Algebra One Mark Online Test (10th Standard Mathematics)

A system of three linear equations in three variables is inconsistent if their planes

The solution of the system \(x + y - 3z = -6\), \(-y + z = 1\), \(3z = 9\) is

If \((x - 6)\) is the HCF of \(x^2 - 2x - 24\) and \(x^2 - kx - 6\), then the value of \(k\) is

\(\frac{3y - 3}{y} \div \frac{7y - 7}{3y^2}\) is

\(y^2 + \frac{1}{y^2}\) is not equal to

\(\frac{x}{x^2 - 25} - \frac{8}{x^2 + 6x + 5}\) gives

The square root of \(\frac{256x^8 y^4 z^{10}}{25x^6 y^6 z^6}\) is equal to

Which of the following should be added to make \(x^4 + 64\) a perfect square?

The solution of \((2x - 1)^2 = 9\) is equal to

The values of \(a\) and \(b\) if \(4x^4 - 24x^3 + 76x^2 + ax + b\) is a perfect square are

If the roots of the equation \(q^2 x^2 + p^2 x + r^2 = 0\) are the squares of the roots of the equation \(qx^2 + px + r = 0\), then \(q, p, r\) are in

Graph of a linear equation is a

The number of points of intersection of the quadratic polynomial \(x^2 + 4x + 4\) with the \(X\)-axis is

For the given matrix \(A = \begin{pmatrix} 1 & 3 & 5 & 7 \\ 2 & 4 & 6 & 8 \\ 9 & 11 & 13 & 15 \end{pmatrix}\) the order of the matrix \(A^T\) is

If \(A\) is a \(2 \times 3\) matrix and \(B\) is a \(3 \times 4\) matrix, how many columns does \(AB\) have

If a number of columns and rows are not equal in a matrix then it is said to be a

Transpose of a column matrix is

Find the matrix \(X\) if \(2X + \begin{bmatrix} 1 & 3 \\ 5 & 7 \end{bmatrix} = \begin{bmatrix} 5 & 7 \\ 9 & 5 \end{bmatrix}\)

Which of the following can be calculated from the given matrices \(A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{bmatrix}\) and \(B = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}\)?\n(i) \(A^2\)\n(ii) \(B^2\)\n(iii) \(AB\)\n(iv) \(BA\)

If \(A = \begin{bmatrix} 1 & 2 & 3 \\ 3 & 2 & 1 \end{bmatrix}\), \(B = \begin{bmatrix} 1 & 0 \\ 2 & -1 \\ 0 & 2 \end{bmatrix}\) and \(C = \begin{bmatrix} 0 & 1 \\ -2 & 5 \end{bmatrix}\), which of the following statements are correct?\n(i) \(AB + C = \begin{bmatrix} 5 & 5 \\ 5 & 5 \end{bmatrix}\)\n(ii) \(BC = \begin{bmatrix} 0 & 1 \\ 2 & -3 \\ -4 & 10 \end{bmatrix}\)\n(iii) \(BA + C = \begin{bmatrix} 2 & 5 \\ 3 & 0 \end{bmatrix}\)\n(iv) \((AB)C = \begin{bmatrix} -8 & 20 \\ -8 & 13 \end{bmatrix}\)

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?

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

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

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

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?

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

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

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

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

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

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 \(AB\)?

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

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

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?