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

Mathematics Number Systems Proof of irrationality of square root 2 and square root 3 Hard Class 9 Level 6

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Question 1/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(3^7 \div 3^3\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

C. 81

Explanation

Simple Explanation

भाग में घातें घटती हैं। \(3^4=81\)। / Subtract exponents in division. \(3^4=81\).

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Question 2/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

यदि \(x=2^3\) तो \(x^2\) का मान क्या है?

If \(x=2^3\) then what is \(x^2\)?

Explanation opens after your attempt

Correct Answer

B. 64

Explanation

Simple Explanation

(x=8) इसलिए \(x^2=64\)। पहले आधार मान निकालें। / (x=8), so \(x^2=64\). Evaluate stepwise.

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Question 3/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(10^4 \div 10^2\) बराबर है

\(10^4 \div 10^2\) equals

Explanation opens after your attempt

Correct Answer

B. 100

Explanation

Simple Explanation

\(10^{4-2}=10^2=100\)। / \(10^{4-2}=10^2=100\).

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

\(4^3 \times 4^2\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

C. 1024

Explanation

Simple Explanation

\(4^{3+2}=4^5=1024\)। / \(4^{3+2}=4^5=1024\).

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Question 5/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(7^0+7^1\) का मान क्या है?

What is the value of \(7^0+7^1\)?

Explanation opens after your attempt

Correct Answer

C. 8

Explanation

Simple Explanation

\(7^0=1\) और \(7^1=7\)। योग 8 है। / \(7^0=1\) and \(7^1=7\). Sum is 8.

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Question 6/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(9^2 \div 3^2\) का मान क्या है?

What is the value of \(9^2 \div 3^2\)?

Explanation opens after your attempt

Correct Answer

B. 9

Explanation

Simple Explanation

((9/3)²=3²=9)। / ((9/3)²=3²=9).

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Question 7/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

(\(2^4 \times 2^3\)\div2⁵) का मान क्या है?

What is the value of (\(2^4 \times 2^3\)\div2⁵)?

Explanation opens after your attempt

Correct Answer

B. 4

Explanation

Simple Explanation

घातें जोड़कर फिर घटाएँ। \(2^{7-5}=2^2=4\)। / Add then subtract exponents. \(2^2=4\).

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Question 8/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(6^2 \times 6^0\) का मान क्या है?

What is the value of \(6^2 \times 6^0\)?

Explanation opens after your attempt

Correct Answer

C. 36

Explanation

Simple Explanation

\(6^0=1\)। इसलिए मान 36 है। / \(6^0=1\). Hence value is 36.

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Question 9/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(8^2-2^5\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

C. 32

Explanation

Simple Explanation

(64-32=32)। पहले घात निकालें। / (64-32=32). Evaluate powers first.

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Question 10/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(3^4+3^2\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. 90

Explanation

Simple Explanation

(81+9=90)। / (81+9=90).

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Question 11/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

कौन सा \(2^6\) के बराबर है?

Which is equal to \(2^6\)?

Explanation opens after your attempt

Correct Answer

B. \(8^2\)

Explanation

Simple Explanation

\(8^2=64=2^6\)। / \(8^2=64=2^6\).

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Question 12/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(5^3 \div 5\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

A. 25

Explanation

Simple Explanation

\(5^{3-1}=5^2=25\)। / \(5^{3-1}=5^2=25\).

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Question 13/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(12^2 \div 6^2\) का मान क्या है?

What is the value of \(12^2 \div 6^2\)?

Explanation opens after your attempt

Correct Answer

B. 4

Explanation

Simple Explanation

((12/6)²=2²=4)। / ((12/6)²=4).

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Question 14/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(11^1+11^0\) का मान क्या है?

What is the value of \(11^1+11^0\)?

Explanation opens after your attempt

Correct Answer

B. 12

Explanation

Simple Explanation

(11+1=12)। / (11+1=12).

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Question 15/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(2^3 \times 5^3\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. 1000

Explanation

Simple Explanation

(\(2\times5\)³=10³=1000)। / (\(2\times5\)³=1000).

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Question 16/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(7^2+2^5\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. 81

Explanation

Simple Explanation

(49+32=81)। / (49+32=81).

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Question 17/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(13^2-5^2\) का मान क्या है?

What is the value of \(13^2-5^2\)?

