Recent questions tagged easy

Find the approximate change in the surface area of a cube of side $x$ metres caused by decreasing the side by $1\%$.

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Find the approximate change in the volume V of a cube of side $x$ metres caused by increasing the side by $1\%$.

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Using differentials, find the approximate value of each of the following up to $3$ places of decimal. $(i)\;\sqrt{25.3}$

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the line $y = x + 1$ is a tangent to the curve $y^2 = 4x$ at the point

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the slope of the normal to the curve $ y = 2x^2 + 3 \sin\: x$ at $x = 0$ is

asked Nov 26, 2012 by thanvigandhi_1

1 answer

If $ x\begin{bmatrix} 2 \\ 3 \end{bmatrix} + y\begin{bmatrix} -1 \\ 1 \end{bmatrix} = \begin{bmatrix} 10 \\ 5 \end{bmatrix} $, find the values of $x$ and $y$.

asked Nov 25, 2012 by pady_1

1 answer

Given $3\begin{bmatrix} x & y \\ z & w \end{bmatrix}$ = $\begin{bmatrix} x & 6 \\ -1 & 2w \end{bmatrix}$ + $\begin{bmatrix} 4 & x + y \\ z + w & 3 \end{bmatrix}$, find the values of $x, y, z$ and $w$.

asked Nov 25, 2012 by pady_1

1 answer

if $ F( x ) = \begin{bmatrix} cos\;x & -sin\;x & 0 \\ sin\;x & cos\;x & 0 \\ 0 & 0 & 1 \end{bmatrix}, $ show that $ F( x )\; F( y ) = F( x + y ). $

asked Nov 25, 2012 by pady_1

1 answer

Find $ A^2 -5A + 6I $ , if $ A = \begin{bmatrix} 2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0 \end{bmatrix} $

asked Nov 25, 2012 by pady_1

1 answer

If $ A = \begin{bmatrix} 3 & -2 \\ 4 & -2 \end{bmatrix} $ and $ I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} $ find $k$ so that $A^2 = kA - 2I$

asked Nov 25, 2012 by pady_1

1 answer

A trust fund has Rs 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of: $$ \text{(a) Rs 1800} \qquad \qquad \text{(b) Rs 2000} $$

asked Nov 25, 2012 by pady_1

1 answer

if $ A = \begin{bmatrix} -1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1 \end{bmatrix} \text{ and } B = \begin{bmatrix} -4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1 \end{bmatrix} \text{, then verify that } $ $$ \text{ (i) } (A+B)' = A' + B' $$

asked Nov 25, 2012 by pady_1

1 answer

If $ A' = \begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{bmatrix} \text{ and } B = \begin{bmatrix} -1 & 2 &1 \\ 1 & 2 & 3 \end{bmatrix} \text{ , then verify that } $$ \text{ (i) } (A + B )' = A' + B' \qquad \qquad $

asked Nov 25, 2012 by pady_1

1 answer

If $A' = \begin{bmatrix} -2 & 3 \\ 1 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} -1 & 0 \\ 1 & 2 \end{bmatrix}$, then find $(A + 2B)'$

asked Nov 25, 2012 by pady_1

1 answer

For the matrices $A$ and $B$, verify that $(AB)' = B'A'$ , where $$ \text{ (i) } A = \begin{bmatrix} 1 \\ -4 \\ 3 \end{bmatrix} \text{ , } B = \begin{bmatrix} -1 & 2 & 1 \end{bmatrix} \qquad $$

asked Nov 25, 2012 by pady_1

1 answer

$ (i) A = \begin{bmatrix} cos\alpha & sin\alpha \\ -sin\alpha & cos\alpha \end{bmatrix}$ then verify that $A'A = I$

asked Nov 25, 2012 by pady_1

1 answer

For the matrix $ A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix} $ , verify that $ (i) (A+A') $ is a symmetric matrix.

asked Nov 25, 2012 by pady_1

1 answer

Find the equation of the normal at the point $(am^2,am^3)$ for the curve $ay^2 = x^3.$

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find the points on the curve $x^2 + y^2 - 2x - 3 = 0$ at which the tangents are parallel to the $x$ - axis.

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Show that the tangents to the curve $y = 7x^3 + 11$ at the points where $x = 2$ and $x = -2$ are parallel.

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find the equation of the tangent line to the curve $y = x^2 - 2x +7$ which is $(a)$ parallel to the line $2x - y + 9 = 0$

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find the equations of the tangent and normal to the given curves at the indicated points: $ y = x^4 - 6x^3 + 13x^2 - 10x + 5\; at \;(0, 5)$

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find points on the curve $ \large\frac{x^2}{9} + \frac{y^2}{16} = 1$ at which the tangents are $(i)\; parallel\; to\; x - axis$

asked Nov 24, 2012 by thanvigandhi_1

1 answer

If $A, B$ are symmetric matrices of the same order, then $AB - BA$ is

asked Nov 23, 2012 by pady_1

1 answer

if $A = \begin{bmatrix} cos\alpha & -sin\alpha \\ sin\alpha & cos\alpha \end{bmatrix} $ then $ A + A' = I, $ if the value of $\alpha$ is

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 6 & -3 \\ -2 & 1 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & -6 \\ 1 & -2 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 3 & -1 \\ -4 & 2 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 4 & 5 \\ 3 & 4 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 3 & 1 \\ 5 & 2 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 3 \\ 5 & 7 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 1 \\ 1 & 1 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer