\(7+3^2\cdot5\) का मान क्या है?
What is the value of \(7+3^2\cdot5\)?
#polynomials
#order of operations
#exponents
A (52)
B (80)
C (100)
D (45)
Explanation opens after your attempt
Step 1
Concept
First \(3^2=9\), then \(9\cdot5=45\), and (7+45=52). Evaluate exponents before multiplication.
Step 2
Why this answer is correct
The correct answer is A. (52). First \(3^2=9\), then \(9\cdot5=45\), and (7+45=52). Evaluate exponents before multiplication.
Step 3
Exam Tip
पहले \(3^2=9\), फिर \(9\cdot5=45\), और (7+45=52)। घात का काम गुणा से पहले करें।
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\(4^2+4^3\) का मान क्या है?
What is the value of \(4^2+4^3\)?
#polynomials
#exponents
#common mistake
A \(4^5\)
B (80)
C (64)
D (48)
Explanation opens after your attempt
Step 1
Concept
This is addition, so exponents are not added. \(4^2+4^3=16+64=80\).
Step 2
Why this answer is correct
The correct answer is B. (80). This is addition, so exponents are not added. \(4^2+4^3=16+64=80\).
Step 3
Exam Tip
यहाँ जोड़ है इसलिए घातें नहीं जुड़तीं। \(4^2+4^3=16+64=80\) है।
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\(\frac{35x^6}{7x^3}\) का सरल रूप क्या है यदि \(x\neq0\)?
What is the simplified form of \(\frac{35x^6}{7x^3}\) if \(x\neq0\)?
#polynomials
#monomial division
#exponents
A \(5x^3\)
B \(28x^3\)
C \(5x^9\)
D \(245x^3\)
Explanation opens after your attempt
Correct Answer
A. \(5x^3\)
Step 1
Concept
The coefficient part is \(\frac{35}{7}=5\) and the variable part is \(\frac{x^6}{x^3}=x^3\). Thus the simplified form is \(5x^3\).
Step 2
Why this answer is correct
The correct answer is A. \(5x^3\). The coefficient part is \(\frac{35}{7}=5\) and the variable part is \(\frac{x^6}{x^3}=x^3\). Thus the simplified form is \(5x^3\).
Step 3
Exam Tip
गुणांक \(\frac{35}{7}=5\) और चर भाग \(\frac{x^6}{x^3}=x^3\) है। इसलिए सरल रूप \(5x^3\) है।
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\(6x\cdot5x^2\) का गुणनफल क्या है?
What is the product of \(6x\cdot5x^2\)?
#polynomials
#monomial multiplication
#exponents
A \(11x^3\)
B \(30x^2\)
C \(30x^3\)
D \(30x^4\)
Explanation opens after your attempt
Correct Answer
C. \(30x^3\)
Step 1
Concept
The coefficients give \(6\cdot5=30\), and \(x\cdot x^2=x^3\). Therefore the answer is \(30x^3\).
Step 2
Why this answer is correct
The correct answer is C. \(30x^3\). The coefficients give \(6\cdot5=30\), and \(x\cdot x^2=x^3\). Therefore the answer is \(30x^3\).
Step 3
Exam Tip
गुणांक \(6\cdot5=30\) और \(x\cdot x^2=x^3\) है। इसलिए उत्तर \(30x^3\) है।
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\(v^4\cdot v^5\) का सरल रूप क्या है?
What is the simplified form of \(v^4\cdot v^5\)?
#polynomials
#algebraic terms
#exponents
A \(v^9\)
B \(v^{20}\)
C \(2v^9\)
D (v)
Explanation opens after your attempt
Correct Answer
A. \(v^9\)
Step 1
Concept
For the same base (v), exponents add as (4+5=9). Therefore \(v^4\cdot v^5=v^9\).
Step 2
Why this answer is correct
The correct answer is A. \(v^9\). For the same base (v), exponents add as (4+5=9). Therefore \(v^4\cdot v^5=v^9\).
Step 3
Exam Tip
समान आधार (v) में घातें (4+5=9) जुड़ती हैं। इसलिए \(v^4\cdot v^5=v^9\) है।
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(\left\(\frac{m}{n}\right\)4 ) का सही रूप क्या है यदि \(n\neq0\)?