Explanation opens after your attempt

Correct Answer

A. 144

Explanation

Simple Explanation

(169-25=144)। पहले घातों का मान निकालें। / (169-25=144). Evaluate powers first.

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Question 18/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

(\(3^2\)² \times 3) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. 243

Explanation

Simple Explanation

\(3^{4}\times3=3^5=243\)। / \(3^4\times3=3^5=243\).

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Question 19/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(15^2 \div 5^2\) का मान क्या है?

What is the value of \(15^2 \div 5^2\)?

Explanation opens after your attempt

Correct Answer

C. 9

Explanation

Simple Explanation

((15/5)²=3²=9)। / ((15/5)²=9).

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Question 20/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

(\(2^3\times2^2\)²) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. 1024

Explanation

Simple Explanation

अंदर \(2^5\) और फिर (\(2^5\)²=2^{10})। / Inside becomes \(2^5\), then \(2^{10}=1024\).

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Question 21/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(3^5+2^5\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

D. 275

Explanation

Simple Explanation

(243+32=275)। / (243+32=275).

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Question 22/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(25^2 \div 5^2\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. 25

Explanation

Simple Explanation

((25/5)²=5²=25)। / ((25/5)²=25).

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Question 23/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(2^4+4^3\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

C. 80

Explanation

Simple Explanation

(16+64=80)। / (16+64=80).

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Question 24/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(14^2-10^2\) का मान क्या है?

What is the value of \(14^2-10^2\)?

Explanation opens after your attempt

Correct Answer

A. 96

Explanation

Simple Explanation

(196-100=96)। / (196-100=96).

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Question 25/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(8^3 \div 2^3\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. 64

Explanation

Simple Explanation

((8/2)³=4³=64)। / ((8/2)³=64).

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Question 26/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(2^7-2^4\) का मान क्या है?

What is the value of \(2^7-2^4\)?

Explanation opens after your attempt

Correct Answer

D. 112

Explanation

Simple Explanation

(128-16=112)। / (128-16=112).

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Question 27/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

(\(5^3\)²) का मान क्या है?

What is the value of (\(5^3\)²)?

Explanation opens after your attempt

Correct Answer

B. 15625

Explanation

Simple Explanation

\(5^{6}=15625\)। / \(5^6=15625\).

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Question 28/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(16^2 \div 4^2\) का मान क्या है?

What is the value of \(16^2 \div 4^2\)?

Explanation opens after your attempt

Correct Answer

C. 16

Explanation

Simple Explanation

((16/4)²=4²=16)। / ((16/4)²=16).

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Question 29/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(11^2+2^6\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. 165

Explanation

Simple Explanation

(121+64=185)। / (121+64=185).

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Question 30/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(12^2+5^2\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

A. 169

Explanation

Simple Explanation

(144+25=169)। / (144+25=169).

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Question 31/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(10^3-9^2\) का मान क्या है?

What is the value of \(10^3-9^2\)?

Explanation opens after your attempt

Correct Answer

B. 919

Explanation

Simple Explanation

(1000-81=919)। / (1000-81=919).

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Question 32/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(7^3+6^2\) का मान क्या है?

What is the value of \(7^3+6^2\)?

Explanation opens after your attempt

Correct Answer

C. 379

Explanation

Simple Explanation

(343+36=379)। / (343+36=379).

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Question 33/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(13^2 + 3^4\) का मान क्या है?

What is the value of \(13^2 + 3^4\)?

Explanation opens after your attempt

Correct Answer

B. 250

Explanation

Simple Explanation

13² = 13 × 13 = 169 और 3⁴ = 3 × 3 × 3 × 3 = 81। अतः \(13^2 + 3^4\) = 169 + 81 = 250। विकल्प A (240) गलत है — यह किसी गणना त्रुटि का परिणाम हो सकता है \(उदाहरण के लिए 3^4 को गलत‑तौर पर 71 माना जाना\)। परीक्षा सलाह: घातों को अलग‑अलग चरणबद्ध रूप से निकालें और फिर जोड़कर उत्तर की जाँच करें। / 13² = 13 × 13 = 169 and 3⁴ = 3 × 3 × 3 × 3 = 81. Therefore \(13^2 + 3^4\) = 169 + 81 = 250. Option A (240) is incorrect — it likely arises from an arithmetic mistake \(for example, computing 3^4 incorrectly\). Exam tip: evaluate each power separately, then add and recheck the addition to avoid simple errors.

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Question 34/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(2^9 \div 2^6\) का मान क्या है?

What is the value of \(2^9 \div 2^6\)?

Explanation opens after your attempt

Correct Answer

B. 8

Explanation

Simple Explanation

\(2^{3}=8\)। / \(2^3=8\).

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Question 35/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

(\(3^3\)³) का मान क्या है?

What is the value of (\(3^3\)³)?

Explanation opens after your attempt

Correct Answer

A. 19683

Explanation

Simple Explanation

\(3^9=19683\)। / \(3^9=19683\).

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Question 36/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(18^2 \div 3^2\) का मान क्या है?

What is the value of \(18^2 \div 3^2\)?

Explanation opens after your attempt

Correct Answer

B. 36

Explanation

Simple Explanation

((18/3)²=6²=36)। / ((18/3)²=36).

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Question 37/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(15^2-12^2\) का मान क्या है?

What is the value of \(15^2-12^2\)?

Explanation opens after your attempt

Correct Answer

C. 81

Explanation

Simple Explanation

(225-144=81)। / (225-144=81).

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Question 38/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(19^2-11^2\) का मान क्या है?

What is the value of \(19^2-11^2\)?

Explanation opens after your attempt

Correct Answer

A. 240

Explanation

Simple Explanation

(361-121=240)। पहले घातों का मान निकालें। / (361-121=240). Evaluate powers first.

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Question 39/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(2^4 \times 3^4\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

A. 1296

Explanation

Simple Explanation

(\(2\times3\)⁴=6⁴=1296)। / (\(2\times3\)⁴=6⁴=1296).

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Question 40/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(27^2 \div 3^4\) का मान क्या है?

What is the value of \(27^2 \div 3^4\)?

Explanation opens after your attempt

Correct Answer

B. 9

Explanation

Simple Explanation

\(27=3^3\)। इसलिए \(3^6\div3^4=3^2=9\)। / \(27=3^3\). So \(3^6\div3^4=3^2=9\).

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Question 41/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

(\(2^5\)² \div 2⁶) का मान क्या है?

What is the value of (\(2^5\)² \div 2⁶)?

Explanation opens after your attempt

Correct Answer

C. 16

Explanation

Simple Explanation

\(2^{10}\div2^6=2^4=16\)। / \(2^{10}\div2^6=2^4=16\).

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Question 42/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(2^6+3^5\) का मान क्या है?

What is the value of \(2^6+3^5\)?

Explanation opens after your attempt

Correct Answer

A. 307

Explanation

Simple Explanation

(64+243=307)। / (64+243=307).

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Question 43/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(14^2+5^3\) का मान क्या है?

What is the value of \(14^2+5^3\)?

Explanation opens after your attempt

Correct Answer

B. 321

Explanation

Simple Explanation

(196+125=321)। / (196+125=321).

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Question 44/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(3^8 \div 3^5\) का मान क्या है?

What is the value of \(3^8 \div 3^5\)?

Explanation opens after your attempt

Correct Answer

C. 27

Explanation

Simple Explanation

\(3^{8-5}=3^3=27\)। / \(3^{8-5}=3^3=27\).

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Question 45/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

(\(4^2\)³ \div 4⁴) का मान क्या है?

What is the value of (\(4^2\)³ \div 4⁴)?

Explanation opens after your attempt

Correct Answer

D. 16

Explanation

Simple Explanation

\(4^6\div4^4=4^2=16\)। / \(4^6\div4^4=4^2=16\).

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Question 46/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(21^2-20^2\) का मान क्या है?

What is the value of \(21^2-20^2\)?

Explanation opens after your attempt

Correct Answer

A. 41

Explanation

Simple Explanation

(441-400=41)। / (441-400=41).

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Question 47/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(8^2+7^3\) का मान क्या है?

What is the value of \(8^2+7^3\)?

Explanation opens after your attempt

Correct Answer

C. 407

Explanation

Simple Explanation

(64+343=407)। / (64+343=407).

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Question 48/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(9^3 \div 3^5\) का मान क्या है?

What is the value of \(9^3 \div 3^5\)?

Explanation opens after your attempt

Correct Answer

D. 3

Explanation

Simple Explanation

(9³=\(3^2\)³=3⁶)। \(3^6\div3^5=3\)। / (9³=\(3^2\)³=3⁶). Then \(3^6\div3^5=3\).

