कौन सा व्यंजक (x) में बहुपद नहीं है लेकिन देखने में द्विघात जैसा लगता है?
Which expression is not a polynomial in (x) though it looks similar to a quadratic?
#not polynomial
#denominator
#negative exponent
A \(x^2+2x+1\)
B \(2x^2-5x+3\)
C \(x^2+\frac{1}{x}+4\)
D \(7x^2-9\)
Explanation opens after your attempt
Correct Answer
C. \(x^2+\frac{1}{x}+4\)
Step 1
Concept
\(x^2+\frac{1}{x}+4\) contains \(x^{-1}\), which is not allowed in a polynomial. Be careful when the variable is in the denominator.
Step 2
Why this answer is correct
The correct answer is C. \(x^2+\frac{1}{x}+4\). \(x^2+\frac{1}{x}+4\) contains \(x^{-1}\), which is not allowed in a polynomial. Be careful when the variable is in the denominator.
Step 3
Exam Tip
\(x^2+\frac{1}{x}+4\) में \(x^{-1}\) है, जो बहुपद में मान्य नहीं है। हर में चर हो तो सावधान रहें।
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निम्न में से कौन सा (x) में बहुपद नहीं है?
Which of the following is not a polynomial in (x)?
#not-polynomial
#negative-exponent
A \(x^2+1\)
B \(4x^3-2\)
C \(\frac{5}{x^2}+1\)
D (7x+8)
Explanation opens after your attempt
Correct Answer
C. \(\frac{5}{x^2}+1\)
Step 1
Concept
\(\frac{5}{x^2}=5x^{-2}\) has a negative power. Such powers are not allowed in a polynomial.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{5}{x^2}+1\). \(\frac{5}{x^2}=5x^{-2}\) has a negative power. Such powers are not allowed in a polynomial.
Step 3
Exam Tip
\(\frac{5}{x^2}=5x^{-2}\) में ऋणात्मक घात है। बहुपद में ऐसी घात मान्य नहीं होती।
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\(2^7\cdot16^{-1}\) का मान क्या है?
What is the value of \(2^7\cdot16^{-1}\)?
#polynomials
#powers of two
#negative exponent
A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
(16^{-1}=\(2^4\)^{-1}=2^{-4}). Hence \(2^7\cdot2^{-4}=2^3=8\).
Step 2
Why this answer is correct
The correct answer is B. (8). (16^{-1}=\(2^4\)^{-1}=2^{-4}). Hence \(2^7\cdot2^{-4}=2^3=8\).
Step 3
Exam Tip
(16^{-1}=\(2^4\)^{-1}=2^{-4}) है। इसलिए \(2^7\cdot2^{-4}=2^3=8\) है।
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(\left\(5^2\right\)0 +2^{-3}) का मान क्या है?
What is the value of (\left\(5^2\right\)0 +2^{-3})?
#polynomials
#zero exponent
#negative exponent
A \(\frac{1}{8}\)
B \(\frac{9}{8}\)
C (25)
D \(\frac{25}{8}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{9}{8}\)
Step 1
Concept
(\left\(5^2\right\)0 =1) and \(2^{-3}=\frac{1}{8}\). Therefore the sum is \(\frac{9}{8}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{9}{8}\). (\left\(5^2\right\)0 =1) and \(2^{-3}=\frac{1}{8}\). Therefore the sum is \(\frac{9}{8}\).
Step 3
Exam Tip
(\left\(5^2\right\)0 =1) और \(2^{-3}=\frac{1}{8}\) है। इसलिए योग \(\frac{9}{8}\) है।
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(\left\(\frac{a^{-2}}{b^{-4}}\right\)^{-1}) का सरल रूप क्या है यदि \(a\neq0\) और \(b\neq0\)?
What is the simplified form of (\left\(\frac{a^{-2}}{b^{-4}}\right\)^{-1}) if \(a\neq0\) and \(b\neq0\)?
