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Class 9 Mathematics - Number Systems - Proof of irrationality of square root 2 and square root 3 Expert Quiz

Mathematics Number Systems Proof of irrationality of square root 2 and square root 3 Expert Class 9 Level 4

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Question 1/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(2^8 \times 2^5 \div 2^9\) का मान क्या है?

What is the value of \(2^8 \times 2^5 \div 2^9\)?

Explanation opens after your attempt
Correct Answer

A. 16

Explanation

Simple Explanation

घातों को जोड़कर और घटाकर \(2^4\) मिलता है। नियम याद रखें। / Adding and subtracting exponents gives \(2^4\). Remember the law.

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Question 2/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(2^{12}\div2^8\) का मान क्या है?

What is the value of \(2^{12}\div2^8\)?

Explanation opens after your attempt
Correct Answer

A. 16

Explanation

Simple Explanation

\(2^{12-8}=2^4\)। घातों के भाग का नियम प्रयोग करें। / \(2^{12-8}=2^4\). Use the quotient rule.

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Question 3/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

(\(3^2\)4 \div 35) का मान क्या है?

What is the value of (\(3^2\)4 \div 35)?

Explanation opens after your attempt
Correct Answer

B. 27

Explanation

Simple Explanation

\(3^8 \div 3^5=3^3\)। घातों के नियम लागू करें। / \(3^8 \div 3^5=3^3\). Apply exponent laws.

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Question 4/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(5^6 \div 25^2\) का मान क्या है?

What is the value of \(5^6 \div 25^2\)?

Explanation opens after your attempt
Correct Answer

C. 25

Explanation

Simple Explanation

(252=\(5^2\)2=54)। इसलिए \(5^2=25\)। / (252=\(5^2\)2=54). Hence \(5^2=25\).

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Question 5/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(4^5 \div 2^8\) का मान क्या है?

What is the value of \(4^5 \div 2^8\)?

Explanation opens after your attempt
Correct Answer

D. 4

Explanation

Simple Explanation

(45=\(2^2\)5=2^{10})। \(2^{10}\div2^8=2^2\)। / (45=\(2^2\)5=2^{10}). Then \(2^{10}\div2^8=2^2\).

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Question 6/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(9^3 \div 3^4\) का मान क्या है?

What is the value of \(9^3 \div 3^4\)?

Explanation opens after your attempt
Correct Answer

A. 9

Explanation

Simple Explanation

(93=\(3^2\)3=36)। \(3^6\div3^4=3^2\)। / (93=\(3^2\)3=36). Then \(3^6\div3^4=3^2\).

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Question 7/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(10^4\div10^2\) का मान क्या है?

What is the value of \(10^4\div10^2\)?

Explanation opens after your attempt
Correct Answer

A. 100

Explanation

Simple Explanation

\(10^{4-2}=10^2\)। / \(10^{4-2}=10^2\).

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Question 8/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

(\(2^3 \times 5^3\)\div102) का मान क्या है?

What is the value of (\(2^3 \times 5^3\)\div102)?

Explanation opens after your attempt
Correct Answer

B. 10

Explanation

Simple Explanation

\(2^3 \times 5^3=10^3\)। \(10^3\div10^2=10\)। / \(2^3 \times 5^3=10^3\). Then \(10^3\div10^2=10\).

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Question 9/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(2^5\times2^4\div2^6\) का मान क्या है?

What is the value of \(2^5\times2^4\div2^6\)?

Explanation opens after your attempt
Correct Answer

B. 8

Explanation

Simple Explanation

\(2^{5+4-6}=2^3\)। / \(2^{5+4-6}=2^3\).

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Question 10/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

(\(7^2\)2 \div 72) का मान क्या है?

What is the value of (\(7^2\)2 \div 72)?

Explanation opens after your attempt
Correct Answer

C. 343

Explanation

Simple Explanation

\(7^4\div7^2=7^2=49\)। सही विकल्प देखें। / \(7^4\div7^2=7^2=49\). Check the correct option.

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Question 11/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(8^2 \times 2^3 \div 4^2\) का मान क्या है?

What is the value of \(8^2 \times 2^3 \div 4^2\)?

Explanation opens after your attempt
Correct Answer

D. 32

Explanation

Simple Explanation

\(2^6\times2^3\div2^4=2^5\)। / \(2^6\times2^3\div2^4=2^5\).

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Question 12/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(9^2-5^2\) का मान क्या है?

What is the value of \(9^2-5^2\)?

Explanation opens after your attempt
Correct Answer

D. 56

Explanation

Simple Explanation

(81-25=56)। / (81-25=56).

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Question 13/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

यदि \(x=2^4\) तो \(x^2\div2^5\) का मान क्या है?

If \(x=2^4\), what is \(x^2\div2^5\)?