What is the correct form of (\left\(\frac{m}{n}\right\)4 ) if \(n\neq0\)?
#polynomials
#fraction law
#exponents
A \(\frac{m^4}{n^4}\)
B \(\frac{m^4}{n}\)
C \(\frac{m}{n^4}\)
D \(\frac{m+n}{4}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{m^4}{n^4}\)
Step 1
Concept
The exponent of a fraction applies to both numerator and denominator. Thus (\left\(\frac{m}{n}\right\)4 =\frac{m-4 }{n-4 }).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{m^4}{n^4}\). The exponent of a fraction applies to both numerator and denominator. Thus (\left\(\frac{m}{n}\right\)4 =\frac{m-4 }{n-4 }).
Step 3
Exam Tip
भिन्न की घात अंश और हर दोनों पर लगती है। इसलिए (\left\(\frac{m}{n}\right\)4 =\frac{m-4 }{n-4 }) है।
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यदि \(w\neq0\) है तो \(\frac{w^a}{w^b}\) का सही रूप क्या है?
If \(w\neq0\), what is the correct form of \(\frac{w^a}{w^b}\)?
#polynomials
#quotient law
#exponents
A \(w^{a+b}\)
B \(w^{a-b}\)
C \(w^{ab}\)
D \(w^{b-a}\)
Explanation opens after your attempt
Correct Answer
B. \(w^{a-b}\)
Step 1
Concept
In division with the same base, exponents are subtracted. Therefore \(\frac{w^a}{w^b}=w^{a-b}\).
Step 2
Why this answer is correct
The correct answer is B. \(w^{a-b}\). In division with the same base, exponents are subtracted. Therefore \(\frac{w^a}{w^b}=w^{a-b}\).
Step 3
Exam Tip
समान आधार के भाग में घातें घटती हैं। इसलिए \(\frac{w^a}{w^b}=w^{a-b}\) है।
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\(6^2+3^3\) का मान क्या है?
What is the value of \(6^2+3^3\)?
#polynomials
#real number operations
#exponents
A (63)
B (54)
C (45)
D (39)
Explanation opens after your attempt
Step 1
Concept
Find powers first: \(6^2=36\) and \(3^3=27\). Hence (36+27=63).
Step 2
Why this answer is correct
The correct answer is A. (63). Find powers first: \(6^2=36\) and \(3^3=27\). Hence (36+27=63).
Step 3
Exam Tip
पहले घात निकालें \(6^2=36\) और \(3^3=27\)। इसलिए (36+27=63) है।
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\(21^1\) का मान क्या है?
What is the value of \(21^1\)?
#polynomials
#first power
#exponents
A (0)
B (1)
C (21)
D (441)
Explanation opens after your attempt
Step 1
Concept
The first power of a number is the number itself. Therefore \(21^1=21\).
Step 2
Why this answer is correct
The correct answer is C. (21). The first power of a number is the number itself. Therefore \(21^1=21\).
Step 3
Exam Tip
किसी संख्या की (1) घात वही संख्या होती है। इसलिए \(21^1=21\) है।
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\(15^6\div15^2\) का सरल रूप क्या है?
What is the simplified form of \(15^6\div15^2\)?
#polynomials
#division law
#exponents
A \(15^4\)
B \(15^8\)
C \(15^{12}\)
D \(1^4\)
Explanation opens after your attempt
Correct Answer
A. \(15^4\)
Step 1
Concept
For division with the same base, (6-2=4). Therefore \(15^6\div15^2=15^4\).
Step 2
Why this answer is correct
The correct answer is A. \(15^4\). For division with the same base, (6-2=4). Therefore \(15^6\div15^2=15^4\).
Step 3
Exam Tip
भाग में समान आधार होने पर (6-2=4) होता है। इसलिए \(15^6\div15^2=15^4\) है।
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\(12^2\cdot12^3\) के बराबर कौन सा है?
Which is equal to \(12^2\cdot12^3\)?
#polynomials
#same base
#exponents
A \(12^5\)
B \(12^6\)
C \(24^5\)
D \(12^1\)
Explanation opens after your attempt
Correct Answer
A. \(12^5\)
Step 1
Concept
For the same base (12), exponents (2) and (3) are added. So the correct answer is \(12^5\).
Step 2
Why this answer is correct
The correct answer is A. \(12^5\). For the same base (12), exponents (2) and (3) are added. So the correct answer is \(12^5\).
Step 3
Exam Tip
समान आधार (12) में घातें (2) और (3) जुड़ती हैं। इसलिए सही उत्तर \(12^5\) है।
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(\left\(\frac{7}{8}\right\)2 ) का मान क्या है?
What is the value of (\left\(\frac{7}{8}\right\)2 )?
#polynomials
#fraction power
#exponents
A \(\frac{14}{16}\)
B \(\frac{49}{64}\)
C \(\frac{7}{64}\)
D \(\frac{49}{8}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{49}{64}\)
Step 1
Concept
The power of a fraction applies to both numerator and denominator. Hence (\left\(\frac{7}{8}\right\)2 =\frac{49}{64}).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{49}{64}\). The power of a fraction applies to both numerator and denominator. Hence (\left\(\frac{7}{8}\right\)2 =\frac{49}{64}).
Step 3
Exam Tip
भिन्न की घात अंश और हर दोनों पर लगती है। इसलिए (\left\(\frac{7}{8}\right\)2 =\frac{49}{64}) है।
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(\(6\cdot7\)2 ) का सही रूप क्या है?
What is the correct form of (\(6\cdot7\)2 )?
#polynomials
#product power
#exponents
A \(6^2\cdot7^2\)
B \(6^2\cdot7\)
C \(6\cdot7^2\)
D \(13^2\)
Explanation opens after your attempt
Correct Answer
A. \(6^2\cdot7^2\)
Step 1
Concept
The power of a product applies to every factor. Therefore (\(6\cdot7\)2 =62 \cdot72 ).
Step 2
Why this answer is correct
The correct answer is A. \(6^2\cdot7^2\). The power of a product applies to every factor. Therefore (\(6\cdot7\)2 =62 \cdot72 ).
Step 3
Exam Tip
गुणनफल की घात हर गुणक पर लगती है। इसलिए (\(6\cdot7\)2 =62 \cdot72 ) है।
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(\(2^4\)2 ) का सरल रूप क्या है?
What is the simplified form of (\(2^4\)2 )?
#polynomials
#exponents
#power law
A \(2^6\)
B \(2^8\)
C \(2^{16}\)
D \(4^4\)
Explanation opens after your attempt
Correct Answer
B. \(2^8\)
Step 1
Concept
In a power of a power, exponents are multiplied, so (\(2^4\)2 =28 ). Adding the exponents here is a mistake.
Step 2
Why this answer is correct
The correct answer is B. \(2^8\). In a power of a power, exponents are multiplied, so (\(2^4\)2 =28 ). Adding the exponents here is a mistake.
Step 3
Exam Tip
घात की घात में घातों का गुणा होता है इसलिए (\(2^4\)2 =28 )। यहाँ घातों को जोड़ना गलती है।
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\(\frac{10^8}{10^5}\) का सरल रूप क्या है?
What is the simplified form of \(\frac{10^8}{10^5}\)?
#polynomials
#exponents
#quotient law
A \(10^{13}\)
B \(10^3\)
C \(10^{40}\)
D \(1^3\)
Explanation opens after your attempt
Correct Answer
B. \(10^3\)
Step 1
Concept
When bases are the same in division, exponents are subtracted, so \(\frac{10^8}{10^5}=10^3\). Subtract the lower exponent from the upper exponent.
Step 2
Why this answer is correct
The correct answer is B. \(10^3\). When bases are the same in division, exponents are subtracted, so \(\frac{10^8}{10^5}=10^3\). Subtract the lower exponent from the upper exponent.
Step 3
Exam Tip
समान आधार में भाग करने पर घातें घटती हैं इसलिए \(\frac{10^8}{10^5}=10^3\)। भाग में ऊपर की घात से नीचे की घात घटाएँ।
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\(4^2\cdot4^3\) का सरल रूप क्या है?