#polynomials
#negative exponent
#complex simplification
A \(a^2b^{-4}\)
B \(a^{-2}b^4\)
C \(\frac{b^4}{a^2}\)
D \(\frac{a^2}{b^4}\)
Explanation opens after your attempt
Correct Answer
D. \(\frac{a^2}{b^4}\)
Step 1
Concept
Inside, \(\frac{a^{-2}}{b^{-4}}=a^{-2}b^4\). The outside power (-1) gives \(\frac{a^2}{b^4}\).
Step 2
Why this answer is correct
The correct answer is D. \(\frac{a^2}{b^4}\). Inside, \(\frac{a^{-2}}{b^{-4}}=a^{-2}b^4\). The outside power (-1) gives \(\frac{a^2}{b^4}\).
Step 3
Exam Tip
अंदर \(\frac{a^{-2}}{b^{-4}}=a^{-2}b^4\) है। बाहरी (-1) घात से \(\frac{a^2}{b^4}\) मिलता है।
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यदि (a=5) है तो \(a^2-a^{-1}\) का मान क्या है?
If (a=5), what is the value of \(a^2-a^{-1}\)?
#polynomials
#substitution
#negative exponent
A \(\frac{124}{5}\)
B \(\frac{126}{5}\)
C (24)
D (26)
Explanation opens after your attempt
Correct Answer
A. \(\frac{124}{5}\)
Step 1
Concept
\(5^2=25\) and \(5^{-1}=\frac{1}{5}\). Thus \(25-\frac{1}{5}=\frac{124}{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{124}{5}\). \(5^2=25\) and \(5^{-1}=\frac{1}{5}\). Thus \(25-\frac{1}{5}=\frac{124}{5}\).
Step 3
Exam Tip
\(5^2=25\) और \(5^{-1}=\frac{1}{5}\) है। इसलिए \(25-\frac{1}{5}=\frac{124}{5}\) है।
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((0.04)^{-1}) का मान क्या है?
What is the value of ((0.04)^{-1})?
#polynomials
#decimals
#negative exponent
A (4)
B (25)
C (40)
D (100)
Explanation opens after your attempt
Step 1
Concept
\(0.04=\frac{4}{100}=\frac{1}{25}\). Therefore ((0.04)^{-1}=25).
Step 2
Why this answer is correct
The correct answer is B. (25). \(0.04=\frac{4}{100}=\frac{1}{25}\). Therefore ((0.04)^{-1}=25).
Step 3
Exam Tip
\(0.04=\frac{4}{100}=\frac{1}{25}\) है। इसलिए ((0.04)^{-1}=25) होता है।
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\(3^5\cdot9^{-1}\) का मान क्या है?
What is the value of \(3^5\cdot9^{-1}\)?
#polynomials
#powers of three
#negative exponent
A (9)
B (27)
C (81)
D (243)
Explanation opens after your attempt
Step 1
Concept
(9^{-1}=\(3^2\)^{-1}=3^{-2}). Hence \(3^5\cdot3^{-2}=3^3=27\).
Step 2
Why this answer is correct
The correct answer is B. (27). (9^{-1}=\(3^2\)^{-1}=3^{-2}). Hence \(3^5\cdot3^{-2}=3^3=27\).
Step 3
Exam Tip
(9^{-1}=\(3^2\)^{-1}=3^{-2}) है। इसलिए \(3^5\cdot3^{-2}=3^3=27\) है।
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(\left\(3^2\right\)0 +4^{-1}) का मान क्या है?
What is the value of (\left\(3^2\right\)0 +4^{-1})?
#polynomials
#zero exponent
#negative exponent
A \(\frac{1}{4}\)
B \(\frac{5}{4}\)
C (9)
D \(\frac{13}{4}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{5}{4}\)
Step 1
Concept
(\left\(3^2\right\)0 =1) and \(4^{-1}=\frac{1}{4}\). Therefore the sum is \(\frac{5}{4}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{5}{4}\). (\left\(3^2\right\)0 =1) and \(4^{-1}=\frac{1}{4}\). Therefore the sum is \(\frac{5}{4}\).