Explanation opens after your attempt
Correct Answer

A. 8

Explanation

Simple Explanation

\(x^2=2^8\)। \(2^8\div2^5=2^3\)। / \(x^2=2^8\). Then \(2^8\div2^5=2^3\).

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Question 14/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(8^2\div2^4\) का मान क्या है?

What is the value of \(8^2\div2^4\)?

Explanation opens after your attempt
Correct Answer

A. 4

Explanation

Simple Explanation

\(8^2=2^6\)। \(2^6\div2^4=2^2\)। / \(8^2=2^6\). \(2^6\div2^4=2^2\).

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Question 15/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(6^3 \times 6^2 \div 6^4\) का मान क्या है?

What is the value of \(6^3 \times 6^2 \div 6^4\)?

Explanation opens after your attempt
Correct Answer

B. 6

Explanation

Simple Explanation

\(6^{3+2-4}=6^1\)। / \(6^{3+2-4}=6^1\).

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Question 16/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

(\(3^3\)2\div34) का मान क्या है?

What is the value of (\(3^3\)2\div34)?

Explanation opens after your attempt
Correct Answer

B. 9

Explanation

Simple Explanation

\(3^6\div3^4=3^2\)। / \(3^6\div3^4=3^2\).

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Question 17/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(6^3\div6\) का मान क्या है?

What is the value of \(6^3\div6\)?

Explanation opens after your attempt
Correct Answer

C. 36

Explanation

Simple Explanation

\(6^{3-1}=6^2=36\)। / \(6^{3-1}=6^2=36\).

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Question 18/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

(2^{10}\div\(2^3\)2) का मान क्या है?

What is the value of (2^{10}\div\(2^3\)2)?

Explanation opens after your attempt
Correct Answer

D. 16

Explanation

Simple Explanation

\(2^{10}\div2^6=2^4\)। / \(2^{10}\div2^6=2^4\).

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Question 19/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(25^2\div5^3\) का मान क्या है?

What is the value of \(25^2\div5^3\)?

Explanation opens after your attempt
Correct Answer

D. 25

Explanation

Simple Explanation

\(25^2=5^4\)। \(5^4\div5^3=5\)। / \(25^2=5^4\). \(5^4\div5^3=5\).

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Question 20/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(125^2 \div 5^4\) का मान क्या है?

What is the value of \(125^2 \div 5^4\)?

Explanation opens after your attempt
Correct Answer

A. 25

Explanation

Simple Explanation

\(125=5^3\)। \(5^6\div5^4=5^2\)। / \(125=5^3\). Then \(5^6\div5^4=5^2\).

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Question 21/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

(\(4^3\)2 \div 162) का मान क्या है?

What is the value of (\(4^3\)2 \div 162)?

Explanation opens after your attempt
Correct Answer

B. 16

Explanation

Simple Explanation

(46\div\(4^2\)2=42)। / (46\div\(4^2\)2=42).

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Question 22/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(11^2+4^3\) का मान क्या है?

What is the value of \(11^2+4^3\)?

Explanation opens after your attempt
Correct Answer

B. 185

Explanation

Simple Explanation

(121+64=185)। / (121+64=185).

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Question 23/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(3^5+2^7\) का मान क्या है?

What is the value of \(3^5+2^7\)?

Explanation opens after your attempt
Correct Answer

C. 371

Explanation

Simple Explanation

(243+128=371)। पहले घात निकालें। / (243+128=371). Evaluate powers first.

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Question 24/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(2^{10}\div32\) का मान क्या है?

What is the value of \(2^{10}\div32\)?

Explanation opens after your attempt
Correct Answer

C. 32

Explanation

Simple Explanation

\(32=2^5\)। \(2^{10}\div2^5=2^5\)। / \(32=2^5\). \(2^{10}\div2^5=2^5\).

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Question 25/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(13^2-12^2\) का मान क्या है?

What is the value of \(13^2-12^2\)?

Explanation opens after your attempt
Correct Answer

D. 25

Explanation

Simple Explanation

(169-144=25)। / (169-144=25).

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Question 26/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

(\(2^4\)2\div26) का मान क्या है?

What is the value of (\(2^4\)2\div26)?

Explanation opens after your attempt
Correct Answer

A. 4

Explanation

Simple Explanation

\(2^8\div2^6=2^2\)। / \(2^8\div2^6=2^2\).

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Question 27/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(3^4\times3^2\div3^5\) का मान क्या है?

What is the value of \(3^4\times3^2\div3^5\)?

Explanation opens after your attempt
Correct Answer

B. 3

Explanation

Simple Explanation

\(3^{4+2-5}=3\)। / \(3^{4+2-5}=3\).

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Question 28/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(7^3\div7^2\) का मान क्या है?

