B. क्योंकि चर की घात भिन्न है/Because the variable has a fractional power
Step 1
Concept
In \(x^{\frac{1}{2}}\), the power is fractional. In a polynomial, the variable power must be a non-negative integer.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि चर की घात भिन्न है / Because the variable has a fractional power. In \(x^{\frac{1}{2}}\), the power is fractional. In a polynomial, the variable power must be a non-negative integer.
Step 3
Exam Tip
\(x^{\frac{1}{2}}\) में घात भिन्न है। बहुपद में चर की घात अऋणात्मक पूर्णांक होनी चाहिए।
A. क्योंकि \(x^{-4}\) की घात ऋणात्मक है/Because \(x^{-4}\) has a negative power
Step 1
Concept
In \(x^{-4}\), the variable has a negative power. Negative powers are not accepted in a polynomial.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि \(x^{-4}\) की घात ऋणात्मक है / Because \(x^{-4}\) has a negative power. In \(x^{-4}\), the variable has a negative power. Negative powers are not accepted in a polynomial.
Step 3
Exam Tip
\(x^{-4}\) में चर की घात ऋणात्मक है। बहुपद में ऋणात्मक घात स्वीकार नहीं होती।
A. हां, क्योंकि \(x^0=1\) और (x) की घात (1) है/Yes, because \(x^0=1\) and the power of (x) is (1)
Step 1
Concept
The power in \(x^0\) is (0), which is valid in a polynomial. Therefore it is a polynomial.
Step 2
Why this answer is correct
The correct answer is A. हां, क्योंकि \(x^0=1\) और (x) की घात (1) है / Yes, because \(x^0=1\) and the power of (x) is (1). The power in \(x^0\) is (0), which is valid in a polynomial. Therefore it is a polynomial.
Step 3
Exam Tip
\(x^0\) की घात (0) है जो बहुपद में मान्य है। इसलिए यह बहुपद है।
B. हां, क्योंकि (x) की घात (1) है/Yes, because the power of (x) is (1)
Step 1
Concept
In \(\frac{7x}{3}\), the power of (x) is (1) and the coefficient is \(\frac{7}{3}\). A fractional coefficient is valid.
Step 2
Why this answer is correct
The correct answer is B. हां, क्योंकि (x) की घात (1) है / Yes, because the power of (x) is (1). In \(\frac{7x}{3}\), the power of (x) is (1) and the coefficient is \(\frac{7}{3}\). A fractional coefficient is valid.
Step 3
Exam Tip
\(\frac{7x}{3}\) में (x) की घात (1) है और गुणांक \(\frac{7}{3}\) है। भिन्न गुणांक मान्य है।
A. हां, क्योंकि गुणांक वास्तविक हैं और घातें मान्य हैं/Yes, because coefficients are real and powers are valid
Step 1
Concept
Coefficients can be negative or fractional. Here the powers of (x) are (2), (1), and (0).
Step 2
Why this answer is correct
The correct answer is A. हां, क्योंकि गुणांक वास्तविक हैं और घातें मान्य हैं / Yes, because coefficients are real and powers are valid. Coefficients can be negative or fractional. Here the powers of (x) are (2), (1), and (0).
Step 3
Exam Tip
गुणांक ऋणात्मक या भिन्न हो सकते हैं। यहां (x) की घातें (2), (1), और (0) हैं।
C. शून्य बहुपद की डिग्री परिभाषित नहीं होती और अशून्य नियतांक की डिग्री (0) होती है/The zero polynomial degree is not defined and a non-zero constant has degree (0)
Step 1
Concept
The degree of the zero polynomial is not defined. The degree of a non-zero constant polynomial is (0).
Step 2
Why this answer is correct
The correct answer is C. शून्य बहुपद की डिग्री परिभाषित नहीं होती और अशून्य नियतांक की डिग्री (0) होती है / The zero polynomial degree is not defined and a non-zero constant has degree (0). The degree of the zero polynomial is not defined. The degree of a non-zero constant polynomial is (0).
Step 3
Exam Tip
शून्य बहुपद की डिग्री परिभाषित नहीं होती। अशून्य नियतांक बहुपद की डिग्री (0) होती है।
B. नहीं, क्योंकि \(\frac{5}{x}\) में चर हर में है/No, because in \(\frac{5}{x}\) the variable is in the denominator
Step 1
Concept
In \(\frac{5}{x}\), the power of (x) is (-1). Therefore this expression is not a polynomial.
Step 2
Why this answer is correct
The correct answer is B. नहीं, क्योंकि \(\frac{5}{x}\) में चर हर में है / No, because in \(\frac{5}{x}\) the variable is in the denominator. In \(\frac{5}{x}\), the power of (x) is (-1). Therefore this expression is not a polynomial.
