\(2^{10}\div2^6\) का मान क्या है?
What is the value of \(2^{10}\div2^6\)?
#exponents
#laws
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A 16
B 8
C 32
D 64
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Explanation
Simple Explanation
\(2^{10-6}=2^4\)। भाग के नियम का प्रयोग करें। / \(2^{10-6}=2^4\). Use the quotient rule.
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\(3^{2x-1}=243\) में (x) का मान क्या है?
What is the value of (x) if \(3^{2x-1}=243\)?
#exponents
#expert
#powers
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A (2)
B (3)
C (4)
D (5)
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Explanation
Simple Explanation
\(243=3^5\) इसलिए (2x-1=5)। घातों को समान आधार में लिखें। / \(243=3^5\) so (2x-1=5). Write powers with the same base.
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(\(3^2\)3 \div34 ) का मान क्या है?
What is the value of (\(3^2\)3 \div34 )?
#exponents
#power_rule
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A 27
B 9
C 81
D 3
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Explanation
Simple Explanation
\(3^6\div3^4=3^2\)। / \(3^6\div3^4=3^2\).
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\(\frac{5^8}{5^3}\) का मान क्या है?
What is the value of \(\frac{5^8}{5^3}\)?
#exponents
#expert
#laws
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A \(5^6\)
B \(5^4\)
C \(5^5\)
D \(25^3\)
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Correct Answer
C. \(5^5\)
Explanation
Simple Explanation
भाग में घातें घटती हैं। नियम याद रखें। / Exponents subtract in division. Remember the law.
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(\(2^4\)3 ) का मान किस घात के बराबर है?
(\(2^4\)3 ) equals which power?
#exponents
#expert
#power
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A \(2^{12}\)
B \(2^7\)
C \(2^{64}\)
D \(2^1\)
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Correct Answer
A. \(2^{12}\)
Explanation
Simple Explanation
घात की घात में गुणा होता है। नियम का प्रयोग करें। / Multiply exponents for a power of a power. Apply the law.
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यदि \(7^x \times 7^2=7^9\) तो (x=)?
If \(7^x \times 7^2=7^9\) then (x=)?
#exponents
#expert
#multiplication
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A (5)
B (6)
C (7)
D (8)
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Explanation
Simple Explanation
समान आधार पर घातें जुड़ती हैं। (x+2=9)। / For same bases exponents add. (x+2=9).
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\(\frac{2^{-3}}{2^{-5}}\) का मान क्या है?
What is the value of \(\frac{2^{-3}}{2^{-5}}\)?
#exponents
#expert
#negative
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A \(2^{-8}\)
B \(2^2\)
C \(2^{-2}\)
D \(4^{-1}\)
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Correct Answer
B. \(2^2\)
Explanation
Simple Explanation
भाग में घातें घटती हैं। ऋणात्मक घातों से न घबराएँ। / Subtract exponents in division. Handle negative exponents carefully.
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\(7^2+5^3\) का मान क्या है?
What is the value of \(7^2+5^3\)?
#exponents
#evaluation
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A 164
B 174
C 184
D 194
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Explanation
Simple Explanation
(49+125=174)। / (49+125=174).
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\(9^x=27\) होने पर (x=)?
If \(9^x=27\), find (x).
#exponents
#expert
#equation
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A \(\frac{2}{3}\)
B \(\frac{3}{2}\)
C (2)
D \(\frac{1}{3}\)
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Correct Answer
B. \(\frac{3}{2}\)
Explanation
Simple Explanation
\(9=3^2\) और \(27=3^3\)। आधार समान करें। / \(9=3^2\) and \(27=3^3\). Convert to same base.
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\(12^2-8^2\) का मान क्या है?
What is the value of \(12^2-8^2\)?
#exponents
#difference
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A 64
B 70
C 80
D 96
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Explanation
Simple Explanation
(144-64=80)। / (144-64=80).
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(\(5^2 \times 5^3\)\div54 ) का मान क्या है?
Find (\(5^2 \times 5^3\)\div54 ).
#exponents
#expert
#laws
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A (5)
B (25)
C (125)
D (1)
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Explanation
Simple Explanation
पहले घात जोड़ें फिर घटाएँ। उत्तर \(5^1\) है। / Add exponents then subtract. Result is \(5^1\).
