6 results found for "fourth-power" in Class 10.
Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि \(x^2-5x+1=0\) की जड़ें \(\alpha,\beta\) हैं, तो \(\alpha^4+\beta^4\) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-5x+1=0\), what is \(\alpha^4+\beta^4\)?
#quadratic-roots
#fourth-power
#root-expression
A (527)
B (529)
C (531)
D (533)
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=5\) and \(\alpha\beta=1\). First \(\alpha^2+\beta^2=23\), then \(\alpha^4+\beta^4=23^2-2=527\).
Step 2
Why this answer is correct
The correct answer is A. (527). Here \(\alpha+\beta=5\) and \(\alpha\beta=1\). First \(\alpha^2+\beta^2=23\), then \(\alpha^4+\beta^4=23^2-2=527\).
Step 3
Exam Tip
\(\alpha+\beta=5\) और \(\alpha\beta=1\) है। पहले \(\alpha^2+\beta^2=23\), फिर \(\alpha^4+\beta^4=23^2-2=527\)।
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Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि \(x^2-3x+1=0\) की जड़ें \(\alpha,\beta\) हैं, तो \(\alpha^4+\beta^4\) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-3x+1=0\), what is \(\alpha^4+\beta^4\)?
#quadratic-roots
#fourth-power
#root-expression
A (43)
B (45)
C (47)
D (49)
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=3\) and \(\alpha\beta=1\). First \(\alpha^2+\beta^2=7\), then \(\alpha^4+\beta^4=7^2-2=47\).
Step 2
Why this answer is correct
The correct answer is C. (47). Here \(\alpha+\beta=3\) and \(\alpha\beta=1\). First \(\alpha^2+\beta^2=7\), then \(\alpha^4+\beta^4=7^2-2=47\).
Step 3
Exam Tip
\(\alpha+\beta=3\) और \(\alpha\beta=1\) है। पहले \(\alpha^2+\beta^2=7\), फिर \(\alpha^4+\beta^4=7^2-2=47\)।
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Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
यदि \(x^2-4x+1=0\) की जड़ें \(\alpha,\beta\) हैं, तो \(\alpha^4+\beta^4\) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-4x+1=0\), what is \(\alpha^4+\beta^4\)?
#quadratic-roots
#fourth-power
#root-expression
A (194)
B (196)
C (198)
D (200)
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=4\) and \(\alpha\beta=1\). First \(\alpha^2+\beta^2=14\), then \(\alpha^4+\beta^4=14^2-2=194\).
Step 2
Why this answer is correct
The correct answer is A. (194). Here \(\alpha+\beta=4\) and \(\alpha\beta=1\). First \(\alpha^2+\beta^2=14\), then \(\alpha^4+\beta^4=14^2-2=194\).
Step 3
Exam Tip
\(\alpha+\beta=4\) और \(\alpha\beta=1\) है। पहले \(\alpha^2+\beta^2=14\), फिर \(\alpha^4+\beta^4=14^2-2=194\)।
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Question
Expert Mathematics
Real Numbers 1: Euclid’s Division Lemma Class 10 Level 1
किसी संख्या को 13 से भाग देने पर शेषफल 7 है। उसी संख्या के चौथे घात को 13 से भाग देने पर शेषफल क्या होगा?
A number leaves remainder 7 when divided by 13. What is the remainder when its fourth power is divided by 13?
#euclids-division-lemma
#power-remainder
#advanced
A 1
B 3
C 5
D 9
Explanation opens after your attempt
Step 1
Concept
\(7^2=49\), and 49 leaves remainder 10 when divided by 13.
Step 2
Why this answer is correct
For \(7^4\), check \(10^2=100\).
Step 3
Exam Tip
\(100=13\times7+9\), so the remainder is 9. चरण 1: \(7^2=49\), और 49 को 13 से भाग देने पर शेषफल 10 है। चरण 2: \(7^4\) के लिए \(10^2=100\) देखें। चरण 3: \(100=13\times7+9\), इसलिए शेषफल 9 है।
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Question
Hard Mathematics
Real Numbers 1: Euclid’s Division Lemma Class 10 Level 3
किसी संख्या को 9 से भाग देने पर शेषफल 7 है। उसी संख्या के चौथे घात को 9 से भाग देने पर शेषफल क्या होगा?
A number leaves remainder 7 when divided by 9. What is the remainder when its fourth power is divided by 9?
#euclids-division-lemma
#power-remainder
#advanced
A 1
B 4
C 7
D 8
Explanation opens after your attempt
Step 1
Concept
\(7^2=49\), which leaves remainder 4 on division by 9.
Step 2
Why this answer is correct
For \(7^4\), use \(4^2=16\), and 16 leaves remainder 7 on division by 9.
Step 3
Exam Tip
In higher powers, reduce the remainder after each step. चरण 1: \(7^2=49\), और 49 को 9 से भाग देने पर शेषफल 4 है। चरण 2: \(7^4\) के लिए \(4^2=16\), और 16 का 9 से शेषफल 7 नहीं, बल्कि 7 है; इसलिए सही शेषफल 7 होगा। चरण 3: बड़ी घातों में हर चरण के बाद शेषफल घटाना जरूरी है।
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Question
Hard Mathematics
Real Numbers 1: Euclid’s Division Lemma Class 10 Level 2
किसी संख्या को 7 से भाग देने पर शेषफल 4 है। उसी संख्या के चौथे घात को 7 से भाग देने पर शेषफल क्या होगा?
A number leaves remainder 4 when divided by 7. What is the remainder when its fourth power is divided by 7?
#euclids-division-lemma
#power-remainder
#advanced
A 1
B 2
C 3
D 4
Explanation opens after your attempt
Step 1
Concept
For the fourth power, look at the remainder of \(4^4\).
Step 2
Why this answer is correct
\(4^2=16\), which leaves remainder 2 when divided by 7; then \(4^4\) leaves the same remainder as \(2^2=4\).
Step 3
Exam Tip
For higher powers, reduce remainders step by step. चरण 1: चौथे घात के लिए \(4^4\) का शेषफल देखें। चरण 2: \(4^2=16\), जिसका 7 से शेषफल 2 है; फिर \(4^4\) का शेषफल \(2^2=4\) होगा। चरण 3: बड़ी घातों में छोटे-छोटे चरणों में शेषफल निकालें।
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