Step 3
Exam Tip
(\left\(3^2\right\)0 =1) और \(4^{-1}=\frac{1}{4}\) है। इसलिए योग \(\frac{5}{4}\) है।
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(\left\(\frac{x^{-3}}{y^{-2}}\right\)^{-1}) का सरल रूप क्या है यदि \(x\neq0\) और \(y\neq0\)?
What is the simplified form of (\left\(\frac{x^{-3}}{y^{-2}}\right\)^{-1}) if \(x\neq0\) and \(y\neq0\)?
#polynomials
#negative exponent
#complex simplification
A \(x^3y^{-2}\)
B \(x^{-3}y^2\)
C \(\frac{y^2}{x^3}\)
D \(\frac{x^3}{y^2}\)
Explanation opens after your attempt
Correct Answer
D. \(\frac{x^3}{y^2}\)
Step 1
Concept
Inside, \(\frac{x^{-3}}{y^{-2}}=x^{-3}y^2\). The outside power (-1) gives \(\frac{x^3}{y^2}\).
Step 2
Why this answer is correct
The correct answer is D. \(\frac{x^3}{y^2}\). Inside, \(\frac{x^{-3}}{y^{-2}}=x^{-3}y^2\). The outside power (-1) gives \(\frac{x^3}{y^2}\).
Step 3
Exam Tip
अंदर \(\frac{x^{-3}}{y^{-2}}=x^{-3}y^2\) है। बाहरी (-1) घात से \(\frac{x^3}{y^2}\) मिलता है।
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(\left\(\frac{4}{3}\right\)^{-2}\cdot\left\(\frac{16}{9}\right\)) का मान क्या है?
What is the value of (\left\(\frac{4}{3}\right\)^{-2}\cdot\left\(\frac{16}{9}\right\))?
#polynomials
#fraction powers
#negative exponent
A (1)
B \(\frac{16}{9}\)
C \(\frac{9}{16}\)
D \(\frac{256}{81}\)
Explanation opens after your attempt
Step 1
Concept
(\left\(\frac{4}{3}\right\)^{-2}=\left\(\frac{3}{4}\right\)2 =\frac{9}{16}). Hence \(\frac{9}{16}\cdot\frac{16}{9}=1\).
Step 2
Why this answer is correct
The correct answer is A. (1). (\left\(\frac{4}{3}\right\)^{-2}=\left\(\frac{3}{4}\right\)2 =\frac{9}{16}). Hence \(\frac{9}{16}\cdot\frac{16}{9}=1\).
Step 3
Exam Tip
(\left\(\frac{4}{3}\right\)^{-2}=\left\(\frac{3}{4}\right\)2 =\frac{9}{16}) है। इसलिए \(\frac{9}{16}\cdot\frac{16}{9}=1\) है।
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((0.25)^{-2}) का मान क्या है?
What is the value of ((0.25)^{-2})?
#polynomials
#negative exponent
#decimals
A (4)
B (8)
C (16)
D (0.0625)
Explanation opens after your attempt
Step 1
Concept
\(0.25=\frac{1}{4}\). Therefore ((0.25)^{-2}=\left\(\frac{1}{4}\right\)^{-2}=16).
Step 2
Why this answer is correct
The correct answer is C. (16). \(0.25=\frac{1}{4}\). Therefore ((0.25)^{-2}=\left\(\frac{1}{4}\right\)^{-2}=16).
Step 3
Exam Tip
\(0.25=\frac{1}{4}\) है। इसलिए ((0.25)^{-2}=\left\(\frac{1}{4}\right\)^{-2}=16) होता है।
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(\frac{\(5^2\)3 }{54 \cdot5^{-1}}) का सरल रूप क्या है?
What is the simplified form of (\frac{\(5^2\)3 }{54 \cdot5^{-1}})?
#polynomials
#exponent laws
#negative exponent
A \(5^3\)
B \(5^1\)
C \(5^9\)
D \(5^{-3}\)
Explanation opens after your attempt
Correct Answer
A. \(5^3\)
Step 1
Concept
First (\(5^2\)3 =56 ). The total exponent is (6-4-(-1)=3), so the answer is \(5^3\).
