If f(x) = 2x + 3, then f⁻¹(x) is:

A relation R in the set A = {1, 2,3, 4} is given by R = {(1,1), (2,2), (1,2), (2,3), (3,4), (4,4), (1,3), (2,4), (1,4)} is

If $P(A) = \frac{3}{5}$, $P(B) = \frac{1}{2}$ and $P(A \cap B) = \frac{1}{4}$, then $P(\overline{A} | \overline{B})$ is

The maximum value of a LPP $z = 3x + 4y$ subject to the constraints: $x + y \leq 6$, $x \geq 0$, $y \geq 0$ is:

Match List-I with List-II | List-I | List-II | |---|---| | (A) The number of possible matrices of order 3x3 with each entry 1 or 0 | (I) $2^4$ | | (B) The number of possible matrices of order 2x3 with each entry 1 or 0 | (II) $2^9$ | | (C) The number of possible matrices of order 2x3 with each entry 0,1,2 | (III) $2^6$ | | (D) The number of possible matrices of order 2x2 with each entry 1 or 0 | (IV) $3^6$ | Choose the correct answer from the options given below:

If $A$ and $B$ are invertible matrices of order $3$ then match List-I with List-II | List-I | List-II | | --- | --- | | (A) $\text{adj}(A)$ | (I) $B^{-1} A^{-1}$ | | (B) $(AB)^{-1}$ | (II) $\vert A\vert ^{-1}$ | | (C) $\vert A^{-1}\vert $ | (III) $\vert A\vert ^2$ | | (D) $\vert \text{adj} A\vert $ | (IV) $\vert A\vert A^{-1}$ | Choose the correct answer from the options given below: