3+1=(2x)^3+1^3=(2x+1)(4x^2-2x+1)). In exams, remember the identity for sum of cubes.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((x-2)\(x^2+2x+4\)) का विस्तार क्या है?

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

Explanation opens after your attempt

Correct Answer

A. \(,x^3-8,\)

Step 1

Concept

This matches ((a-b)\(a^2+ab+b^2\)=a^-3-b^-3), so the answer is \(x^3-8\). In exams, identifying the identity makes expansion faster.

Step 2

Why this answer is correct

The correct answer is A. \(,x^3-8,\). This matches ((a-b)\(a^2+ab+b^2\)=a^-3-b^-3), so the answer is \(x^3-8\). In exams, identifying the identity makes expansion faster.

Step 3

Exam Tip

यह ((a-b)\(a^2+ab+b^2\)=a^-3-b^-3) का रूप है, इसलिए उत्तर \(x^3-8\) है। परीक्षा में identity पहचानने से विस्तार जल्दी होता है।

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AI Video Prompt 16:9 + 9:16

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Create a premium AI MCQ quiz video for Muft Shiksha in BOTH formats: 16:9 landscape and 9:16 vertical short.

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Question Page:
https://muftshiksha.com/question/what-is-the-expansion-of-x-2-x-2-2x-4

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Hard
Level: 44

Question Hindi:
((x-2)(x^2+2x+4)) का विस्तार क्या है?

Question English:
What is the expansion of ((x-2)(x^2+2x+4))?

Options:
A. (,x^3-8,)
B. (,x^3+8,)
C. (,x^3-4x-8,)
D. (,x^3+4x-8,)

Correct Answer:
A. (,x^3-8,)

Explanation Hindi:
यह ((a-b)(a^2+ab+b^2)=a^3-b^3) का रूप है, इसलिए उत्तर (x^3-8) है। परीक्षा में identity पहचानने से विस्तार जल्दी होता है।

Explanation English:
This matches ((a-b)(a^2+ab+b^2)=a^3-b^3), so the answer is (x^3-8). In exams, identifying the identity makes expansion faster.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\(x^3-27\)) को ((x-3)) से भाग देने पर भागफल क्या होगा?

What is the quotient when (\(x^3-27\)) is divided by ((x-3))?

Explanation opens after your attempt

Correct Answer

A. \(,x^2+3x+9,\)

Step 1

Concept

Because (x^-3-27=(x-3)\(x^2+3x+9\)), the quotient is \(x^2+3x+9\). In exams, identify the difference of cubes.

Step 2

Why this answer is correct

The correct answer is A. \(,x^2+3x+9,\). Because (x^-3-27=(x-3)\(x^2+3x+9\)), the quotient is \(x^2+3x+9\). In exams, identify the difference of cubes.

Step 3

Exam Tip

क्योंकि (x^-3-27=(x-3)\(x^2+3x+9\)), इसलिए भागफल \(x^2+3x+9\) है। परीक्षा में घन के अंतर की पहचान करें।

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AI Video Prompt 16:9 + 9:16

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- Name: Muft Shiksha
- Website: https://muftshiksha.com
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Question Page:
https://muftshiksha.com/question/what-is-the-quotient-when-x-3-27-is-divided-by-x-3

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Hard
Level: 44

Question Hindi:
((x^3-27)) को ((x-3)) से भाग देने पर भागफल क्या होगा?

Question English:
What is the quotient when ((x^3-27)) is divided by ((x-3))?

Options:
A. (,x^2+3x+9,)
B. (,x^2-3x+9,)
C. (,x^2+9x+3,)
D. (,x^2-9,)

Correct Answer:
A. (,x^2+3x+9,)

Explanation Hindi:
क्योंकि (x^3-27=(x-3)(x^2+3x+9)), इसलिए भागफल (x^2+3x+9) है। परीक्षा में घन के अंतर की पहचान करें।

Explanation English:
Because (x^3-27=(x-3)(x^2+3x+9)), the quotient is (x^2+3x+9). In exams, identify the difference of cubes.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

Custom Support:
- Make 16:9 version for YouTube/Facebook.
- Make 9:16 version for Shorts/Reels.
- Add Hindi-English natural voice-over.
- Add readable subtitles.
- Add light background music, low volume.
- Keep all text inside safe margins.
- Use smooth transitions, no clutter, no watermark except Muft Shiksha branding.
- Formula/Math/Chemistry text must stay exactly readable; use LaTeX-style clean rendering where needed.

Output Needed:
- Final narration script.
- Scene-by-scene visual direction.
- Text overlays for 16:9 and 9:16.
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- Hashtags: #MuftShiksha #FreeEducation #MCQ #Quiz #Class10 #Study

Open Question

Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\(x^3-8\)) को ((x-2)) से भाग देने पर भागफल क्या होगा?

What is the quotient when (\(x^3-8\)) is divided by ((x-2))?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

Because (x^-3-8=(x-2)\(x^2+2x+4\)), the quotient is \(x^2+2x+4\). In exams, remember the identity for cubes.

Step 2

Why this answer is correct

The correct answer is A. \(,x^2+2x+4,\). Because (x^-3-8=(x-2)\(x^2+2x+4\)), the quotient is \(x^2+2x+4\). In exams, remember the identity for cubes.

Step 3

Exam Tip

क्योंकि (x^-3-8=(x-2)\(x^2+2x+4\)), इसलिए भागफल \(x^2+2x+4\) है। परीक्षा में cubes की identity याद रखें।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Hard
Level: 43

Question Hindi:
((x^3-8)) को ((x-2)) से भाग देने पर भागफल क्या होगा?

Question English:
What is the quotient when ((x^3-8)) is divided by ((x-2))?

Options:
A. (,x^2+2x+4,)
B. (,x^2-2x+4,)
C. (,x^2+4x+2,)
D. (,x^2-4,)

Correct Answer:
A. (,x^2+2x+4,)

Explanation Hindi:
क्योंकि (x^3-8=(x-2)(x^2+2x+4)), इसलिए भागफल (x^2+2x+4) है। परीक्षा में cubes की identity याद रखें।

Explanation English:
Because (x^3-8=(x-2)(x^2+2x+4)), the quotient is (x^2+2x+4). In exams, remember the identity for cubes.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि \(x^2-10x+21=0\) के मूल \(\alpha\) और \(\beta\) हैं तो \(\alpha^3+\beta^3\) का मान क्या है?

If \(\alpha\) and \(\beta\) are roots of \(x^2-10x+21=0\), what is the value of \(\alpha^3+\beta^3\)?

Explanation opens after your attempt

Correct Answer

A. (370)

Step 1

Concept

\(\alpha+\beta=10\) and \(\alpha\beta=21\). (\alpha^-3+\beta^-3=10³-3(21)(10)=370).

Step 2

Why this answer is correct

The correct answer is A. (370). \(\alpha+\beta=10\) and \(\alpha\beta=21\). (\alpha^-3+\beta^-3=10³-3(21)(10)=370).

Step 3

Exam Tip

\(\alpha+\beta=10\) और \(\alpha\beta=21\) है। (\alpha^-3+\beta^-3=10³-3(21)(10)=370) होगा।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Roots of a Quadratic Equation
Difficulty: Hard
Level: 32

Question Hindi:
यदि (x^2-10x+21=0) के मूल (\alpha) और (\beta) हैं तो (\alpha^3+\beta^3) का मान क्या है?

Question English:
If (\alpha) and (\beta) are roots of (x^2-10x+21=0), what is the value of (\alpha^3+\beta^3)?

Options:
A. (370)
B. (1000)
C. (630)
D. (210)

Correct Answer:
A. (370)

Explanation Hindi:
(\alpha+\beta=10) और (\alpha\beta=21) है। (\alpha^3+\beta^3=10^3-3(21)(10)=370) होगा।

Explanation English:
(\alpha+\beta=10) and (\alpha\beta=21). (\alpha^3+\beta^3=10^3-3(21)(10)=370).

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1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
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7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

यदि \(x^2-9x+20=0\) के मूल \(\alpha\) और \(\beta\) हैं तो \(\alpha^3+\beta^3\) का मान क्या है?

If \(\alpha\) and \(\beta\) are roots of \(x^2-9x+20=0\), what is the value of \(\alpha^3+\beta^3\)?

Explanation opens after your attempt

Correct Answer

A. (369)

Step 1

Concept

\(\alpha+\beta=9\) and \(\alpha\beta=20\). (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=729-540=189).

Step 2

Why this answer is correct

The correct answer is A. (369). \(\alpha+\beta=9\) and \(\alpha\beta=20\). (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=729-540=189).