What is the simplified form of \(4^2\cdot4^3\)?
#polynomials
#exponents
#product law
A \(4^5\)
B \(4^6\)
C \(16^5\)
D \(4^1\)
Explanation opens after your attempt
Correct Answer
A. \(4^5\)
Step 1
Concept
When bases are the same in multiplication, exponents are added, so \(4^2\cdot4^3=4^5\). Add exponents when bases are the same.
Step 2
Why this answer is correct
The correct answer is A. \(4^5\). When bases are the same in multiplication, exponents are added, so \(4^2\cdot4^3=4^5\). Add exponents when bases are the same.
Step 3
Exam Tip
समान आधार में गुणा करने पर घातें जुड़ती हैं इसलिए \(4^2\cdot4^3=4^5\)। आधार समान हो तो घात जोड़ें।
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\(4^2\cdot4^0\cdot4^3\) का सरल रूप क्या है?
What is the simplified form of \(4^2\cdot4^0\cdot4^3\)?
#polynomials
#mixed exponent law
#exponents
A \(4^5\)
B \(4^6\)
C \(4^0\)
D \(4^1\)
Explanation opens after your attempt
Correct Answer
A. \(4^5\)
Step 1
Concept
For the same base, the exponents add as (2+0+3=5). Hence the simplified form is \(4^5\).
Step 2
Why this answer is correct
The correct answer is A. \(4^5\). For the same base, the exponents add as (2+0+3=5). Hence the simplified form is \(4^5\).
Step 3
Exam Tip
समान आधार में घातें (2+0+3=5) जुड़ती हैं। इसलिए सरल रूप \(4^5\) है।
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\(30a^6\div5a^3\) का सरल रूप क्या है यदि \(a\neq0\)?
What is the simplified form of \(30a^6\div5a^3\) if \(a\neq0\)?
#polynomials
#monomial division
#exponents
A \(6a^3\)
B \(25a^3\)
C \(6a^9\)
D \(150a^3\)
Explanation opens after your attempt
Correct Answer
A. \(6a^3\)
Step 1
Concept
\(\frac{30}{5}=6\) and \(\frac{a^6}{a^3}=a^3\). Therefore the answer is \(6a^3\).
Step 2
Why this answer is correct
The correct answer is A. \(6a^3\). \(\frac{30}{5}=6\) and \(\frac{a^6}{a^3}=a^3\). Therefore the answer is \(6a^3\).
Step 3
Exam Tip
\(\frac{30}{5}=6\) और \(\frac{a^6}{a^3}=a^3\) है। इसलिए उत्तर \(6a^3\) है।
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\(4x^3\cdot3x^2\) का गुणनफल क्या है?
What is the product of \(4x^3\cdot3x^2\)?
#polynomials
#monomial multiplication
#exponents
A \(7x^5\)
B \(12x^5\)
C \(12x^6\)
D (12x)
Explanation opens after your attempt
Correct Answer
B. \(12x^5\)
Step 1
Concept
The coefficients give \(4\cdot3=12\), and \(x^3\cdot x^2=x^5\). So the product is \(12x^5\).
Step 2
Why this answer is correct
The correct answer is B. \(12x^5\). The coefficients give \(4\cdot3=12\), and \(x^3\cdot x^2=x^5\). So the product is \(12x^5\).
Step 3
Exam Tip
गुणांक \(4\cdot3=12\) और \(x^3\cdot x^2=x^5\) है। इसलिए गुणनफल \(12x^5\) है।
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\(9x^2+5x^2\) का सरल रूप क्या है?
What is the simplified form of \(9x^2+5x^2\)?
#polynomials
#like terms
#exponents
A \(14x^2\)
B \(14x^4\)
C \(45x^2\)
D \(4x^2\)
Explanation opens after your attempt
Correct Answer
A. \(14x^2\)
Step 1
Concept
These are like terms, so the coefficients (9+5=14) are added. The exponent (2) does not change.
Step 2
Why this answer is correct
The correct answer is A. \(14x^2\). These are like terms, so the coefficients (9+5=14) are added. The exponent (2) does not change.