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यदि \(4^x=64\) तो (x=)?
If \(4^x=64\), then (x=)?
#exponents
#expert
#equation
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A (2)
B (3)
C (4)
D (5)
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Explanation
Simple Explanation
\(64=4^3\)। समान आधार पहचानें। / \(64=4^3\). Identify the common base.
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(\left\(\frac{1}{3}\right\)^{-4}) का मान क्या है?
What is the value of (\left\(\frac{1}{3}\right\)^{-4})?
#exponents
#expert
#negative
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A (81)
B (27)
C \(\frac{1}{81}\)
D (9)
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Explanation
Simple Explanation
ऋणात्मक घात व्युत्क्रम बनाती है। नियम याद रखें। / Negative exponent takes reciprocal. Remember the law.
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(\(5^2\)2 \div53 ) का मान क्या है?
What is the value of (\(5^2\)2 \div53 )?
#exponents
#power
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A 125
B 5
C 25
D 625
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Explanation
Simple Explanation
\(5^4\div5^3=5\)। / \(5^4\div5^3=5\).
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\(16^{3/4}\) का मान क्या है?
Find \(16^{3/4}\).
#exponents
#expert
#fractional
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A (4)
B (16)
C (8)
D (64)
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Explanation
Simple Explanation
चतुर्थ मूल लेकर फिर घन करें। क्रम समझें। / Take fourth root then cube. Follow the order.
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\(6^3+4^4\) का मान क्या है?
What is the value of \(6^3+4^4\)?
#exponents
#addition
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A 452
B 462
C 472
D 482
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Explanation
Simple Explanation
(216+256=472)। / (216+256=472).
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यदि \(2^{x+1}=32\) तो (x=)?
If \(2^{x+1}=32\), find (x).
#exponents
#expert
#equation
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A (3)
B (4)
C (5)
D (6)
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Explanation
Simple Explanation
\(32=2^5\)। घातों की तुलना करें। / \(32=2^5\). Compare exponents.
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निम्नलिखित का मान क्या है: \(15^2 - 11^2\)?
What is the value of \(15^2 - 11^2\)?
#exponents
#difference of squares
#algebra
#mental arithmetic
#number systems
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A 84
B 94
C 114
D 104
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Explanation
Simple Explanation
घातांक के अंतर के सूत्र का उपयोग करें: \(a^2-b^2=(a-b)(a+b)\)। यहां \(15^2-11^2=(15-11)(15+11)=4\times26=104\)। निकटतम विचलक \(94\) गलत है क्योंकि वह गलत घटाव या गलत वर्ग (जैसे \(121\) की जगह \(131\) मानने) का परिणाम हो सकता है; सही गणना के बाद परिणाम \(104\) ही आता है। परीक्षात्मक युक्ति: बड़े वर्ग घटाने के बजाय हमेशा \(a^2-b^2\) को \((a-b)(a+b)\) में बदलकर मस्तिष्कगणना तेज करें। / Use the difference of squares identity: \(a^2-b^2=(a-b)(a+b)\). Here \(15^2-11^2=(15-11)(15+11)=4\times26=104\). The closest distractor 94 is wrong — it would correspond to a subtraction or squaring error (for example misreading 121 as 131). Correct application of the identity gives 104. Exam tip: convert \(a^2-b^2\) to \((a-b)(a+b)\) to simplify mental calculation and avoid large subtractions.
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\(\frac{10^6}{10^2\times10}\) का मान क्या है?
What is \(\frac{10^6}{10^2\times10}\)?
#exponents
#expert
#powers
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A \(10^4\)
B \(10^3\)
C \(10^2\)
D \(10^5\)
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Correct Answer
B. \(10^3\)
Explanation
Simple Explanation
हर में घातें जोड़ें। फिर भाग का नियम लगाएँ। / Add exponents in denominator. Then apply division law.
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(\(2^5\)2 \div28 ) का मान क्या है?
What is the value of (\(2^5\)2 \div28 )?
#exponents
#power_laws
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A 4
B 8
C 16
D 32
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Explanation
Simple Explanation
\(2^{10}\div2^8=2^2\)। / \(2^{10}\div2^8=2^2\).