What is the value of \(7^3\div7^2\)?

Explanation opens after your attempt
Correct Answer

D. 7

Explanation

Simple Explanation

\(7^{3-2}=7\)। / \(7^{3-2}=7\).

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Question 29/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(16^2\div4^3\) का मान क्या है?

What is the value of \(16^2\div4^3\)?

Explanation opens after your attempt
Correct Answer

A. 4

Explanation

Simple Explanation

\(16^2=4^4\)। \(4^4\div4^3=4\)। / \(16^2=4^4\). \(4^4\div4^3=4\).

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Question 30/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

निम्नलिखित का मान क्या है: \(2^6 + 3^4\)?

What is the value of \(2^6 + 3^4\)?

Explanation opens after your attempt
Correct Answer

B. 145

Explanation

Simple Explanation

पहले घातों का मान निकालें: \(2^6 = 64\) और \(3^4 = 81\)। दोनों को जोड़ने पर \(64+81=145\) मिलता है, इसलिए सही उत्तर 145 है। नज़दीकी ग़लत विकल्प जैसे 135 या 155 अक्सर गणना में एक अंक चूक या गलत घात मान लेने से आते हैं (उदाहरण के लिए अगर \(3^4\) को 71 या 91 मान लिया जाए)। परीक्षा-सुझाव: छोटे घातों के सामान्य मान याद रखें और जोड़ते समय दो बार जल्दी से जोड़कर परिणाम पुष्टि करें। / Compute the powers first: \(2^6=64\) and \(3^4=81\). Adding them gives \(64+81=145\), so 145 is correct. Common wrong choices (e.g. 135 or 155) arise from mis-evaluating a power or a single-digit addition error. Exam tip: memorize small powers and recheck the final addition quickly to avoid slip errors.

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Question 31/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(81\div3^3\) का मान क्या है?

What is the value of \(81\div3^3\)?

Explanation opens after your attempt
Correct Answer

D. 3

Explanation

Simple Explanation

\(81=3^4\)। \(3^4\div3^3=3\)। / \(81=3^4\). \(3^4\div3^3=3\).

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Question 32/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

(\(10^2\)2\div103) का मान क्या है?

What is the value of (\(10^2\)2\div103)?

Explanation opens after your attempt
Correct Answer

A. 10

Explanation

Simple Explanation

\(10^4\div10^3=10\)। / \(10^4\div10^3=10\).

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Question 33/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(2^7\div2^2\) का मान क्या है?

What is the value of \(2^7\div2^2\)?

Explanation opens after your attempt
Correct Answer

C. 32

Explanation

Simple Explanation

\(2^{7-2}=2^5=32\)। / \(2^{7-2}=2^5=32\).

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Question 34/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

(\(6^2\)2\div63) का मान क्या है?

What is the value of (\(6^2\)2\div63)?

Explanation opens after your attempt
Correct Answer

D. 36

Explanation

Simple Explanation

\(6^4\div6^3=6\)। / \(6^4\div6^3=6\).

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Question 35/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(3^5\div9^2\) का मान क्या है?

What is the value of \(3^5\div9^2\)?

Explanation opens after your attempt
Correct Answer

A. 3

Explanation

Simple Explanation

\(9^2=3^4\)। \(3^5\div3^4=3\)। / \(9^2=3^4\). \(3^5\div3^4=3\).

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Question 36/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(4^4\div2^6\) का मान क्या है?

What is the value of \(4^4\div2^6\)?

Explanation opens after your attempt
Correct Answer

B. 4

Explanation

Simple Explanation

\(4^4=2^8\)। \(2^8\div2^6=2^2\)। / \(4^4=2^8\). \(2^8\div2^6=2^2\).

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Question 37/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(15^2 + 2^4\) का मान क्या है?

What is the value of \(15^2 + 2^4\)?

Explanation opens after your attempt
Correct Answer

C. 241

Explanation

Simple Explanation

पहले घातों को अलग-अलग निकालें: \(15^2=225\) और \(2^4=16\)। इन्हें जोड़ने पर \(225+16=241\) मिलता है इसलिए उत्तर 241 है। गलत विकल्पों पर टिप्पणी: B (233) वह गलती दर्शाता है जहाँ किसी ने \(2^4\) को \(8\) मान लिया (दरअसल \(2^3=8\))। A (225) तब आता है जब कोई \(2^4\) जोड़ना भूल जाए। D (256) किसी अन्य घात का मान है (उदाहरण: \(4^4\) या \(16^2\)) और यहाँ अप्रासंगिक है। परीक्षा-सुझाव: घातों को अलग-अलग हल करके छोटे पावर (जैसे \(2^1,2^2,2^3,2^4\)) याद रखें और फिर जोड़ें। / Evaluate the powers separately: \(15^2=225\) and \(2^4=16\). Adding gives \(225+16=241\), so the correct value is 241. Notes on distractors: B (233) reflects the mistake of treating \(2^4\) as 8 (which is \(2^3\)). A (225) corresponds to omitting the \(2^4\) term. D (256) is the value of a different power (for example \(4^4\) or \(16^2\)) and is not relevant here. Exam tip: compute each power first, remember small powers of 2, then perform the addition to avoid slip errors.