Step 3
Exam Tip
ये समान पद हैं इसलिए गुणांक (9+5=14) जुड़ते हैं। घात (2) नहीं बदलती।
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\(5+2^3\cdot4\) का मान क्या है?
What is the value of \(5+2^3\cdot4\)?
#polynomials
#order of operations
#exponents
A (37)
B (52)
C (100)
D (32)
Explanation opens after your attempt
Step 1
Concept
First \(2^3=8\), then \(8\cdot4=32\), and (5+32=37). Evaluate exponents before multiplication.
Step 2
Why this answer is correct
The correct answer is A. (37). First \(2^3=8\), then \(8\cdot4=32\), and (5+32=37). Evaluate exponents before multiplication.
Step 3
Exam Tip
पहले \(2^3=8\), फिर \(8\cdot4=32\), और (5+32=37)। घात का काम गुणा से पहले करें।
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\(3^2+3^3\) का मान क्या है?
What is the value of \(3^2+3^3\)?
#polynomials
#exponents
#common mistake
A \(3^5\)
B (36)
C (27)
D (30)
Explanation opens after your attempt
Step 1
Concept
This is addition, so exponents are not added. \(3^2+3^3=9+27=36\).
Step 2
Why this answer is correct
The correct answer is B. (36). This is addition, so exponents are not added. \(3^2+3^3=9+27=36\).
Step 3
Exam Tip
यहाँ जोड़ है इसलिए घातें नहीं जुड़तीं। \(3^2+3^3=9+27=36\) है।
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\(\frac{24x^5}{6x^2}\) का सरल रूप क्या है यदि \(x\neq0\)?
What is the simplified form of \(\frac{24x^5}{6x^2}\) if \(x\neq0\)?
#polynomials
#monomial division
#exponents
A \(4x^3\)
B \(18x^3\)
C \(4x^7\)
D \(144x^3\)
Explanation opens after your attempt
Correct Answer
A. \(4x^3\)
Step 1
Concept
The coefficient part is \(\frac{24}{6}=4\) and \(\frac{x^5}{x^2}=x^3\). Thus the simplified form is \(4x^3\).
Step 2
Why this answer is correct
The correct answer is A. \(4x^3\). The coefficient part is \(\frac{24}{6}=4\) and \(\frac{x^5}{x^2}=x^3\). Thus the simplified form is \(4x^3\).
Step 3
Exam Tip
गुणांक \(\frac{24}{6}=4\) और \(\frac{x^5}{x^2}=x^3\) है। इसलिए सरल रूप \(4x^3\) है।
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\(5x\cdot4x^3\) का गुणनफल क्या है?
What is the product of \(5x\cdot4x^3\)?
#polynomials
#monomial multiplication
#exponents
A \(9x^4\)
B \(20x^3\)
C \(20x^4\)
D \(20x^5\)
Explanation opens after your attempt
Correct Answer
C. \(20x^4\)
Step 1
Concept
The coefficients give \(5\cdot4=20\), and \(x\cdot x^3=x^4\). Therefore the answer is \(20x^4\).
Step 2
Why this answer is correct
The correct answer is C. \(20x^4\). The coefficients give \(5\cdot4=20\), and \(x\cdot x^3=x^4\). Therefore the answer is \(20x^4\).
Step 3
Exam Tip
गुणांक \(5\cdot4=20\) और \(x\cdot x^3=x^4\) है। इसलिए उत्तर \(20x^4\) है।
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\(t^3\cdot t^4\) का सरल रूप क्या है?
What is the simplified form of \(t^3\cdot t^4\)?
#polynomials
#algebraic terms
#exponents
A \(t^7\)
B \(t^{12}\)
C \(2t^7\)
D (t)
Explanation opens after your attempt
Correct Answer
A. \(t^7\)
Step 1
Concept
For the same base (t), exponents add as (3+4=7). Therefore \(t^3\cdot t^4=t^7\).
Step 2
Why this answer is correct
The correct answer is A. \(t^7\). For the same base (t), exponents add as (3+4=7). Therefore \(t^3\cdot t^4=t^7\).