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\(81^{1/2}\times81^{1/2}\) का मान क्या है?
Find \(81^{1/2}\times81^{1/2}\).
#exponents
#expert
#roots
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A (9)
B (18)
C (81)
D (27)
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Explanation
Simple Explanation
समान आधार पर घातें जुड़ती हैं। कुल घात 1 बनती है। / Exponents add for same base. Total exponent becomes 1.
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\(25^{x}=5^6\) होने पर (x=)?
If \(25^{x}=5^6\), then (x=)?
#exponents
#expert
#equation
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A (2)
B (3)
C (4)
D (6)
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Explanation
Simple Explanation
\(25=5^2\)। घातों की तुलना करें। / \(25=5^2\). Compare exponents.
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\(3^6\div9^2\) का मान क्या है?
What is the value of \(3^6\div9^2\)?
#exponents
#conversion
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A 81
B 27
C 9
D 3
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Explanation
Simple Explanation
\(9^2=3^4\)। \(3^6\div3^4=3^2\)। / \(9^2=3^4\). \(3^6\div3^4=3^2\).
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\(16^2\div2^6\) का मान क्या है?
What is the value of \(16^2\div2^6\)?
#exponents
#base_change
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A 2
B 16
C 8
D 4
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Explanation
Simple Explanation
\(16^2=2^8\)। \(2^8\div2^6=2^2=4\)। / \(16^2=2^8\). \(2^8\div2^6=2^2=4\).
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यदि \(8^{x}=2^{12}\) तो (x=)?
If \(8^{x}=2^{12}\), find (x).
#exponents
#expert
#equation
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A (3)
B (4)
C (5)
D (6)
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Explanation
Simple Explanation
\(8=2^3\)। समान आधार बनाकर हल करें। / \(8=2^3\). Convert to same base.
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\(\frac{7^4\times7^{-2}}{7}\) का मान क्या है?
Find \(\frac{7^4\times7^{-2}}{7}\).
#exponents
#expert
#laws
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A \(7^2\)
B (7)
C (1)
D \(7^3\)
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Explanation
Simple Explanation
घातें जोड़कर फिर 1 घटाएँ। उत्तर \(7^1\) है। / Add exponents then subtract 1. Result is \(7^1\).
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\(64^{2/3}\) का मान क्या है?
What is \(64^{2/3}\)?
#exponents
#expert
#fractional
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A (8)
B (16)
C (32)
D (4)
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Explanation
Simple Explanation
घनमूल 4 है फिर वर्ग करें। चरणबद्ध हल करें। / Cube root is 4 then square it. Solve stepwise.
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यदि \(5^{2x}=125\) तो (x=)?
If \(5^{2x}=125\), then (x=)?
#exponents
#expert
#equation
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A \(\frac{3}{2}\)
B (3)
C (2)
D \(\frac{1}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{3}{2}\)
Explanation
Simple Explanation
\(125=5^3\)। इसलिए (2x=3)। / \(125=5^3\). Hence (2x=3).
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\(\frac{3^5-3^4}{3^4}\) का मान क्या है?
Find \(\frac{3^5-3^4}{3^4}\).
#exponents
#expert
#simplification
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A (1)
B (2)
C (3)
D (4)
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Explanation
Simple Explanation
\(3^4\) सार्व गुणनखंड लें। सरलीकरण करें। / Take \(3^4\) common. Simplify carefully.
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\(14^2+6^2\) का मान क्या है?
What is the value of \(14^2+6^2\)?
#exponents
#evaluation
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A 222
B 232
C 242
D 252
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Explanation
Simple Explanation
(196+36=232)। / (196+36=232).
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यदि \(27^{x}=9\) तो (x=)?
If \(27^{x}=9\), then (x=)?
#exponents
#expert
#equation
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A \(\frac{2}{3}\)
B \(\frac{3}{2}\)
C (2)
D \(\frac{1}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{2}{3}\)
Explanation
Simple Explanation
दोनों को आधार 3 में लिखें। घातों की तुलना करें। / Write both in base 3. Compare exponents.