Step 2
Why this answer is correct
The correct answer is A. \(5^3\). First (\(5^2\)3 =56 ). The total exponent is (6-4-(-1)=3), so the answer is \(5^3\).
Step 3
Exam Tip
पहले (\(5^2\)3 =56 ) होता है। कुल घात (6-4-(-1)=3) है इसलिए उत्तर \(5^3\) है।
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\(2^5\cdot4^{-1}\) का मान क्या है?
What is the value of \(2^5\cdot4^{-1}\)?
#polynomials
#powers of two
#negative exponent
A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
(4^{-1}=\(2^2\)^{-1}=2^{-2}). Hence \(2^5\cdot2^{-2}=2^3=8\).
Step 2
Why this answer is correct
The correct answer is B. (8). (4^{-1}=\(2^2\)^{-1}=2^{-2}). Hence \(2^5\cdot2^{-2}=2^3=8\).
Step 3
Exam Tip
(4^{-1}=\(2^2\)^{-1}=2^{-2}) है। इसलिए \(2^5\cdot2^{-2}=2^3=8\) है।
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(\left\(2^3\right\)0 +5^{-1}) का मान क्या है?
What is the value of (\left\(2^3\right\)0 +5^{-1})?
#polynomials
#zero exponent
#negative exponent
A \(\frac{1}{5}\)
B \(\frac{6}{5}\)
C (8)
D \(\frac{9}{5}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{6}{5}\)
Step 1
Concept
(\left\(2^3\right\)0 =1) and \(5^{-1}=\frac{1}{5}\). Therefore the sum is \(\frac{6}{5}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{6}{5}\). (\left\(2^3\right\)0 =1) and \(5^{-1}=\frac{1}{5}\). Therefore the sum is \(\frac{6}{5}\).
Step 3
Exam Tip
(\left\(2^3\right\)0 =1) और \(5^{-1}=\frac{1}{5}\) है। इसलिए योग \(\frac{6}{5}\) है।
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(\left\(\frac{x^{-2}}{y^{-3}}\right\)^{-1}) का सरल रूप क्या है यदि \(x\neq0\) और \(y\neq0\)?
What is the simplified form of (\left\(\frac{x^{-2}}{y^{-3}}\right\)^{-1}) if \(x\neq0\) and \(y\neq0\)?
#polynomials
#negative exponent
#complex simplification
A \(x^2y^{-3}\)
B \(x^{-2}y^3\)
C \(\frac{y^3}{x^2}\)
D \(\frac{x^2}{y^3}\)
Explanation opens after your attempt
Correct Answer
D. \(\frac{x^2}{y^3}\)
Step 1
Concept
Inside, \(\frac{x^{-2}}{y^{-3}}=x^{-2}y^3\). The outside power (-1) gives \(\frac{x^2}{y^3}\).
Step 2
Why this answer is correct
The correct answer is D. \(\frac{x^2}{y^3}\). Inside, \(\frac{x^{-2}}{y^{-3}}=x^{-2}y^3\). The outside power (-1) gives \(\frac{x^2}{y^3}\).
Step 3
Exam Tip
अंदर \(\frac{x^{-2}}{y^{-3}}=x^{-2}y^3\) है। बाहरी (-1) घात से \(\frac{x^2}{y^3}\) मिलता है।
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(\left\(\frac{3}{2}\right\)^{-2}\cdot\left\(\frac{9}{4}\right\)) का मान क्या है?
What is the value of (\left\(\frac{3}{2}\right\)^{-2}\cdot\left\(\frac{9}{4}\right\))?
#polynomials
#fraction powers
#negative exponent
A (1)
B \(\frac{9}{4}\)
C \(\frac{4}{9}\)
D \(\frac{81}{16}\)
Explanation opens after your attempt
Step 1
Concept
(\left\(\frac{3}{2}\right\)^{-2}=\left\(\frac{2}{3}\right\)2 =\frac{4}{9}). Hence \(\frac{4}{9}\cdot\frac{9}{4}=1\).
Step 2
Why this answer is correct
The correct answer is A. (1). (\left\(\frac{3}{2}\right\)^{-2}=\left\(\frac{2}{3}\right\)2 =\frac{4}{9}). Hence \(\frac{4}{9}\cdot\frac{9}{4}=1\).
Step 3
Exam Tip
(\left\(\frac{3}{2}\right\)^{-2}=\left\(\frac{2}{3}\right\)2 =\frac{4}{9}) है। इसलिए \(\frac{4}{9}\cdot\frac{9}{4}=1\) है।
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((0.2)^{-2}) का मान क्या है?
What is the value of ((0.2)^{-2})?
#polynomials
#negative exponent
#decimals
A (5)
B (10)
C (25)
D (0.04)
Explanation opens after your attempt
Step 1
Concept
\(0.2=\frac{1}{5}\), so ((0.2)^{-2}=\left\(\frac{1}{5}\right\)^{-2}=25). Converting decimals to fractions helps.
Step 2
Why this answer is correct
The correct answer is C. (25). \(0.2=\frac{1}{5}\), so ((0.2)^{-2}=\left\(\frac{1}{5}\right\)^{-2}=25). Converting decimals to fractions helps.
Step 3
Exam Tip
\(0.2=\frac{1}{5}\), इसलिए ((0.2)^{-2}=\left\(\frac{1}{5}\right\)^{-2}=25)। दशमलव को भिन्न में बदलना आसान होता है।
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यदि \(y\neq0\) है तो \(y^{-5}\) का सही रूप क्या है?
If \(y\neq0\), what is the correct form of \(y^{-5}\)?
#polynomials
#negative exponent
#algebra
A \(y^5\)
B \(\frac{1}{y^5}\)
C \(-y^5\)
D \(\frac{1}{5y}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{1}{y^5}\)
Step 1
Concept
A negative exponent moves the base to the denominator. Therefore \(y^{-5}=\frac{1}{y^5}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{1}{y^5}\). A negative exponent moves the base to the denominator. Therefore \(y^{-5}=\frac{1}{y^5}\).
Step 3
Exam Tip
ऋणात्मक घात आधार को हर में ले जाती है। इसलिए \(y^{-5}=\frac{1}{y^5}\) है।
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\(3^{-2}\) किसके बराबर है?
What is \(3^{-2}\) equal to?
#polynomials
#negative exponent
#basics
A \(\frac{1}{9}\)
B (9)
C (-9)
D \(\frac{1}{6}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{9}\)
Step 1
Concept
A negative exponent moves the base to the denominator, so \(3^{-2}=\frac{1}{3^2}=\frac{1}{9}\). A negative exponent does not mean a negative answer.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{9}\). A negative exponent moves the base to the denominator, so \(3^{-2}=\frac{1}{3^2}=\frac{1}{9}\). A negative exponent does not mean a negative answer.
Step 3
Exam Tip
ऋणात्मक घात आधार को हर में ले जाती है इसलिए \(3^{-2}=\frac{1}{3^2}=\frac{1}{9}\)। ऋणात्मक घात का अर्थ ऋणात्मक उत्तर नहीं होता।
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यदि \(x\neq0\) है तो \(x^{-4}\) का सही रूप क्या है?
If \(x\neq0\), what is the correct form of \(x^{-4}\)?
#polynomials
#negative exponent
#algebra
A \(x^4\)
B \(\frac{1}{x^4}\)
C \(-x^4\)
D \(\frac{1}{4x}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{1}{x^4}\)
Step 1
Concept
A negative exponent moves the base to the denominator. Therefore \(x^{-4}=\frac{1}{x^4}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{1}{x^4}\). A negative exponent moves the base to the denominator. Therefore \(x^{-4}=\frac{1}{x^4}\).
Step 3
Exam Tip
ऋणात्मक घात आधार को हर में ले जाती है। इसलिए \(x^{-4}=\frac{1}{x^4}\) है।
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\(2^{-3}\) किसके बराबर है?