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Question 38/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(2^9\div2^7\) का मान क्या है?

What is the value of \(2^9\div2^7\)?

Explanation opens after your attempt
Correct Answer

D. 4

Explanation

Simple Explanation

\(2^{9-7}=2^2=4\)। / \(2^{9-7}=2^2=4\).

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Question 39/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

(\(7^2\)3\div75) का मान क्या है?

What is the value of (\(7^2\)3\div75)?

Explanation opens after your attempt
Correct Answer

A. 7

Explanation

Simple Explanation

\(7^6\div7^5=7\)। / \(7^6\div7^5=7\).

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Question 40/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(18^2-17^2\) का मान क्या है?

What is the value of \(18^2-17^2\)?

Explanation opens after your attempt
Correct Answer

B. 35

Explanation

Simple Explanation

(324-289=35)। / (324-289=35).

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Question 41/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(5^3+4^4\) का मान क्या है?

What is the value of \(5^3+4^4\)?

Explanation opens after your attempt
Correct Answer

C. 381

Explanation

Simple Explanation

(125+256=381)। / (125+256=381).

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Question 42/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(2^5\times2^3\div2^4\) का मान क्या है?

What is the value of \(2^5\times2^3\div2^4\)?

Explanation opens after your attempt
Correct Answer

D. 16

Explanation

Simple Explanation

\(2^{5+3-4}=2^4=16\)। / \(2^{5+3-4}=2^4=16\).

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Question 43/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

(\(8^2\times2^3\)\div27) का मान क्या है?

What is the value of (\(8^2\times2^3\)\div27)?

Explanation opens after your attempt
Correct Answer

C. 4

Explanation

Simple Explanation

\(8^2=2^6\)। \(2^6\times2^3\div2^7=2^2=4\)। / \(8^2=2^6\). \(2^6\times2^3\div2^7=2^2=4\).

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Question 44/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(11^2+6^3\) का मान क्या है?

What is the value of \(11^2+6^3\)?

Explanation opens after your attempt
Correct Answer

D. 337

Explanation

Simple Explanation

(121+216=337)। / (121+216=337).

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Question 45/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

(2^{11}\div\(2^2\)4) का मान क्या है?

What is the value of (2^{11}\div\(2^2\)4)?

Explanation opens after your attempt
Correct Answer

A. 8

Explanation

Simple Explanation

(\(2^2\)4=28)। \(2^{11}\div2^8=2^3=8\)। / (\(2^2\)4=28). \(2^{11}\div2^8=2^3=8\).

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Question 46/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(49^2\div7^3\) का मान क्या है?

What is the value of \(49^2\div7^3\)?

Explanation opens after your attempt
Correct Answer

B. 7

Explanation

Simple Explanation

(492=\(7^2\)2=74)। \(7^4\div7^3=7\)। / (492=\(7^2\)2=74). \(7^4\div7^3=7\).

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Question 47/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

(\(3^4\times3^2\)\div92) का मान क्या है?

What is the value of (\(3^4\times3^2\)\div92)?

Explanation opens after your attempt
Correct Answer

C. 9

Explanation

Simple Explanation

\(3^6\div3^4=3^2=9\)। / \(3^6\div3^4=3^2=9\).

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Question 48/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

(\(5^3\)2\div252) का मान क्या है?

What is the value of (\(5^3\)2\div252)?

Explanation opens after your attempt
Correct Answer

A. 25

Explanation

Simple Explanation

\(5^6\div5^4=5^2=25\)। / \(5^6\div5^4=5^2=25\).

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Question 49/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

(\(12^2-5^2\)\div7) का मान क्या है?

What is the value of (\(12^2-5^2\)\div7)?

Explanation opens after your attempt
Correct Answer

C. 17

Explanation

Simple Explanation

(144-25=119) और \(119\div7=17\)। पहले घातों का मान निकालें। / (144-25=119) and \(119\div7=17\). Evaluate powers first.

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Question 50/50 Expert Mathematics Number Systems Exponents Class 9 Level 4

\(2^8+3^6\) का मान क्या है?

What is the value of \(2^8+3^6\)?

Explanation opens after your attempt
Correct Answer

B. 985

Explanation

Simple Explanation

\(2^8=256\) और \(3^6=729\)। योग (985) है। / \(2^8=256\) and \(3^6=729\). Their sum is (985).

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