Step 3

Exam Tip

\(\alpha+\beta=9\) और \(\alpha\beta=20\) है। (\alpha^-3+\beta^-3=\(\alpha+\beta\)³-3\alpha\beta\(\alpha+\beta\)=729-540=189) नहीं बल्कि (189) होगा।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Roots of a Quadratic Equation
Difficulty: Hard
Level: 31

Question Hindi:
यदि (x^2-9x+20=0) के मूल (\alpha) और (\beta) हैं तो (\alpha^3+\beta^3) का मान क्या है?

Question English:
If (\alpha) and (\beta) are roots of (x^2-9x+20=0), what is the value of (\alpha^3+\beta^3)?

Options:
A. (369)
B. (189)
C. (729)
D. (180)

Correct Answer:
A. (369)

Explanation Hindi:
(\alpha+\beta=9) और (\alpha\beta=20) है। (\alpha^3+\beta^3=(\alpha+\beta)^3-3\alpha\beta(\alpha+\beta)=729-540=189) नहीं बल्कि (189) होगा।

Explanation English:
(\alpha+\beta=9) and (\alpha\beta=20). (\alpha^3+\beta^3=(\alpha+\beta)^3-3\alpha\beta(\alpha+\beta)=729-540=189).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 27

कौन सा विकल्प \(\sqrt[3]{20}\) के बारे में सही है?

Which option is correct about \(\sqrt[3]{20}\)?

Explanation opens after your attempt

Correct Answer

A. यह अपरिमेय हैIt is irrational

Step 1

Concept

(20) is not a perfect cube so \(\sqrt[3]{20}\) is irrational. Identify perfect cubes in cube roots.

Step 2

Why this answer is correct

The correct answer is A. यह अपरिमेय है / It is irrational. (20) is not a perfect cube so \(\sqrt[3]{20}\) is irrational. Identify perfect cubes in cube roots.

Step 3

Exam Tip

(20) पूर्ण घन नहीं है इसलिए \(\sqrt[3]{20}\) अपरिमेय है। घनमूल में पूर्ण घन पहचानें।

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Question Page:
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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Irrational numbers and real numbers
Difficulty: Medium
Level: 27

Question Hindi:
कौन सा विकल्प (\sqrt[3]{20}) के बारे में सही है?

Question English:
Which option is correct about (\sqrt[3]{20})?

Options:
A. यह अपरिमेय है / It is irrational
B. यह (4) है / It is (4)
C. यह (5) है / It is (5)
D. यह पूर्णांक है / It is an integer

Correct Answer:
A. यह अपरिमेय है / It is irrational

Explanation Hindi:
(20) पूर्ण घन नहीं है इसलिए (\sqrt[3]{20}) अपरिमेय है। घनमूल में पूर्ण घन पहचानें।

Explanation English:
(20) is not a perfect cube so (\sqrt[3]{20}) is irrational. Identify perfect cubes in cube roots.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 26

कौन सा विकल्प \(\sqrt[3]{12}\) के लिए सही है?

Which option is correct for \(\sqrt[3]{12}\)?

Explanation opens after your attempt

Correct Answer

A. यह अपरिमेय हैIt is irrational

Step 1

Concept

(12) is not a perfect cube so \(\sqrt[3]{12}\) is irrational. Check perfect cubes in cube roots.

Step 2

Why this answer is correct

The correct answer is A. यह अपरिमेय है / It is irrational. (12) is not a perfect cube so \(\sqrt[3]{12}\) is irrational. Check perfect cubes in cube roots.

Step 3

Exam Tip

(12) पूर्ण घन नहीं है इसलिए \(\sqrt[3]{12}\) अपरिमेय है। घनमूल में पूर्ण घन देखें।

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Question Page:
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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Irrational numbers and real numbers
Difficulty: Medium
Level: 26

Question Hindi:
कौन सा विकल्प (\sqrt[3]{12}) के लिए सही है?

Question English:
Which option is correct for (\sqrt[3]{12})?

Options:
A. यह अपरिमेय है / It is irrational
B. यह (4) है / It is (4)
C. यह (3) है / It is (3)
D. यह सांत दशमलव है / It is a terminating decimal

Correct Answer:
A. यह अपरिमेय है / It is irrational

Explanation Hindi:
(12) पूर्ण घन नहीं है इसलिए (\sqrt[3]{12}) अपरिमेय है। घनमूल में पूर्ण घन देखें।

Explanation English:
(12) is not a perfect cube so (\sqrt[3]{12}) is irrational. Check perfect cubes in cube roots.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Medium Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\sqrt[3]{16}\) के लिए सही है?