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Question 49/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

(\(12^2+5^2\)\div13) का मान क्या है?

What is the value of (\(12^2+5^2\)\div13)?

Explanation opens after your attempt

Correct Answer

C. 13

Explanation

Simple Explanation

(144+25=169) और \(169\div13=13\)। पहले घातों का मान निकालें। / (144+25=169) and \(169\div13=13\). Evaluate powers first.

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Question 50/50 Hard Mathematics Number Systems Exponents Class 9 Level 6

\(2^7+3^4-5^2\) का मान क्या है?

What is the value of \(2^7+3^4-5^2\)?

Explanation opens after your attempt

Correct Answer

B. 184

Explanation

Simple Explanation

(128+81-25=184)। क्रम से घात और फिर गणना करें। / (128+81-25=184). Evaluate powers before arithmetic.

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

\(3^7 \div 3^3\) का मान क्या है?

Simple Explanation

यदि \(x=2^3\) तो \(x^2\) का मान क्या है?

Simple Explanation

\(10^4 \div 10^2\) बराबर है

Simple Explanation

\(4^3 \times 4^2\) का मान क्या है?

Simple Explanation

\(7^0+7^1\) का मान क्या है?

Simple Explanation

\(9^2 \div 3^2\) का मान क्या है?

Simple Explanation

(\(2^4 \times 2^3\)\div25) का मान क्या है?

Simple Explanation

\(6^2 \times 6^0\) का मान क्या है?

Simple Explanation

\(8^2-2^5\) का मान क्या है?

Simple Explanation

\(3^4+3^2\) का मान क्या है?

Simple Explanation

कौन सा \(2^6\) के बराबर है?

Simple Explanation

\(5^3 \div 5\) का मान क्या है?

Simple Explanation

\(12^2 \div 6^2\) का मान क्या है?

Simple Explanation

\(11^1+11^0\) का मान क्या है?

Simple Explanation

\(2^3 \times 5^3\) का मान क्या है?

Simple Explanation

\(7^2+2^5\) का मान क्या है?

Simple Explanation

\(13^2-5^2\) का मान क्या है?

Simple Explanation

(\(3^2\)2 \times 3) का मान क्या है?

Simple Explanation

\(15^2 \div 5^2\) का मान क्या है?

Simple Explanation

(\(2^3\times2^2\)2) का मान क्या है?

Simple Explanation

\(3^5+2^5\) का मान क्या है?

Simple Explanation

\(25^2 \div 5^2\) का मान क्या है?

Simple Explanation

\(2^4+4^3\) का मान क्या है?

Simple Explanation

\(14^2-10^2\) का मान क्या है?

Simple Explanation

\(8^3 \div 2^3\) का मान क्या है?

Simple Explanation

\(2^7-2^4\) का मान क्या है?

Simple Explanation

(\(5^3\)2) का मान क्या है?

Simple Explanation

\(16^2 \div 4^2\) का मान क्या है?

Simple Explanation

\(11^2+2^6\) का मान क्या है?

Simple Explanation

\(12^2+5^2\) का मान क्या है?

Simple Explanation

\(10^3-9^2\) का मान क्या है?

Simple Explanation

\(7^3+6^2\) का मान क्या है?

Simple Explanation

\(13^2 + 3^4\) का मान क्या है?

Simple Explanation

\(2^9 \div 2^6\) का मान क्या है?

Simple Explanation

(\(3^3\)3) का मान क्या है?

Simple Explanation

\(18^2 \div 3^2\) का मान क्या है?

Simple Explanation

\(15^2-12^2\) का मान क्या है?

Simple Explanation

\(19^2-11^2\) का मान क्या है?

Simple Explanation

\(2^4 \times 3^4\) का मान क्या है?

Simple Explanation

\(27^2 \div 3^4\) का मान क्या है?

(\(2^4 \times 2^3\)\div2⁵) का मान क्या है?

(\(3^2\)² \times 3) का मान क्या है?

(\(2^3\times2^2\)²) का मान क्या है?

(\(5^3\)²) का मान क्या है?

(\(3^3\)³) का मान क्या है?

(\(2^5\)² \div 2⁶) का मान क्या है?

(\(4^2\)³ \div 4⁴) का मान क्या है?