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\(81\div3^2\) का मान क्या है?
What is the value of \(81\div3^2\)?
#exponents
#simple
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A 3
B 81
C 9
D 27
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Explanation
Simple Explanation
\(81\div9=9\)। / \(81\div9=9\).
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\(\frac{4^5}{2^8}\) का मान क्या है?
What is \(\frac{4^5}{2^8}\)?
#exponents
#expert
#conversion
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A (2)
B (4)
C (8)
D (16)
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Explanation
Simple Explanation
(45 =\(2^2\)5 =2^{10})। फिर भाग करें। / (45 =\(2^2\)5 =2^{10}). Then divide.
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(\(10^3\)2 \div105 ) का मान क्या है?
What is the value of (\(10^3\)2 \div105 )?
#exponents
#powers
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A 100
B 1000
C 1
D 10
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Explanation
Simple Explanation
\(10^6\div10^5=10\)। / \(10^6\div10^5=10\).
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(\(9^{1/2}+16^{1/2}\)2 ) का मान क्या है?
Find (\(9^{1/2}+16^{1/2}\)2 ).
#exponents
#expert
#roots
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A (25)
B (36)
C (49)
D (64)
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Explanation
Simple Explanation
मूल निकालकर जोड़ें। फिर वर्ग करें। / Evaluate roots first. Then square the sum.
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यदि \(2^{x-2}=16\) तो (x=)?
If \(2^{x-2}=16\), find (x).
#exponents
#expert
#equation
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A (4)
B (5)
C (6)
D (7)
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Explanation
Simple Explanation
\(16=2^4\)। इसलिए (x-2=4)। / \(16=2^4\). Hence (x-2=4).
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\(2^8+5^3\) का मान क्या है?
What is the value of \(2^8+5^3\)?
#exponents
#addition
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A 371
B 381
C 391
D 401
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Explanation
Simple Explanation
(256+125=381)। / (256+125=381).
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\(\frac{6^3\times6^{-1}}{6^2}\) का मान क्या है?
What is \(\frac{6^3\times6^{-1}}{6^2}\)?
#exponents
#expert
#laws
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A (6)
B (1)
C (36)
D \(\frac{1}{6}\)
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Explanation
Simple Explanation
घातें जोड़कर फिर घटाएँ। कुल घात 0 है। / Add exponents then subtract. Net exponent is 0.
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(\(6^2\)2 \div62 ) का मान क्या है?
What is the value of (\(6^2\)2 \div62 )?
#exponents
#careful
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A 36
B 216
C 1296
D 6
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Explanation
Simple Explanation
\(6^4\div6^2=6^2=36\)। सही विकल्प देखें। / \(6^4\div6^2=6^2=36\). Check the correct option.
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\(125^{2/3}\) का मान क्या है?
Find \(125^{2/3}\).
#exponents
#expert
#fractional
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? Hint Small clue
A (15)
B (20)
C (25)
D (30)
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Explanation
Simple Explanation
घनमूल 5 है फिर वर्ग करें। / Cube root is 5 then square it.
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यदि \(32^{x}=8\) तो (x=)?
If \(32^{x}=8\), then (x=)?
#exponents
#expert
#equation
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A \(\frac{2}{5}\)
B \(\frac{3}{5}\)
C \(\frac{4}{5}\)
D \(\frac{5}{3}\)
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Correct Answer
B. \(\frac{3}{5}\)
Explanation
Simple Explanation
दोनों को आधार 2 में लिखें। तुलना करें। / Write both in base 2. Compare exponents.
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\(11^2+8^2\) का मान क्या है?
What is the value of \(11^2+8^2\)?
#exponents
#sum
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A 175
B 185
C 195
D 205
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Explanation
Simple Explanation
(121+64=185)। / (121+64=185).
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\(\frac{9^{-1}}{3^{-4}}\) का मान क्या है?
Find \(\frac{9^{-1}}{3^{-4}}\).
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#expert
#negative
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A (9)
B (3)
C (27)
D (81)
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Explanation
Simple Explanation
\(9^{-1}=3^{-2}\)। फिर भाग का नियम लगाएँ। / \(9^{-1}=3^{-2}\). Then apply division law.
