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Algebraic Properties

Class 9 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf \(S_n\) denotes the sum of the first \(n\) natural numbers, which of the following relations is always true?Class 9Sequences and ProgressionsSum of first n natural numbersHard MathematicsLet \(p(x)=ax+b\), where \(a\) and \(b\) are real numbers and \(a\ne0\). Which statement about the zeroes of \(p(x)\) is always true?Class 9Introduction to PolynomialsLinear polynomialsHard MathematicsIf \(p(x)=ax+b\), where \(a\ne 0\), which statement about the zeroes of this linear polynomial is always true?Class 9Introduction to PolynomialsLinear polynomialsHard MathematicsIf \(p(x)\) and \(q(x)\) are non-zero polynomials, which statement about the degree of their product is always true?Class 9Introduction to PolynomialsDegree of a PolynomialExpert MathematicsIf P(x) and Q(x) are two non-zero polynomials with degrees 4 and 6 respectively, which of the following statement is always true?Class 9Introduction to PolynomialsDegree of a PolynomialExpert MathematicsLet \(a\) be a rational number and \(b\) be an irrational number. Which of the following expressions will always be irrational?Class 9Number SystemsIrrational numbersExpert MathematicsLet \(p\) be a non-zero rational number and \(x\) be an irrational number. Which of the following statements is always true?Class 9Number SystemsIrrational numbersExpert MathematicsIf \(x\) is an irrational number, which of the following expressions will always be rational?Class 9Number SystemsIrrational numbersExpert MathematicsIf \(x\) is an irrational number and \(r\) is a rational number, which of the following expressions will be irrational in every case?Class 9Number SystemsIrrational numbersExpert MathematicsLet \(x\) be a non-zero irrational number, and let \(a\) and \(b\) be rational numbers, where \(b\ne0\). Which of the following expressions is always irrational?Class 9Number SystemsIrrational numbersHard MathematicsIf \(x\) is an irrational number, which of the following expressions will always be irrational?Class 9Number SystemsIrrational numbersHard MathematicsWhile applying the zero-exponent rule \(a^0=1\), which of the following bases must be excluded?Class 9Number SystemsExponentsExpert MathematicsWhich of the following correctly represents a law of exponents for a non-zero real number \(a\) and integers \(m,n\)?Class 9Number SystemsExponentsExpert MathematicsFor a non-zero real number \(a\) and integers \(m\) and \(n\), which law of exponents is always correct?Class 9Number SystemsExponentsExpert MathematicsFor a non-zero real number \(a\) and integers \(m,n\), which of the following law of exponents is always correct?Class 9Number SystemsExponentsHard