यदि \(\sqrt{n}=3\sqrt{7}\), तो (n) का मान क्या है?
If \(\sqrt{n}=3\sqrt{7}\), what is the value of (n)?
#polynomials
#roots
#real-numbers
#equations
A (,63,)
B (,21,)
C (,42,)
D (,49,)
Explanation opens after your attempt
Step 1
Concept
Squaring both sides gives (n=\(3\sqrt{7}\)2 =9\times 7=63). In exams, square both sides in a square root equation.
Step 2
Why this answer is correct
The correct answer is A. (,63,). Squaring both sides gives (n=\(3\sqrt{7}\)2 =9\times 7=63). In exams, square both sides in a square root equation.
Step 3
Exam Tip
दोनों पक्षों का वर्ग करने पर (n=\(3\sqrt{7}\)2 =9\times 7=63)। परीक्षा में square root equation में दोनों पक्षों का वर्ग करें।
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यदि \(a \neq 0\), \(a \neq 1\) और \(\dfrac{a^5}{a^k}=a^2\), तो (k) का मान क्या है?
If \(a \neq 0\), \(a \neq 1\), and \(\dfrac{a^5}{a^k}=a^2\), what is the value of (k)?
#polynomials
#exponents
#equations
#division-law
A (,3,)
B (,2,)
C (,5,)
D (,7,)
Explanation opens after your attempt
Step 1
Concept
\(\dfrac{a^5}{a^k}=a^{5-k}\), so (5-k=2) and (k=3). In exams, subtract exponents using the division law.
Step 2
Why this answer is correct
The correct answer is A. (,3,). \(\dfrac{a^5}{a^k}=a^{5-k}\), so (5-k=2) and (k=3). In exams, subtract exponents using the division law.
Step 3
Exam Tip
\(\dfrac{a^5}{a^k}=a^{5-k}\), इसलिए (5-k=2) और (k=3)। परीक्षा में division law से घातांक घटाएं।
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यदि \(3^{2x-1}=81\), तो (x) का मान क्या है?
If \(3^{2x-1}=81\), what is the value of (x)?
#polynomials
#exponents
#equations
#same-base
A \(,\dfrac{5}{2},\)
B (,2,)
C \(,\dfrac{3}{2},\)
D (,4,)
Explanation opens after your attempt
Correct Answer
A. \(,\dfrac{5}{2},\)
Step 1
Concept
Since \(81=3^4\), we get (2x-1=4) and \(x=\dfrac{5}{2}\). In exams, equate exponents when the bases are the same.
Step 2
Why this answer is correct
The correct answer is A. \(,\dfrac{5}{2},\). Since \(81=3^4\), we get (2x-1=4) and \(x=\dfrac{5}{2}\). In exams, equate exponents when the bases are the same.
Step 3
Exam Tip
क्योंकि \(81=3^4\), इसलिए (2x-1=4) और \(x=\dfrac{5}{2}\)। परीक्षा में समान आधार होने पर घातांकों को बराबर करें।
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यदि \(4^{x+1}=128\), तो (x) का मान क्या है?
If \(4^{x+1}=128\), what is the value of (x)?
#polynomials
#exponents
#equations
#same-base
A \(,\dfrac{5}{2},\)
B \(,\dfrac{7}{2},\)
C (,3,)
D (,2,)
Explanation opens after your attempt
Correct Answer
A. \(,\dfrac{5}{2},\)
Step 1
Concept
Since \(4^{x+1}=2^{2x+2}\) and \(128=2^7\), we get (2x+2=7) and \(x=\dfrac{5}{2}\). In exams, write both sides with the same base.
Step 2
Why this answer is correct
The correct answer is A. \(,\dfrac{5}{2},\). Since \(4^{x+1}=2^{2x+2}\) and \(128=2^7\), we get (2x+2=7) and \(x=\dfrac{5}{2}\). In exams, write both sides with the same base.
Step 3
Exam Tip
क्योंकि \(4^{x+1}=2^{2x+2}\) और \(128=2^7\), इसलिए (2x+2=7) तथा \(x=\dfrac{5}{2}\)। परीक्षा में दोनों पक्षों को समान आधार में लिखें।
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यदि \(2^x=3\), तो \(8^x\) का मान क्या होगा?
If \(2^x=3\), what is the value of \(8^x\)?
#polynomials
#exponents
#equations
#power-of-power
A (,27,)
B (,9,)
C (,24,)
D (,6,)
Explanation opens after your attempt
Step 1
Concept
Since (8^x=\(2^3\)^x=\(2^x\)3 =33 =27). In exams, rewrite the expression using the known base.
Step 2
Why this answer is correct
The correct answer is A. (,27,). Since (8^x=\(2^3\)^x=\(2^x\)3 =33 =27). In exams, rewrite the expression using the known base.
Step 3
Exam Tip
क्योंकि (8^x=\(2^3\)^x=\(2^x\)3 =33 =27)। परीक्षा में दिए गए expression को known base के रूप में बदलें।
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यदि \(5^n=\dfrac{1}{125}\), तो (n) का मान क्या है?
If \(5^n=\dfrac{1}{125}\), what is the value of (n)?
#polynomials
#negative-exponents
#equations
#same-base
A (,-3,)
B (,3,)
C (,-2,)
D \(,\dfrac{1}{3},\)
Explanation opens after your attempt
Step 1
Concept
Since \(125=5^3\), \(\dfrac{1}{125}=5^{-3}\), so (n=-3). In exams, connect a reciprocal with a negative exponent.
Step 2
Why this answer is correct
The correct answer is A. (,-3,). Since \(125=5^3\), \(\dfrac{1}{125}=5^{-3}\), so (n=-3). In exams, connect a reciprocal with a negative exponent.
Step 3
Exam Tip
क्योंकि \(125=5^3\), इसलिए \(\dfrac{1}{125}=5^{-3}\) और (n=-3)। परीक्षा में reciprocal को negative exponent से जोड़ें।
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यदि \(3^a=9\) और \(2^b=8\), तो (a+b) का मान क्या होगा?
If \(3^a=9\) and \(2^b=8\), what is the value of (a+b)?
#polynomials
#exponents
#equations
#real-numbers
A (,5,)
B (,6,)
C (,4,)
D (,3,)
Explanation opens after your attempt
Step 1
Concept
From \(9=3^2\), (a=2), and from \(8=2^3\), (b=3), so (a+b=5). In exams, remembering small powers gives faster solutions.
Step 2
Why this answer is correct
The correct answer is A. (,5,). From \(9=3^2\), (a=2), and from \(8=2^3\), (b=3), so (a+b=5). In exams, remembering small powers gives faster solutions.
Step 3
Exam Tip
\(9=3^2\) से (a=2) और \(8=2^3\) से (b=3), इसलिए (a+b=5)। परीक्षा में छोटे powers को याद रखना तेज समाधान देता है।
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यदि \(2^{x+1}=32\), तो (x) का मान क्या है?
If \(2^{x+1}=32\), what is the value of (x)?
#polynomials
#exponents
#equations
#same-base
A (,4,)
B (,5,)
C (,3,)
D (,6,)
Explanation opens after your attempt
Step 1
Concept
Since \(32=2^5\), we get (x+1=5) and (x=4). In exams, first make the bases the same on both sides.
Step 2
Why this answer is correct
The correct answer is A. (,4,). Since \(32=2^5\), we get (x+1=5) and (x=4). In exams, first make the bases the same on both sides.
Step 3
Exam Tip
क्योंकि \(32=2^5\), इसलिए (x+1=5) और (x=4)। परीक्षा में पहले दोनों पक्षों का आधार समान बनाएं।
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यदि \(2^{x-1}=32\) है तो (x) का मान क्या है?
If \(2^{x-1}=32\), what is the value of (x)?
#polynomials
#exponents
#equations
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
\(32=2^5\), so (x-1=5). This gives (x=6).
Step 2
Why this answer is correct
The correct answer is C. (6). \(32=2^5\), so (x-1=5). This gives (x=6).
Step 3
Exam Tip
\(32=2^5\), इसलिए (x-1=5) है। इससे (x=6) मिलता है।
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यदि \(5^{x-2}=125\) है तो (x) का मान क्या है?
If \(5^{x-2}=125\), what is the value of (x)?
#polynomials
#exponents
#equations
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(125=5^3\), so (x-2=3). This gives (x=5).
Step 2
Why this answer is correct
The correct answer is C. (5). \(125=5^3\), so (x-2=3). This gives (x=5).
Step 3
Exam Tip
\(125=5^3\), इसलिए (x-2=3) है। इससे (x=5) मिलता है।
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यदि \(3^{x+1}=81\) है तो (x) का मान क्या है?
If \(3^{x+1}=81\), what is the value of (x)?
#polynomials
#exponents
#equations
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(81=3^4\), so (x+1=4). This gives (x=3).
Step 2
Why this answer is correct
The correct answer is B. (3). \(81=3^4\), so (x+1=4). This gives (x=3).
Step 3
Exam Tip
\(81=3^4\), इसलिए (x+1=4) है। इससे (x=3) मिलता है।
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\(2.37\overline{5}\) को भिन्न में बदलने के लिए कौन-सा समीकरण-जोड़ा सबसे उपयुक्त है?
Which pair of equations is most suitable for converting \(2.37\overline{5}\) into a fraction?
#recurring-decimal-method
#equations
#fraction-conversion
#hard
A \(100x=237.555\ldots\), \(1000x=2375.555\ldots\)
B \(10x=23.7555\ldots\), \(100x=237.555\ldots\)
C \(x=2.37555\ldots\), \(10x=23.7555\ldots\)
D \(1000x=2375.555\ldots\), \(10000x=23755.555\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(100x=237.555\ldots\), \(1000x=2375.555\ldots\)
Step 1
Concept
In \(x=2.37555\ldots\), (37) is the non-repeating part and (5) is repeating.
Step 2
Why this answer is correct
Taking (100x) and (1000x) aligns the repeating parts. Subtracting then gives the fraction.
Step 3
Exam Tip
First note the length of the non-repeating part and then the repeating part. चरण 1: \(x=2.37555\ldots\) में दशमलव के बाद (37) सांत भाग है और (5) आवर्ती है। चरण 2: (100x) और (1000x) लेने से आवर्ती भाग एक जैसी स्थिति में आ जाता है। फिर घटाने से भिन्न मिलती है। चरण 3: पहले सांत भाग की लंबाई और फिर आवर्ती भाग की लंबाई देखें।
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