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unknown exponent MCQ Questions for Class 10

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4 questions tagged with unknown exponent.

Question 1/4 Expert Mathematics Chapter 1: Real Numbers 3: Prime factorisation Class 10 Level 7

यदि \(2^3\times3^2\times5^x\) के कुल गुणनखंड (96) हैं, तो (x) का मान क्या है?

If \(2^3\times3^2\times5^x\) has (96) total factors, what is the value of (x)?

Explanation opens after your attempt
Correct Answer

A. (7)

Step 1

Concept

Total factors are ((3+1)(2+1)(x+1)).

Step 2

Why this answer is correct

\(4\times3\times(x+1)=96\), so (x+1=8) and (x=7).

Step 3

Exam Tip

Multiply known parts first, then solve for the unknown exponent. चरण 1: कुल गुणनखंड ((3+1)(2+1)(x+1)) होंगे। चरण 2: \(4\times3\times(x+1)=96\), इसलिए (x+1=8) और (x=7)। चरण 3: पहले ज्ञात गुणनखंडों का गुणनफल निकालें।

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Question 2/4 Expert Mathematics Chapter 1: Real Numbers 3: Prime factorisation Class 10 Level 7

यदि \(2^x\times3^2\times7^4\) के कुल गुणनखंड (45) हैं, तो (x) का मान क्या है?

If \(2^x\times3^2\times7^4\) has (45) total factors, what is the value of (x)?

Explanation opens after your attempt
Correct Answer

A. (2)

Step 1

Concept

Total factors are ((x+1)(2+1)(4+1)).

Step 2

Why this answer is correct

((x+1)\times3\times5=45), so (x+1=3) and (x=2).

Step 3

Exam Tip

Divide the given factor count by the known parts first. चरण 1: कुल गुणनखंड ((x+1)(2+1)(4+1)) होंगे। चरण 2: ((x+1)\times3\times5=45), इसलिए (x+1=3) और (x=2)। चरण 3: दिए गए कुल गुणनखंड को पहले ज्ञात भागों से भाग दें।

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Question 3/4 Expert Mathematics Chapter 1: Real Numbers 3: Prime factorisation Class 10 Level 7

यदि \(a=2^r\times3^2\) के कुल धनात्मक गुणनखंड (15) हैं, तो (r) का मान क्या होगा?

If \(a=2^r\times3^2\) has (15) positive factors, what is the value of (r)?

Explanation opens after your attempt
Correct Answer

A. (4)

Step 1

Concept

Total factors are ((r+1)(2+1)).

Step 2

Why this answer is correct

((r+1)\times3=15), so (r+1=5) and (r=4).

Step 3

Exam Tip

Write the factor-count formula first, then solve the simple equation. चरण 1: कुल गुणनखंड ((r+1)(2+1)) होंगे। चरण 2: ((r+1)\times3=15), इसलिए (r+1=5) और (r=4)। चरण 3: पहले कुल गुणनखंड का नियम लिखें, फिर साधारण समीकरण हल करें।

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Question 4/4 Expert Mathematics Chapter 1: Real Numbers 3: Prime factorisation Class 10 Level 7

यदि किसी संख्या का अभाज्य गुणनखंड रूप \(2^a\times3^2\times5\) है और उसके कुल गुणनखंड (24) हैं, तो (a) का मान क्या है?

If a number has prime factorisation \(2^a\times3^2\times5\) and it has (24) total factors, what is the value of (a)?

Explanation opens after your attempt
Correct Answer

A. (3)

Step 1

Concept

Total factors are ((a+1)(2+1)(1+1)).

Step 2

Why this answer is correct

((a+1)\times3\times2=24), so (a+1=4) and (a=3).

Step 3

Exam Tip

For an unknown exponent, apply the factor-count rule directly. चरण 1: कुल गुणनखंड ((a+1)(2+1)(1+1)) होंगे। चरण 2: ((a+1)\times3\times2=24), इसलिए (a+1=4) और (a=3)। चरण 3: अज्ञात घात वाले प्रश्न में गुणनखंडों का नियम सीधे लगाएं।

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