# Recent questions tagged q5-2

### Find the eccentricity, centre , foci , and vertices of the following hyperbolas and draw their diagrams: $\large\frac{y^{2}}{9}-\frac{x^{2}}{25}=$$1 ### Find the equations of directrices, latus rectum and lengths of latus rectums of the following ellipses: 9x^{2}+16y^{2}=144 ### Find the centre and radius of the following spheres : |\overrightarrow{2r}+(\overrightarrow{3i}-\overrightarrow{j}+\overrightarrow{4k})|=4 ### Find the value of x if : \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} = \begin{bmatrix} x & 3 \\ 2x & 5 \end{bmatrix} ### IfA=\begin{bmatrix} 5 & 2 \\7 & 3 \end{bmatrix}andB=\begin{bmatrix} 2 & -1 \\-1 & 1 \end{bmatrix} verify that$(AB)^{T}=B^{T}A^{T}$ ### State with reason whether following functions have inverse: (ii) $g: \{ 5,6,7,8\} \to \{1,2,3,4\}$ with $g= \{(5,4),(6,3),(7,4),(8,2)\}$ ### Evaluate the determinants: \begin{vmatrix} 3&-4&5 \\ 1&1&-2 \\2&3&1 \end{vmatrix} ### For the matrices A and B, verify that (AB)' = B'A' , where$$ \text{ (ii) } A = \begin{bmatrix} 0 \\ 1 \\ 2 \end{bmatrix} \text{ , } B = \begin{bmatrix} 1 & 5 & 7 \end{bmatrix}$$### Construct a 3 x 4 matrix,whose elements are given by:$\;a_{ij}=2i-j\$

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