Step 3
Exam Tip
\(\frac{5}{x}\) में (x) की घात (-1) है। इसलिए यह व्यंजक बहुपद नहीं है।
C. क्योंकि इसमें \(x^{-1}\) है/Because it has \(x^{-1}\)
Step 1
Concept
In \(x^{-1}\), the power of the variable is negative. Such a power cannot occur in a polynomial.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि इसमें \(x^{-1}\) है / Because it has \(x^{-1}\). In \(x^{-1}\), the power of the variable is negative. Such a power cannot occur in a polynomial.
Step 3
Exam Tip
\(x^{-1}\) में चर की घात ऋणात्मक है। बहुपद में ऐसी घात नहीं हो सकती।
A. हां, क्योंकि सभी घातें अऋणात्मक पूर्णांक हैं/Yes, because all powers are non-negative integers
Step 1
Concept
The powers are (4), (2), (1), and (0). All are valid according to the definition of a polynomial.
Step 2
Why this answer is correct
The correct answer is A. हां, क्योंकि सभी घातें अऋणात्मक पूर्णांक हैं / Yes, because all powers are non-negative integers. The powers are (4), (2), (1), and (0). All are valid according to the definition of a polynomial.
Step 3
Exam Tip
घातें (4), (2), (1), और (0) हैं। ये सभी बहुपद की परिभाषा के अनुसार मान्य हैं।
A. हां, क्योंकि दशमलव गुणांक वास्तविक संख्या है/Yes, because a decimal coefficient is a real number
Step 1
Concept
A decimal coefficient is a real number and the powers of (x) are (2), (1), and (0). Therefore it is a polynomial.
Step 2
Why this answer is correct
The correct answer is A. हां, क्योंकि दशमलव गुणांक वास्तविक संख्या है / Yes, because a decimal coefficient is a real number. A decimal coefficient is a real number and the powers of (x) are (2), (1), and (0). Therefore it is a polynomial.
Step 3
Exam Tip
दशमलव गुणांक वास्तविक संख्या होता है और (x) की घातें (2), (1), और (0) हैं। इसलिए यह बहुपद है।
B. क्योंकि \(\frac{1}{x}=x^{-1}\) है/Because \(\frac{1}{x}=x^{-1}\)
Step 1
Concept
In \(\frac{1}{x}\), the power of (x) is (-1). Negative powers are not valid in a polynomial.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि \(\frac{1}{x}=x^{-1}\) है / Because \(\frac{1}{x}=x^{-1}\). In \(\frac{1}{x}\), the power of (x) is (-1). Negative powers are not valid in a polynomial.
Step 3
Exam Tip
\(\frac{1}{x}\) में (x) की घात (-1) है। बहुपद में ऋणात्मक घात मान्य नहीं होती।
D. क्योंकि \(\sqrt[3]{x}=x^{\frac{1}{3}}\) है/Because \(\sqrt[3]{x}=x^{\frac{1}{3}}\)
Step 1
Concept
The power of \(\sqrt[3]{x}\) is \(\frac{1}{3}\). Fractional powers are not valid in a polynomial.
Step 2
Why this answer is correct
The correct answer is D. क्योंकि \(\sqrt[3]{x}=x^{\frac{1}{3}}\) है / Because \(\sqrt[3]{x}=x^{\frac{1}{3}}\). The power of \(\sqrt[3]{x}\) is \(\frac{1}{3}\). Fractional powers are not valid in a polynomial.
Step 3
Exam Tip
\(\sqrt[3]{x}\) में चर की घात \(\frac{1}{3}\) है। भिन्न घात बहुपद में मान्य नहीं होती।
C. यह बहुपद है क्योंकि गुणांक वास्तविक हैं और घातें मान्य हैं/It is a polynomial because coefficients are real and powers are valid
Step 1
Concept
\(\pi\) and \(\sqrt{2}\) are real coefficients. The powers of (x) are (2), (1), and (0).
Step 2
Why this answer is correct
The correct answer is C. यह बहुपद है क्योंकि गुणांक वास्तविक हैं और घातें मान्य हैं / It is a polynomial because coefficients are real and powers are valid. \(\pi\) and \(\sqrt{2}\) are real coefficients. The powers of (x) are (2), (1), and (0).
Step 3
Exam Tip
\(\pi\) और \(\sqrt{2}\) वास्तविक गुणांक हैं। (x) की घातें (2), (1), और (0) हैं।
D. क्योंकि \(\frac{1}{x^2}=x^{-2}\) है/Because \(\frac{1}{x^2}=x^{-2}\)
Step 1
Concept
In \(\frac{1}{x^2}\), the variable has power (-2). A polynomial cannot have a negative power.