Step 3
Exam Tip
समान आधार (t) में घातें (3+4=7) जुड़ती हैं। इसलिए \(t^3\cdot t^4=t^7\) है।
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(\left\(\frac{p}{q}\right\)2 ) का सही रूप क्या है यदि \(q\neq0\)?
What is the correct form of (\left\(\frac{p}{q}\right\)2 ) if \(q\neq0\)?
#polynomials
#fraction law
#exponents
A \(\frac{p^2}{q^2}\)
B \(\frac{p^2}{q}\)
C \(\frac{p}{q^2}\)
D \(\frac{p+q}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{p^2}{q^2}\)
Step 1
Concept
The exponent of a fraction applies to both numerator and denominator. Therefore (\left\(\frac{p}{q}\right\)2 =\frac{p-2 }{q-2 }).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{p^2}{q^2}\). The exponent of a fraction applies to both numerator and denominator. Therefore (\left\(\frac{p}{q}\right\)2 =\frac{p-2 }{q-2 }).
Step 3
Exam Tip
भिन्न की घात अंश और हर दोनों पर लगती है। इसलिए (\left\(\frac{p}{q}\right\)2 =\frac{p-2 }{q-2 }) है।
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यदि \(d\neq0\) है तो \(\frac{d^r}{d^s}\) का सही रूप क्या है?
If \(d\neq0\), what is the correct form of \(\frac{d^r}{d^s}\)?
#polynomials
#quotient law
#exponents
A \(d^{r+s}\)
B \(d^{r-s}\)
C \(d^{rs}\)
D \(d^{s-r}\)
Explanation opens after your attempt
Correct Answer
B. \(d^{r-s}\)
Step 1
Concept
For division with the same base, the denominator exponent is subtracted from the numerator exponent. Thus \(\frac{d^r}{d^s}=d^{r-s}\).
Step 2
Why this answer is correct
The correct answer is B. \(d^{r-s}\). For division with the same base, the denominator exponent is subtracted from the numerator exponent. Thus \(\frac{d^r}{d^s}=d^{r-s}\).
Step 3
Exam Tip
समान आधार के भाग में ऊपर की घात से नीचे की घात घटती है। इसलिए \(\frac{d^r}{d^s}=d^{r-s}\) है।
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\(5^2+2^3\) का मान क्या है?
What is the value of \(5^2+2^3\)?
#polynomials
#real number operations
#exponents
A (13)
B (25)
C (33)
D (49)
Explanation opens after your attempt
Step 1
Concept
Find powers first: \(5^2=25\) and \(2^3=8\). Hence (25+8=33).
Step 2
Why this answer is correct
The correct answer is C. (33). Find powers first: \(5^2=25\) and \(2^3=8\). Hence (25+8=33).
Step 3
Exam Tip
पहले घात निकालें \(5^2=25\) और \(2^3=8\)। इसलिए (25+8=33) है।
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\(13^1\) का मान क्या है?
What is the value of \(13^1\)?
#polynomials
#first power
#exponents
A (0)
B (1)
C (13)
D (169)
Explanation opens after your attempt
Step 1
Concept
The first power of a number is the number itself. Therefore \(13^1=13\).
Step 2
Why this answer is correct
The correct answer is C. (13). The first power of a number is the number itself. Therefore \(13^1=13\).
Step 3
Exam Tip
किसी संख्या की (1) घात वही संख्या होती है। इसलिए \(13^1=13\) है।
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\(6^9\div6^5\) का सरल रूप क्या है?
What is the simplified form of \(6^9\div6^5\)?
#polynomials
#division law
#exponents
A \(6^4\)
B \(6^{14}\)
C \(6^{45}\)
D \(1^4\)
Explanation opens after your attempt
Correct Answer
A. \(6^4\)
Step 1
Concept
For division with the same base, (9-5=4). Hence \(6^9\div6^5=6^4\).
Step 2
Why this answer is correct
The correct answer is A. \(6^4\). For division with the same base, (9-5=4). Hence \(6^9\div6^5=6^4\).
Step 3
Exam Tip
भाग में समान आधार होने पर (9-5=4) होता है। इसलिए \(6^9\div6^5=6^4\) है।
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