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\(32^2\div2^7\) का मान क्या है?
What is the value of \(32^2\div2^7\)?
#exponents
#bases
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A 16
B 4
C 8
D 32
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Explanation
Simple Explanation
\(32^2=2^{10}\)। \(2^{10}\div2^7=2^3\)। / \(32^2=2^{10}\). \(2^{10}\div2^7=2^3\).
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यदि \(\frac{2^{x+3}}{2^{x-1}}=16\) तो (x) का मान क्या है?
If \(\frac{2^{x+3}}{2^{x-1}}=16\), what is the value of (x)?
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#laws
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A (1)
B (2)
C कोई भी वास्तविक संख्या / Any real number
D (4)
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Correct Answer
C. कोई भी वास्तविक संख्या / Any real number
Explanation
Simple Explanation
घात घटाने पर \(2^4=16\) मिलता है जो सदैव सत्य है। (x) कट जाता है। / Subtracting exponents gives \(2^4=16\), always true. (x) cancels out.
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\((19^2-15^2)\) का मान क्या है?
What is the value of \((19^2-15^2)\)?
#exponents
#difference-of-squares
#algebra
#number-systems
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A 116
B 126
C 146
D 136
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Explanation
Simple Explanation
समस्या को जल्दी हल करने के लिए अंतर-स्क्वायर का सूत्र प्रयोग करें: \(a^2-b^2=(a-b)(a+b)\). यहाँ \(19^2-15^2=(19-15)(19+15)=4\times34=136\). इसलिए उत्तर 136 है। अक्सर गलत उत्तर (जैसे 126) तब आता है जब किसी ने दूसरी संख्या का वर्ग गलत निकाला या घटाना भूल से गलत किया; 146 भी गलत है क्योंकि सही जोड़ \(19+15=34\) है न कि कोई अन्य मान। परीक्षा सुझाव: बड़े वर्गों को सीधे घटने के बजाय \(a^2-b^2\) का रूपांतरण कर लें — यह काम तेज और त्रुटि-रहित होता है। / Use the difference-of-squares identity: \(a^2-b^2=(a-b)(a+b)\). So \(19^2-15^2=(19-15)(19+15)=4\times34=136\). Thus the correct value is 136. Common mistakes: computing one square incorrectly (giving 126 on subtraction) or failing to add correctly; 146 is also incorrect because the correct sum is \(19+15=34\), not a larger value. Exam tip: convert differences of squares to a product to avoid large multiplications and reduce errors.
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(\left\(\frac{27}{8}\right\)^{2/3}) का मान क्या है?
What is the value of (\left\(\frac{27}{8}\right\)^{2/3})?
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#expert
#fractional
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A \(\frac{9}{4}\)
B \(\frac{3}{2}\)
C \(\frac{27}{4}\)
D \(\frac{81}{16}\)
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Correct Answer
A. \(\frac{9}{4}\)
Explanation
Simple Explanation
पहले घनमूल लें फिर वर्ग करें। भिन्नात्मक घात का नियम लगाएँ। / Take the cube root first and then square it. Apply fractional exponent rules.
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(\(7^2\)2 \div73 ) का मान क्या है?
What is the value of (\(7^2\)2 \div73 )?
#exponents
#power_rule
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A 7
B 49
C 343
D 1
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Explanation
Simple Explanation
\(7^4\div7^3=7\)। / \(7^4\div7^3=7\).
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यदि \(4^{x+1}=64^{x-1}\) तो (x=)?
If \(4^{x+1}=64^{x-1}\), then (x=)?
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#expert
#equation
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A \(\frac{7}{4}\)
B \(\frac{5}{2}\)
C (3)
D \(\frac{3}{2}\)
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Correct Answer
A. \(\frac{7}{4}\)
Explanation
Simple Explanation
दोनों पक्षों को आधार (2) में लिखें। (2x+2=6x-6) से हल करें। / Write both sides in base (2). Solve (2x+2=6x-6).
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\(3^5+4^4\) का मान क्या है?
What is the value of \(3^5+4^4\)?
#exponents
#mixed
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A 489
B 499
C 509
D 519
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Explanation
Simple Explanation
(243+256=499)। / (243+256=499).
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