Step 2
Why this answer is correct
The correct answer is D. क्योंकि \(\frac{1}{x^2}=x^{-2}\) है / Because \(\frac{1}{x^2}=x^{-2}\). In \(\frac{1}{x^2}\), the variable has power (-2). A polynomial cannot have a negative power.
Step 3
Exam Tip
\(\frac{1}{x^2}\) में चर की घात (-2) है। बहुपद में ऋणात्मक घात नहीं होती।
C. नहीं, क्योंकि \(x^{-2}\) की घात ऋणात्मक है/No, because \(x^{-2}\) has a negative power
Step 1
Concept
In \(x^{-2}\), the variable has a negative power. One invalid power makes the expression not a polynomial.
Step 2
Why this answer is correct
The correct answer is C. नहीं, क्योंकि \(x^{-2}\) की घात ऋणात्मक है / No, because \(x^{-2}\) has a negative power. In \(x^{-2}\), the variable has a negative power. One invalid power makes the expression not a polynomial.
Step 3
Exam Tip
\(x^{-2}\) में चर की घात ऋणात्मक है। एक अमान्य घात के कारण व्यंजक बहुपद नहीं होता।
B. हां, क्योंकि चर की घातें (2), (1), और (0) हैं/Yes, because the variable powers are (2), (1), and (0)
Step 1
Concept
Fractional coefficients are valid in a polynomial. Here all variable powers are non-negative integers.
Step 2
Why this answer is correct
The correct answer is B. हां, क्योंकि चर की घातें (2), (1), और (0) हैं / Yes, because the variable powers are (2), (1), and (0). Fractional coefficients are valid in a polynomial. Here all variable powers are non-negative integers.
Step 3
Exam Tip
भिन्न गुणांक बहुपद में मान्य होते हैं। यहां सभी चर घातें अऋणात्मक पूर्णांक हैं।
B. क्योंकि \(\sqrt{x}=x^{\frac{1}{2}}\) है/Because \(\sqrt{x}=x^{\frac{1}{2}}\)
Step 1
Concept
In \(\sqrt{x}\), the power of the variable is \(\frac{1}{2}\). In a polynomial, the variable power must be a non-negative integer.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि \(\sqrt{x}=x^{\frac{1}{2}}\) है / Because \(\sqrt{x}=x^{\frac{1}{2}}\). In \(\sqrt{x}\), the power of the variable is \(\frac{1}{2}\). In a polynomial, the variable power must be a non-negative integer.
Step 3
Exam Tip
\(\sqrt{x}\) में चर की घात \(\frac{1}{2}\) है। बहुपद में चर की घात अऋणात्मक पूर्णांक होनी चाहिए।
A. हां, क्योंकि \(\sqrt{11}\) वास्तविक गुणांक है/Yes, because \(\sqrt{11}\) is a real coefficient
Step 1
Concept
\(\sqrt{11}\) is only a coefficient and the powers of (x) are (3), (1), and (0). Therefore it is a polynomial.
Step 2
Why this answer is correct
The correct answer is A. हां, क्योंकि \(\sqrt{11}\) वास्तविक गुणांक है / Yes, because \(\sqrt{11}\) is a real coefficient. \(\sqrt{11}\) is only a coefficient and the powers of (x) are (3), (1), and (0). Therefore it is a polynomial.
Step 3
Exam Tip
\(\sqrt{11}\) केवल गुणांक है और (x) की घातें (3), (1), और (0) हैं। इसलिए यह बहुपद है।
\(\frac{2}{3}\) is a fractional power. In a polynomial, the variable power must be a non-negative integer.
Step 2
Why this answer is correct
The correct answer is B. \(x^{\frac{2}{3}}+5\). \(\frac{2}{3}\) is a fractional power. In a polynomial, the variable power must be a non-negative integer.
Step 3
Exam Tip
\(\frac{2}{3}\) भिन्न घात है। बहुपद में चर की घात अऋणात्मक पूर्णांक होनी चाहिए।
C. क्योंकि \(\frac{3}{x^4}=3x^{-4}\) है/Because \(\frac{3}{x^4}=3x^{-4}\)
Step 1
Concept
In \(\frac{3}{x^4}\), the variable has power (-4). Negative powers are not valid in a polynomial.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि \(\frac{3}{x^4}=3x^{-4}\) है / Because \(\frac{3}{x^4}=3x^{-4}\). In \(\frac{3}{x^4}\), the variable has power (-4). Negative powers are not valid in a polynomial.
Step 3
Exam Tip
\(\frac{3}{x^4}\) में चर की घात (-4) है। बहुपद में ऋणात्मक घात मान्य नहीं होती।
