For the system of linear equations x + y + z = 5000 6x + 7y + 8z = 35800 6x + 7y - 8z = 7000 the values of x, y and z are:

If f(x) = 2x + 3, then f⁻¹(x) is:

If the roots of the equation x² - 5x + k = 0 are in the ratio 2:3, then the value of k is:

If $A = [a_{ij}]$ be square matrix of order 3, such that $a_{ij} = i + j$, $\forall i, j$ then which of the following are correct? (A) A is a skew-symmetric matrix. (B) A is a non-singular matrix. (C) The inverse of A does not exist. (D) A is a symmetric matrix. Choose the correct answer from the options given below:

A function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x) = \frac{x}{x^2+1}$ is (where $\mathbb{R}$ is a set of real number)

Assume $P$, $Q$, $R$ and $W$ are matrices of order $3 \times 3$, $a \times 4$, $b \times c$ and $d \times a$ respectively. If $PQ + WR$ is well defined, then the value of $ab + cd$ is: