Algebra Additional One Mark Online Test

Algebra Additional One Mark Online Test (10th Standard Mathematics)

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In a system of three linear equations in three variables, if the elimination process results in a false statement like \(0 = 5\), what does this indicate about the nature of the solutions?

A.Unique solution B.Infinitely many solutions C.No solution D.Two distinct solutions

What is the Greatest Common Divisor (GCD) of the polynomials \(12x^2 y^3 z\) and \(18x^3 y^2\)?

A.\(6x^2 y^2\) B.\(6x^3 y^3 z\) C.\(36x^3 y^3 z\) D.\(3x^2 y^2\)

What is the Least Common Multiple (LCM) of the algebraic expressions \((x - 1)^2\) and \(x^2 - 1\)?

A.\((x - 1)(x + 1)\) B.\((x - 1)^2(x + 1)\) C.\((x - 1)(x + 1)^2\) D.\((x - 1)^2(x + 1)^2\)

What are the excluded values of the rational expression \(\frac{x + 3}{x^2 - 16}\)?

A.\(-3\) and \(3\) B.\(-4\) and \(4\) C.\(-3\) and \(4\) D.\(-4\) and \(3\)

If the rational expression \(\frac{2x + 1}{x^2 + kx + 9}\) has no real excluded values, what is the range of values that the constant \(k\) can take?

A.\(-6 < k < 6\) B.\(k > 6\) or \(k < -6\) C.\(-3 < k < 3\) D.\(k = \pm 6\)

What is the square root of the algebraic expression \(16x^4 - 24x^2 + 9\)?

A.\(|4x^2 - 3|\) B.\(|4x^2 + 3|\) C.\(|2x^2 - 3|\) D.\(|4x - 3|\)

If the discriminant of a quadratic equation \(ax^2 + bx + c = 0\) is equal to zero, what is the nature of its roots?

A.Real and unequal B.Real and equal C.No real roots D.Imaginary and unequal

Find the quadratic equation whose sum of the roots is \(-5\) and the product of the roots is \(6\).

A.\(x^2 - 5x + 6 = 0\) B.\(x^2 + 5x + 6 = 0\) C.\(x^2 - 5x - 6 = 0\) D.\(x^2 + 5x - 6 = 0\)

If \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(3x^2 - 5x - 2 = 0\), what is the value of \(\alpha^2 + \beta^2\)?

A.\(\frac{13}{9}\) B.\(\frac{37}{9}\) C.\(\frac{19}{9}\) D.\(\frac{25}{9}\)

Q10

If the variables \(x\) and \(y\) vary inversely such that \(xy = k\), where \(k\) is a positive constant, how does \(y\) change when \(x\) is doubled?

A.\(y\) is doubled B.\(y\) is halved C.\(y\) remains unchanged D.\(y\) is quadrupled

Q11

A square matrix in which all the entries above and below the leading main diagonal are zero is called a:

A.Scalar matrix B.Unit matrix C.Diagonal matrix D.Row matrix

Q12

If matrix \(A\) is of order \(3 \times 4\) and matrix \(B\) is of order \(4 \times 2\), what is the order of the product matrix \(AB\)?

A.\(3 \times 2\) B.\(4 \times 4\) C.\(2 \times 3\) D.\(4 \times 2\)

Q13

If \(A\) is a matrix of order \(m \times n\), what is the order of its transpose matrix \(A^T\)?

A.\(m \times n\) B.\(n \times m\) C.\(m \times m\) D.\(n \times n\)

Q14

If \(A\) and \(B\) are two matrices of the same order, which of the following matrix properties is always true?

A.\(AB = BA\) B.\(A + B = B + A\) C.\(A - B = B - A\) D.\((A + B)^T = A^T - B^T\)

Q15

If one root of the quadratic equation \(x^2 + px + q = 0\) is the square of the other, which of the following relations is correct?

A.\(p^3 - q(3p - 1) + q^2 = 0\) B.\(p^3 + q(3p - 1) + q^2 = 0\) C.\(p^3 - q(3p + 1) + q^2 = 0\) D.\(p^3 + q(3p + 1) + q^2 = 0\)

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About this Algebra test

This free online practice test covers Algebra from the 10th Standard Mathematics (Samacheer Kalvi) syllabus. Choose the number of questions and an optional time limit, then answer and submit — everything is checked in your browser, with the correct answers and a worked explanation shown at the end. For the full solutions to every question in this set, see the solved MCQs page.

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