# Recent questions tagged q5-1

### Using Euler's theorem prove the following: if$\;u=\tan^{-1}\large[\frac{x^{3}+y^{3}}{x-y}]$ prove that $x\large\frac{\partial u}{\partial x}$+$y\large\frac{\partial u}{\partial y}=$$\sin 2u ### The radius of a circular disc is given as 24cm with a maximum error in mesurement of 0.02cm Use differentials to estimate the maximum error in the calculated area of the dise. ### The mean weight of 500 male students in a certain college in 151 pounds and the standard deviation is 15 pounds. Assuming the weights are normally distributed, find how many students weigh between 120 and 155 pounds ### The number of accidents in a year involving taxi drivers in a city follows a poisson distribution with mean equal to 3. Out of 1000 taxi drivers find approximately the number of driver with no accident in a year .[e^{-3} = 0.0498]. ### Verify that the following are probability density functions.f(x) = \left\{ \begin{array}{l l} \frac { 2x}{9} & \quad \text{0 \leq x\leq3}\\ 0 & \quad \text{elsewhere} \end{array} \right. ### Find the eccentricity, centre , foci , and vertices of the following hyperbolas and draw their diagrams: 25x^{2}-16y^{2}=400 ### Find the equations of directrices, latus rectum and lengths of latus rectums of the following ellipses: 25x^{2}+169y^{2}=4225. ### Find the centre and radius of the following spheres : | \overrightarrow{r}-(\overrightarrow(2i)-\overrightarrow(j)+\overrightarrow{4k})|=5 ### IfA=\begin{bmatrix} 5 & 2 \\7 & 3 \end{bmatrix} andB=\begin{bmatrix} 2 & -1 \\-1 & 1 \end{bmatrix} verify that $(AB)^{-1}=B^{-1}A^{-1}$ ### State with reason whether following functions have inverses: (i) $f: \{ 1,2,3,4,\} \to \{10\}$ with $f= \{(1,10),(2,10),(3,10), (4,10)\}$ ### Construct a 3 x 4 matrix,whose elements are given by:(i)\;a_{ij}=\frac{1}{2}| -3i+j\;| \qquad ### Find the value of x if : (i) \begin{bmatrix} 2 & 4 \\ 5 & 1 \end{bmatrix} = \begin{bmatrix} 2x & 4 \\ 6 & x \end{bmatrix} ### Answer the following as true or false. \\(i)\; \overrightarrow a and -\overrightarrow a are collinear. ### Evaluate the determinant: \begin{vmatrix} 3&-1&-2 \\ 0&0&-1 \\3&-5&0 \end{vmatrix} ### Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals: \: f (x) = x^3, x \in [– 2, 2] ### For the matrices A and B, verify that (AB)' = B'A' , where$$ \text{ (i) } A = \begin{bmatrix} 1 \\ -4 \\ 3 \end{bmatrix} \text{ , } B = \begin{bmatrix} -1 & 2 & 1 \end{bmatrix} \qquad$\$

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