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SubjectsMathematics
सामान्य अध्याय अभ्यास
This Class 9 Mathematics topic provides focused practice for reviewing common chapter questions and strengthening problem-solving skills. Students work through familiar question types, learn to identify the relevant mathematical concept, choose an appropriate method, and present solutions in clear, logical steps. The practice also supports checking calculations, understanding errors, and revising key ideas from different chapters. It is useful for building confidence before classroom assessments, homework, and independent revision.
TOPIC PRACTICE
Up to 25 questions from this page. Select your focus, then start.
The number multiplying a variable is called its coefficient. In 5m, the variable m is multiplied by 5, so the coefficient of m is 5. Option C (1) is incorrect because 1 would be the coefficient if the term were simply m. Exam tip: Identify the number directly multiplying the variable.
3p and 2p are like terms because both contain the variable p to the first power. Add their coefficients: 3p + 2p = (3 + 2)p = 5p. Therefore, option C is correct. Exam tip: when adding or subtracting like terms, operate only on their coefficients; p² is obtained from p × p, not from adding terms.
A monomial is a polynomial containing exactly one term. In \(3x^2\), there is no plus or minus sign separating terms, so it has only one term and is a monomial. \(x+2\) and \(x^2+x\) have two terms each, while \(x^2+x+1\) has three terms; therefore, none of them is a monomial. Exam tip: count the terms separated by plus or minus signs.
Terms in an algebraic expression are generally separated by \(+\) or \(-\) signs. The expression \((4x+9)\) has two terms: \(4x\) and \(9\). Therefore, the correct answer is 2. Choosing 3 is incorrect because the \(+\) sign itself is not a term. Exam tip: Count the parts separated by \(+\) or \(-\) signs, including the first term.
The polynomial \(x^2+3x+2\) contains three distinct terms: \(x^2\), \(3x\), and \(2\). A polynomial with three terms is called a trinomial, so option D is correct. A binomial has exactly two terms, so it is not the correct classification here. Exam tip: count the terms after combining any like terms.
6x and 2x are like terms because both contain x to the first power. Therefore, subtract their coefficients: 6 − 2 = 4. Hence, 6x − 2x = 4x. The option 4x² is incorrect because adding or subtracting like terms does not change the variable’s exponent. Exam tip: identify like terms first, and then operate only on their coefficients.
Like terms must have the same variables raised to the same powers. The variable in \(2a\) is \(a\), whereas the variable in \(3b\) is \(b\); therefore, they are unlike terms. A difference in coefficients alone does not make terms unlike—for example, \(2a\) and \(5a\) are like terms. In an exam, first compare the variables and their powers.
Substituting \(a=2\) gives \(a^2+1=2^2+1=4+1=5\), so option A is correct. Option B is only the value of \(a^2\) and omits the additional 1. In such questions, evaluate the exponent first and then perform addition or subtraction.
Subtract 4 from both sides to isolate \(x\): \(x+4-4=9-4\). Therefore, \(x=5\), so option B is correct. Option C, 9, is the right-hand side of the equation, not the value of \(x\). Exam tip: verify the answer by substituting it back into the original equation: \(5+4=9\).
By the distributive law, 3 must be multiplied by both terms inside the brackets: \(3(x+2)=3\times x+3 imes2=3x+6\). Therefore, option D is correct. Option A is incorrect because it does not multiply 3 by 2. Exam tip: distribute the outside coefficient to every term inside the brackets.
The term \(a\) is added three times, so repeated addition becomes multiplication by the number of terms: \(a+a+a=3a\). The option \(a^3\) represents multiplying \(a\) by itself three times, not adding it. In such questions, count the identical terms to find the coefficient.
A variable is a letter or symbol whose value can change. In \(9q\), \(q\) is the variable, while \(9\) is its coefficient and \(9q\) is the complete algebraic term. \(0\) is a constant number. In an exam, identify the letter as the variable and the number multiplying it as the coefficient.
In \(x^3\), the number 3 written above \(x\) is its exponent. It means \(x^3=x\times x\times x\), so the correct answer is 3. The nearby distractor 2 would be the exponent in \(x^2\), not in \(x^3\). Exam tip: identify the small raised number attached to the variable as the exponent.
\(2x\) and \(3x\) are like terms, so their coefficients can be added: \(2x+3x=(2+3)x=5x\). The constant term \(4\) remains separate, giving \(5x+4\). Option D incorrectly combines unlike terms. In an exam, first identify like terms and then add their coefficients.
The area of a rectangle is calculated as length × width. Thus, area = 8 × 5 = 40 cm². Option B, 26 cm², is the perimeter found by 2(8 + 5), not the area. In exams, distinguish carefully between area and perimeter formulas.
Here, \(10r\) and \(3r\) are like terms because both contain the variable \(r\) to the same power. Subtract their coefficients: \(10-3=7\), so \(10r-3r=7r\). Option A incorrectly adds the coefficients, while option C changes the power of \(r\) to \(2\). Exam tip: when combining like terms, add or subtract only their coefficients and keep the variable part unchanged.
A binomial is a polynomial with exactly two unlike terms. In \(p-6\), the two terms are \(p\) and \(-6\), so it is a binomial. \(5z\) and \(8\) are monomials, while \(x^2+x+1\) is a trinomial. Exam tip: count the terms separated by plus or minus signs to identify the type of polynomial.
Using the distributive law, multiply \(5\) by each term inside the bracket: \(5(x-1)=5\times x-5 imes1=5x-5\). Therefore, option B is correct. In option A, \(-1\) has not been multiplied by \(5\). Exam tip: When removing brackets, multiply the outside factor by every term inside.
Like terms must have the same variable raised to the same power; only their coefficients may differ. In \(m^2\), the power of \(m\) is 2, whereas in \(m\) it is 1. Therefore, they are unlike terms. The presence of the same variable alone does not make terms like terms. Exam tip: always compare both the variable and its exponent.
To isolate \(p\) in \(2p=12\), divide both sides by 2: \(p=12\div2=6\). Therefore, the correct answer is 6. Do not multiply 12 by 2; division is required because \(p\) is multiplied by 2. Exam tip: use the inverse operation to undo multiplication.
In \(x^2+5x\), the term containing \(x\) is \(5x\). Therefore, the coefficient of \(x\) is 5, so option D is correct. The term \(x^2\) is separate and is not the term being asked about. Exam tip: the coefficient is the number multiplied by the variable.
Every point on the y-axis has x-coordinate 0. In \(P(0,-6)\), x = 0, so the statement is correct. Points with y = 0 lie on the x-axis. Exam tip: check the x-coordinate first.
The discount is \(\frac{15}{100}\times800=120\) rupees. Hence, selling price \(=800-120=680\) rupees. ₹720 would result after a 10% discount. Exam tip: calculate the discount amount first.
The number \(3\) is common to both terms, \(3x\) and \(6\). Factoring gives \(3x+6=3(x+2)\), so the greatest common factor is \(3\). Option 6 is incorrect because 6 is not a factor of \(3x\) in general. Exam tip: Find the HCF of the numerical coefficients and include only the variables common to every term.
\(\sqrt{49}=7\), and 7 is an integer and hence a rational number. Therefore, a square root sign does not always give an irrational number. \(2,3,5\) are not perfect squares. Exam tip: first check whether the number inside the root is a perfect square.
QUIZ COMPLETE