Which option is correct for \(\sqrt[3]{16}\)?

Explanation opens after your attempt

Correct Answer

A. यह अपरिमेय हैIt is irrational

Step 1

Concept

(16) is not a perfect cube so its cube root is irrational. Identify perfect cubes in cube roots.

Step 2

Why this answer is correct

The correct answer is A. यह अपरिमेय है / It is irrational. (16) is not a perfect cube so its cube root is irrational. Identify perfect cubes in cube roots.

Step 3

Exam Tip

(16) पूर्ण घन नहीं है इसलिए इसकी घनमूल अपरिमेय है। घनमूल में पूर्ण घन पहचानें।

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Question Page:
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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Irrational numbers and real numbers
Difficulty: Medium
Level: 25

Question Hindi:
कौन सा विकल्प (\sqrt[3]{16}) के लिए सही है?

Question English:
Which option is correct for (\sqrt[3]{16})?

Options:
A. यह अपरिमेय है / It is irrational
B. यह (4) है / It is (4)
C. यह (8) है / It is (8)
D. यह सांत दशमलव है / It is terminating decimal

Correct Answer:
A. यह अपरिमेय है / It is irrational

Explanation Hindi:
(16) पूर्ण घन नहीं है इसलिए इसकी घनमूल अपरिमेय है। घनमूल में पूर्ण घन पहचानें।

Explanation English:
(16) is not a perfect cube so its cube root is irrational. Identify perfect cubes in cube roots.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

Custom Support:
- Make 16:9 version for YouTube/Facebook.
- Make 9:16 version for Shorts/Reels.
- Add Hindi-English natural voice-over.
- Add readable subtitles.
- Add light background music, low volume.
- Keep all text inside safe margins.
- Use smooth transitions, no clutter, no watermark except Muft Shiksha branding.
- Formula/Math/Chemistry text must stay exactly readable; use LaTeX-style clean rendering where needed.

Output Needed:
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Open Question

Question Easy Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 27

\(\sqrt[3]{9}\) के बारे में सही कथन कौन सा है?

Which statement is correct about \(\sqrt[3]{9}\)?

Explanation opens after your attempt

Correct Answer

A. यह अपरिमेय हैIt is irrational

Step 1

Concept

(9) is not a perfect cube so \(\sqrt[3]{9}\) is irrational. Identifying perfect cubes is important in cube roots.

Step 2

Why this answer is correct

The correct answer is A. यह अपरिमेय है / It is irrational. (9) is not a perfect cube so \(\sqrt[3]{9}\) is irrational. Identifying perfect cubes is important in cube roots.

Step 3

Exam Tip

(9) पूर्ण घन नहीं है इसलिए \(\sqrt[3]{9}\) अपरिमेय है। घनमूल में पूर्ण घन पहचानना जरूरी है।

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AI Video Prompt 16:9 + 9:16

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Question Page:
https://muftshiksha.com/question/which-statement-is-correct-about-sqrt-3-9

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Irrational numbers and real numbers
Difficulty: Easy
Level: 27

Question Hindi:
(\sqrt[3]{9}) के बारे में सही कथन कौन सा है?

Question English:
Which statement is correct about (\sqrt[3]{9})?

Options:
A. यह अपरिमेय है / It is irrational
B. यह (3) है / It is (3)
C. यह पूर्णांक है / It is an integer
D. यह परिमेय है / It is rational

Correct Answer:
A. यह अपरिमेय है / It is irrational

Explanation Hindi:
(9) पूर्ण घन नहीं है इसलिए (\sqrt[3]{9}) अपरिमेय है। घनमूल में पूर्ण घन पहचानना जरूरी है।

Explanation English:
(9) is not a perfect cube so (\sqrt[3]{9}) is irrational. Identifying perfect cubes is important in cube roots.

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Question Easy Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 26

\(\sqrt[3]{4}\) के बारे में कौन सा कथन सही है?

Which statement is correct about \(\sqrt[3]{4}\)?

Explanation opens after your attempt

Correct Answer

A. यह अपरिमेय हैIt is irrational

Step 1

Concept

(4) is not a perfect cube so \(\sqrt[3]{4}\) is irrational. Identify perfect cubes in cube roots.