What is \(2^{-3}\) equal to?
#polynomials
#negative exponent
#basics
A \(\frac{1}{8}\)
B (8)
C (-8)
D \(\frac{1}{6}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{8}\)
Step 1
Concept
A negative exponent moves the base to the denominator, so \(2^{-3}=\frac{1}{2^3}=\frac{1}{8}\). A negative exponent does not mean a negative answer.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{8}\). A negative exponent moves the base to the denominator, so \(2^{-3}=\frac{1}{2^3}=\frac{1}{8}\). A negative exponent does not mean a negative answer.
Step 3
Exam Tip
ऋणात्मक घात में संख्या हर में चली जाती है इसलिए \(2^{-3}=\frac{1}{2^3}=\frac{1}{8}\)। ऋणात्मक घात का अर्थ ऋणात्मक उत्तर नहीं है।
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\(a^{-3}\) का सही रूप क्या है यदि \(a\neq0\)?
What is the correct form of \(a^{-3}\) if \(a\neq0\)?
#polynomials
#negative exponent
#algebra
A \(a^3\)
B \(\frac{1}{a^3}\)
C \(-a^3\)
D \(\frac{1}{3a}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{1}{a^3}\)
Step 1
Concept
A negative exponent gives \(a^{-3}=\frac{1}{a^3}\). The negative sign in the exponent does not make the base negative.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{1}{a^3}\). A negative exponent gives \(a^{-3}=\frac{1}{a^3}\). The negative sign in the exponent does not make the base negative.
Step 3
Exam Tip
ऋणात्मक घात में \(a^{-3}=\frac{1}{a^3}\) होता है। घात का ऋण चिह्न आधार को ऋणात्मक नहीं बनाता।
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\(10^{-2}\) का मान किसके बराबर है?
What is \(10^{-2}\) equal to?
#polynomials
#exponents
#negative exponent
A (100)
B \(\frac{1}{100}\)
C (-100)
D \(\frac{1}{10}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{1}{100}\)
Step 1
Concept
A negative exponent moves the number to the denominator, so \(10^{-2}=\frac{1}{10^2}=\frac{1}{100}\). A negative exponent does not mean a negative value.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{1}{100}\). A negative exponent moves the number to the denominator, so \(10^{-2}=\frac{1}{10^2}=\frac{1}{100}\). A negative exponent does not mean a negative value.
Step 3
Exam Tip
ऋणात्मक घात में संख्या हर में चली जाती है इसलिए \(10^{-2}=\frac{1}{10^2}=\frac{1}{100}\)। ऋणात्मक घात का अर्थ ऋणात्मक मान नहीं होता।
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समीकरण \(\frac{1}{x^2}+x+1=0\) द्विघात समीकरण क्यों नहीं है?
Why is \(\frac{1}{x^2}+x+1=0\) not a quadratic equation?
#quadratic-equations
#non-example
#negative-exponent
A क्योंकि इसमें (x) की ऋणात्मक घात है / Because it has a negative power of (x)
B क्योंकि इसमें (x) पद है / Because it has an (x) term
C क्योंकि इसमें स्थिर पद है / Because it has a constant term
D क्योंकि इसमें (1) है / Because it has (1)
Explanation opens after your attempt
Correct Answer
A. क्योंकि इसमें (x) की ऋणात्मक घात है / Because it has a negative power of (x)
Step 1
Concept
\(\frac{1}{x^2}=x^{-2}\), which is not polynomial form. A quadratic equation cannot have a negative power of the variable.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि इसमें (x) की ऋणात्मक घात है / Because it has a negative power of (x). \(\frac{1}{x^2}=x^{-2}\), which is not polynomial form. A quadratic equation cannot have a negative power of the variable.
Step 3
Exam Tip
\(\frac{1}{x^2}=x^{-2}\) है जो बहुपद रूप नहीं है। द्विघात समीकरण में चर की ऋणात्मक घात नहीं होती।
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