Step 2

Why this answer is correct

The correct answer is A. यह अपरिमेय है / It is irrational. (4) is not a perfect cube so \(\sqrt[3]{4}\) is irrational. Identify perfect cubes in cube roots.

Step 3

Exam Tip

(4) पूर्ण घन नहीं है इसलिए \(\sqrt[3]{4}\) अपरिमेय है। घनमूल में पूर्ण घन पहचानें।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Irrational numbers and real numbers
Difficulty: Easy
Level: 26

Question Hindi:
(\sqrt[3]{4}) के बारे में कौन सा कथन सही है?

Question English:
Which statement is correct about (\sqrt[3]{4})?

Options:
A. यह अपरिमेय है / It is irrational
B. यह (2) है / It is (2)
C. यह पूर्णांक है / It is an integer
D. यह शून्य है / It is zero

Correct Answer:
A. यह अपरिमेय है / It is irrational

Explanation Hindi:
(4) पूर्ण घन नहीं है इसलिए (\sqrt[3]{4}) अपरिमेय है। घनमूल में पूर्ण घन पहचानें।

Explanation English:
(4) is not a perfect cube so (\sqrt[3]{4}) is irrational. Identify perfect cubes in cube roots.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Medium Mathematics Real Numbers 3: Prime factorisation Class 10 Level 12

(729) के अभाज्य गुणनखंडन में (3) की घात कितनी है?

What is the exponent of (3) in the prime factorisation of (729)?

Explanation opens after your attempt

Correct Answer

C. 6

Step 1

Concept

\(729=27 \times 27\).

Step 2

Why this answer is correct

Since \(27=3^3\), \(729=3^3 \times 3^3=3^6\).

Step 3

Exam Tip

For larger powers, split the number into familiar cubes. चरण 1: \(729=27 \times 27\) है। चरण 2: \(27=3^3\), इसलिए \(729=3^3 \times 3^3=3^6\)। चरण 3: बड़ी घातों के लिए संख्या को पहचाने हुए घनों में तोड़ें।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Real Numbers
Topic: 3: Prime factorisation
Difficulty: Medium
Level: 12

Question Hindi:
(729) के अभाज्य गुणनखंडन में (3) की घात कितनी है?

Question English:
What is the exponent of (3) in the prime factorisation of (729)?

Options:
A. 4
B. 5
C. 6
D. 7

Correct Answer:
C. 6

Explanation Hindi:
चरण 1: (729=27 \times 27) है। चरण 2: (27=3^3), इसलिए (729=3^3 \times 3^3=3^6)। चरण 3: बड़ी घातों के लिए संख्या को पहचाने हुए घनों में तोड़ें।

Explanation English:
Step 1: (729=27 \times 27). Step 2: Since (27=3^3), (729=3^3 \times 3^3=3^6). Step 3: For larger powers, split the number into familiar cubes.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Medium Mathematics Real Numbers 3: Prime factorisation Class 10 Level 12

कौन सा विकल्प (675) का सही अभाज्य गुणनखंडन है?

Which option is the correct prime factorisation of (675)?

Explanation opens after your attempt

Correct Answer

B. \(3^3 \times 5^2\)

Step 1

Concept

Write (675) as \(27 \times 25\).

Step 2

Why this answer is correct

\(27=3^3\) and \(25=5^2\), so \(675=3^3 \times 5^2\).

Step 3

Exam Tip

Splitting a number into familiar squares and cubes is a good method. चरण 1: (675) को \(27 \times 25\) लिखें। चरण 2: \(27=3^3\) और \(25=5^2\), इसलिए \(675=3^3 \times 5^2\)। चरण 3: संख्या को आसान वर्ग और घन में तोड़ना अच्छा तरीका है।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Real Numbers
Topic: 3: Prime factorisation
Difficulty: Medium
Level: 12

Question Hindi:
कौन सा विकल्प (675) का सही अभाज्य गुणनखंडन है?

Question English:
Which option is the correct prime factorisation of (675)?

Options:
A. (3^2 \times 5^2)
B. (3^3 \times 5^2)
C. (3^2 \times 5^3)
D. (3^3 \times 5)

Correct Answer:
B. (3^3 \times 5^2)

Explanation Hindi:
चरण 1: (675) को (27 \times 25) लिखें। चरण 2: (27=3^3) और (25=5^2), इसलिए (675=3^3 \times 5^2)। चरण 3: संख्या को आसान वर्ग और घन में तोड़ना अच्छा तरीका है।

Explanation English:
Step 1: Write (675) as (27 \times 25). Step 2: (27=3^3) and (25=5^2), so (675=3^3 \times 5^2). Step 3: Splitting a number into familiar squares and cubes is a good method.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
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Question Medium Mathematics Real Numbers 3: Prime factorisation Class 10 Level 11

कौन सा विकल्प (432) का सही अभाज्य गुणनखंडन है?

Which option is the correct prime factorisation of (432)?

Explanation opens after your attempt

Correct Answer

B. \(2^4 \times 3^3\)

Step 1

Concept

Write (432) as \(16 \times 27\).

Step 2

Why this answer is correct

\(16=2^4\) and \(27=3^3\), so \(432=2^4 \times 3^3\).

Step 3

Exam Tip

Recognising squares and cubes makes factorisation faster. चरण 1: (432) को \(16 \times 27\) लिखें। चरण 2: \(16=2^4\) और \(27=3^3\), इसलिए \(432=2^4 \times 3^3\)। चरण 3: वर्ग और घन संख्याएं पहचानना अभाज्य गुणनखंडन को तेज बनाता है।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Real Numbers
Topic: 3: Prime factorisation
Difficulty: Medium
Level: 11

Question Hindi:
कौन सा विकल्प (432) का सही अभाज्य गुणनखंडन है?

Question English:
Which option is the correct prime factorisation of (432)?

Options:
A. (2^3 \times 3^3)
B. (2^4 \times 3^3)
C. (2^3 \times 3^4)
D. (2^4 \times 3^2)

Correct Answer:
B. (2^4 \times 3^3)

Explanation Hindi:
चरण 1: (432) को (16 \times 27) लिखें। चरण 2: (16=2^4) और (27=3^3), इसलिए (432=2^4 \times 3^3)। चरण 3: वर्ग और घन संख्याएं पहचानना अभाज्य गुणनखंडन को तेज बनाता है।

Explanation English:
Step 1: Write (432) as (16 \times 27). Step 2: (16=2^4) and (27=3^3), so (432=2^4 \times 3^3). Step 3: Recognising squares and cubes makes factorisation faster.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Expert Mathematics Real Numbers 3: Prime factorisation Class 10 Level 9

किस विकल्प में (72) का अभाज्य गुणनखंडन सही रूप में दिया गया है?

Which option gives the prime factorisation of (72) correctly?

Explanation opens after your attempt

Correct Answer

A. \(2^3 \times 3^2\)

Step 1

Concept

Write \(72=8 \times 9\).

Step 2

Why this answer is correct

\(8=2^3\) and \(9=3^2\), so \(72=2^3 \times 3^2\).

Step 3

Exam Tip

Recognising simple squares and cubes speeds up factorisation. चरण 1: \(72=8 \times 9\) लिखें। चरण 2: \(8=2^3\) और \(9=3^2\), इसलिए \(72=2^3 \times 3^2\)। चरण 3: आसान वर्ग और घन पहचानना गुणनखंडन को तेज बनाता है।

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AI Video Prompt 16:9 + 9:16

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Real Numbers
Topic: 3: Prime factorisation
Difficulty: Expert
Level: 9

Question Hindi:
किस विकल्प में (72) का अभाज्य गुणनखंडन सही रूप में दिया गया है?

Question English:
Which option gives the prime factorisation of (72) correctly?

Options:
A. (2^3 \times 3^2)
B. (2^2 \times 3^3)
C. (2^4 \times 3)
D. (2 \times 3^4)

Correct Answer:
A. (2^3 \times 3^2)

Explanation Hindi:
चरण 1: (72=8 \times 9) लिखें। चरण 2: (8=2^3) और (9=3^2), इसलिए (72=2^3 \times 3^2)। चरण 3: आसान वर्ग और घन पहचानना गुणनखंडन को तेज बनाता है।

Explanation English:
Step 1: Write (72=8 \times 9). Step 2: (8=2^3) and (9=3^2), so (72=2^3 \times 3^2). Step 3: Recognising simple squares and cubes speeds up factorisation.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Expert Mathematics Real Numbers 3: Prime factorisation Class 10 Level 9

यदि \(N=2^6 \times 3^2\) है, तो (N) को पूर्ण घन बनाने के लिए कम से कम किससे गुणा करना होगा?

If \(N=2^6 \times 3^2\), by the least number should (N) be multiplied to make it a perfect cube?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

In a perfect cube, every prime exponent must be a multiple of (3).

Step 2

Why this answer is correct

\(2^6\) is fine, but \(3^2\) needs one more (3) to become \(3^3\).

Step 3

Exam Tip

For cubes, make exponents multiples of (3). चरण 1: पूर्ण घन में हर अभाज्य की घात (3) की गुणज होनी चाहिए। चरण 2: \(2^6\) ठीक है क्योंकि (6), (3) की गुणज है; \(3^2\) को \(3^3\) बनाने के लिए एक (3) और चाहिए। चरण 3: पूर्ण घन के लिए घातों को (3,6,9) जैसे गुणज बनाएं।

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Question Page:
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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Real Numbers
Topic: 3: Prime factorisation
Difficulty: Expert
Level: 9

Question Hindi:
यदि (N=2^6 \times 3^2) है, तो (N) को पूर्ण घन बनाने के लिए कम से कम किससे गुणा करना होगा?

Question English:
If (N=2^6 \times 3^2), by the least number should (N) be multiplied to make it a perfect cube?

Options:
A. (3)
B. (2)
C. (6)
D. (9)

Correct Answer:
A. (3)

Explanation Hindi:
चरण 1: पूर्ण घन में हर अभाज्य की घात (3) की गुणज होनी चाहिए। चरण 2: (2^6) ठीक है क्योंकि (6), (3) की गुणज है; (3^2) को (3^3) बनाने के लिए एक (3) और चाहिए। चरण 3: पूर्ण घन के लिए घातों को (3,6,9) जैसे गुणज बनाएं।

Explanation English:
Step 1: In a perfect cube, every prime exponent must be a multiple of (3). Step 2: (2^6) is fine, but (3^2) needs one more (3) to become (3^3). Step 3: For cubes, make exponents multiples of (3).

Video Structure:
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समीकरण \(x^2-7x-18=0\) के मूलों के घनों का योग क्या है?

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समीकरण \(x^2-6x-16=0\) के मूलों के घनों का योग क्या है?

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समीकरण \(x^2-5x-14=0\) के मूलों के घनों का योग क्या है?

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समीकरण \(x^2-3x-10=0\) के मूलों के घनों का योग क्या है?

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समीकरण \(x^2-2x-3=0\) के मूलों के घनों का योग क्या है?

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यदि \(540=2^2\times3^3\times5\), तो (540) के ऐसे गुणनखंडों की संख्या कितनी है जो पूर्ण घन हैं?

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अनुक्रम \(1,8,27,64,\ldots\) समांतर श्रेणी है या नहीं?

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यदि \(y \neq 0\), तो (\dfrac{(x+y)3-(x-y)3}{2y}) का सरल रूप क्या है?

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((x+1)3-(x-1)3) का सरल रूप क्या है?

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(\(8x^3+1\)) को ((2x+1)) से भाग देने पर भागफल क्या है?

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((x-2)\(x^2+2x+4\)) का विस्तार क्या है?

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(\(x^3-27\)) को ((x-3)) से भाग देने पर भागफल क्या होगा?

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(\(x^3-8\)) को ((x-2)) से भाग देने पर भागफल क्या होगा?

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यदि \(x^2-10x+21=0\) के मूल \(\alpha\) और \(\beta\) हैं तो \(\alpha^3+\beta^3\) का मान क्या है?

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यदि \(x^2-9x+20=0\) के मूल \(\alpha\) और \(\beta\) हैं तो \(\alpha^3+\beta^3\) का मान क्या है?

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कौन सा विकल्प \(\sqrt[3]{20}\) के बारे में सही है?

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कौन सा विकल्प \(\sqrt[3]{12}\) के लिए सही है?

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कौन सा विकल्प \(\sqrt[3]{16}\) के लिए सही है?

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\(\sqrt[3]{9}\) के बारे में सही कथन कौन सा है?

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\(\sqrt[3]{4}\) के बारे में कौन सा कथन सही है?

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यदि \(y \neq 0\), तो (\dfrac{(x+y)³-(x-y)³}{2y}) का सरल रूप क्या है?

((x+1)³-(x-1)³) का सरल रूप क्या है?