Email

Chat with tutors

Login

Ask Questions, Get Answers

Menu X

home ask tuition questions practice papers mobile tutors pricing

X

Recent questions tagged ch3

If $x +\large\frac{1}{x} = $$2\; cos\;\theta $ prove that $x^{n} -\large \frac{1}{x^{n}}= $$2i\; sin\;n\theta $

asked Apr 18, 2013 by geethradh

1 answer

If $\; x+\large\frac{1}{x}= $$\;2\;\cos\;\theta \; $ prove that $\;x^{n}+\large\frac{1}{x^{n}}$$= \;2\;\cos\;n\theta\; $

asked Apr 18, 2013 by geethradh

1 answer

If $ \alpha$ and $\beta $ are the roots of $x^{2}-2x+4=0$. Prove that $\alpha ^{n}-\beta ^{n}=i2^{n+1}sin\large\frac{n\pi }{3}$ and calculate $\alpha ^{9}-\beta ^{9}$, where n $\in$ N?

asked Apr 18, 2013 by geethradh

1 answer

If $\alpha $ and $\beta$ are the roots of the equation $ x^{2}-2px+\left ( p^{2} + q^{2}\right )=0 $ and $ tan \; \theta =\large \frac{q}{y+p} $ show that $ \large\frac{\left (y+\alpha \right )^{n}-\left ( y+\beta \right )^{n}}{\alpha -\beta }$ = $ q^{n-1}\large\frac{sin \;n\theta }{sin\;^{n}\theta }$

asked Apr 18, 2013 by geethradh

1 answer

Prove that $\left ( 1+\mathit{i} \right )^{4n}$ and $\left ( 1+\mathit{i} \right )^{4n+2}$ are real and purely imaginary respectively.

asked Apr 16, 2013 by geethradh

1 answer

Prove that $\left ( 1+ \cos \; \theta + \mathit{i}\sin \; \theta \right )^{\mathit{n}} + \left ( 1+ \cos \; \theta - \mathit{i}sin \; \theta \right )^{\mathit{n}} = 2^{\mathit{n+1}} \cos ^{\mathit{n}}\left ( \large\frac{\theta}{2} \right )$$ \cos \;\large\frac{n\theta }{2}$

asked Apr 16, 2013 by geethradh

1 answer

Prove that $\left ( 1+ \mathit{i\sqrt{3}} \right )^{\mathit{n}} + \left ( 1- \mathit{i\sqrt{3}} \right )^{\mathit{n}} = 2^{n+1} \cos \; \large\frac{n\pi}{3}$

asked Apr 16, 2013 by geethradh

1 answer

Prove that $\left ( 1+\mathit{i} \right )^{\mathit{n}} + \left ( 1-\mathit{i} \right )^{\mathit{n}} = 2^{\large\frac{n+2}{2}} \cos \; \large\frac{n\pi}{4}$

asked Apr 16, 2013 by geethradh

1 answer

If $ \cos\;\alpha + \cos\;\beta + \cos\;\gamma = 0 = \sin \;\alpha + \sin \;\beta + \sin \;\gamma $, prove that $\cos^{2}\;\alpha + \cos^{2}\;\beta + \cos^{2}\;\gamma = \sin^{2} \alpha + \sin^{2}\beta + \sin^{2}\gamma = \large\frac{3}{2}$.

asked Apr 10, 2013 by geethradh

1 answer

If a matrix has 7 elements, what are the possible order it can have?

asked Apr 10, 2013 by sreemathi.v

1 answer

If $ \cos\;\alpha + \cos\;\beta + \cos\;\gamma = 0 = \sin \;\alpha + \sin \;\beta + \sin \;\gamma $, prove that $\sin 2\alpha + \sin 2\beta + \sin 2\gamma = 0$

asked Apr 8, 2013 by geethradh

1 answer

If A=$\begin{bmatrix}1 & 2& 2\\2 & 1 & 2\\2 & 2&1\end{bmatrix}$ verify that $A^2-4A-5I=0.$

asked Apr 4, 2013 by sreemathi.v

1 answer

The number of all possible matrices of order $2\times 2$ with each entry 0 & 1.\[(A)\;27 \quad(B)\;18\quad(C)\;81\quad(D)\;16\]

asked Apr 4, 2013 by sreemathi.v

1 answer

If $\cos \alpha + cos \beta + cos \gamma = 0 = sin \alpha + sin \beta + sin \gamma$, prove that $cos 3\alpha + cos 3\beta + cos 3\gamma = 3 cos\left ( \alpha +\beta + \gamma \right )$

asked Apr 4, 2013 by geethradh

1 answer

If A and B are skew symmetric matrices,then prove that ABA is skew symmetric.

asked Apr 4, 2013 by sreemathi.v

1 answer

Simplify: $\Large\frac{\left (cos \;\alpha + \mathit{i} sin \; \alpha \right )^{3}}{\left (sin \;\beta + \mathit{i} cos \;\beta \right)^{4} } \Large$

asked Apr 4, 2013 by geethradh

1 answer

If $A=\begin{bmatrix}3 & 1\\7 & 5\end{bmatrix}$ find x & y such that $A^2+xI=yA$

asked Apr 4, 2013 by sreemathi.v

1 answer

Simplify: $\Large\frac{\left ( cos2 \theta -\mathit{i}sin2 \theta \right )^{7} \left ( cos 3 \theta +\mathit{i} sin3 \theta \right )^{-5}}{\left (cos 4 \theta + \mathit{i} sin4 \theta \right )^{12} \left ( cos 5 \theta -\mathit{i}sin5 \theta \right )^{-6}}\Large$

asked Apr 4, 2013 by geethradh

1 answer

If A=$\begin{bmatrix}3 & 2\\1 & 1\end{bmatrix}$ find the values of a and b, such that $A^2+aA+bI=0.$

asked Apr 4, 2013 by sreemathi.v

1 answer

Find $A^{-1}$ if it exists by using elementary transformations where A=$\begin{bmatrix}6 & -3\\-2 & 1\end{bmatrix}$

asked Apr 4, 2013 by sreemathi.v

1 answer

Find the inverse of the following matrices if it exists using elementary operations $\begin{bmatrix}2 & -6\\1 & -2\end{bmatrix}$

asked Apr 4, 2013 by sreemathi.v

1 answer

Find the inverse of the following matrices if it exists using elementary operations $\begin{bmatrix}2 & 5\\1 & 3\end{bmatrix}$

asked Apr 4, 2013 by sreemathi.v

1 answer

Find the transpose of the matrix $\begin{bmatrix}1 & 3\\2 & 6\\5 & -3\end{bmatrix}$

asked Apr 4, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}1 & -1\\2 & 3\end{bmatrix}$ and $B=\begin{bmatrix}2 & 1\\1 & 0\end{bmatrix}$ prove that $(A+B)^2\neq A^2+2AB+B^2$

asked Apr 4, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}0 & 1\\0 &0\end{bmatrix}$ prove that for all $n\in N.(aI+bA)^n=a^nI+na^{n-1}bA.$where I is the identity matrix of order 2.

asked Apr 4, 2013 by sreemathi.v

1 answer

If A=$\begin{bmatrix}cos\theta & -sin\theta\\sin\theta & cos\theta\end{bmatrix}$.Then show that $A^n=\begin{bmatrix}cos n \theta&-sin n\theta\\sin n\theta & cos n\theta\end{bmatrix}$where n is a positive integer.

asked Apr 4, 2013 by sreemathi.v

1 answer

Find matrix X if $X+\begin{bmatrix}2 & 5\\3 & -1\end{bmatrix}=\begin{bmatrix}3 & 4\\2 & 0\end{bmatrix}$

asked Apr 4, 2013 by sreemathi.v

1 answer

If A and B are square matrices of the same order,then $(iii)\quad [k(A-B)']=\text{________}.$

asked Apr 3, 2013 by sreemathi.v

1 answer

If A and B are square matrices of the same order,then $(ii)\quad (kA)'=\text{________}.$(k is any scalar)

asked Apr 3, 2013 by sreemathi.v

1 answer

If A and B are symmetric matrices,then $(ii)\quad BA-2AB\;is\;a\;\text{_______}$

asked Apr 3, 2013 by sreemathi.v

1 answer

Solve : $6x^{4}-25x^{3}+32x^{2}+3x-10=0$ given that one of the roots is $2-i$.

asked Apr 3, 2013 by geethradh

1 answer

Solve the equation $x^{4}-4x^{3}+11x^{2}-14x+10=0$ if one root is $1+2i$.

asked Apr 3, 2013 by geethradh

1 answer

Solve the equation $x^{4}-8x^{3}+24x^{2}-32x+20$ = 0 if $3+\mathit{i}$ is a root.

asked Apr 3, 2013 by geethradh

1 answer

In the matrix $A=\begin{bmatrix} 2 & 5 & 19 & -7 \\ 35 & -2 & \frac{5}{2} & 12 \\ \sqrt 3 & 1 & -5 & 17 \end{bmatrix} $Write (iii) Write the elements $a_{13},a_{21}.a_{33},a_{24},a_{23}$ .

asked Apr 3, 2013 by sreemathi.v

1 answer

In the matrix $A=\begin{bmatrix} 2 & 5 & 19 & -7 \\ 35 & -2 & \frac{5}{2} & 12 \\ \sqrt 3 & 1 & -5 & 17 \end{bmatrix} $Write (ii) The number of elements .

asked Apr 3, 2013 by sreemathi.v

1 answer

Find the transpose of each of the following matrices : $ (iii)\begin{bmatrix} -1&5&6 \\ \sqrt 3 & 5&6\\2 &3&-1 \end{bmatrix} $.

asked Apr 3, 2013 by sreemathi.v

1 answer

Find the transpose of each of the following matrices : \( (ii)\begin{bmatrix} 1&-1 \\ 2 & 3 \end{bmatrix} \).

asked Apr 3, 2013 by sreemathi.v

1 answer

Find the value of x if : $ \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} = \begin{bmatrix} x & 3 \\ 2x & 5 \end{bmatrix} $

asked Apr 2, 2013 by sreemathi.v

1 answer

If arg $\left ( z-1 \right )$ = $\large\frac{\pi}{6}$ and arg $\left ( z+1 \right )$ = 2$\large\frac{\pi}{3}$ then prove that $\left | z \right |=1$

asked Apr 2, 2013 by geethradh

1 answer

Express the following complex numbers in polar form. $1 - \mathit{i}$

asked Apr 2, 2013 by geethradh

1 answer

Express the following complex numbers in polar form. $-1 - \mathit{i}$

asked Apr 2, 2013 by geethradh

1 answer

Express the following complex number in polar form. $-1 + \mathit{i}\sqrt{3}$

asked Apr 2, 2013 by geethradh

1 answer

Express the following complex number in polar form. $2 + 2\sqrt{3}\mathit{i}$

asked Apr 2, 2013 by geethradh

1 answer

Prove that the points representing the complex numbers $\left ( 7+5\mathit{i} \right )$, $\left ( 5+2\mathit{i} \right )$, $\left ( 4+7\mathit{i} \right )$ and $\left ( 2+4\mathit{i} \right )$ form a parallelogram. (Plot the points and use midpoint formula).

asked Apr 2, 2013 by geethradh

1 answer

If $\left ( 1+\mathit{i} \right )\left ( 1+2\mathit{i} \right )\left ( 1+3\mathit{i} \right )... \left ( 1+\mathit{ni} \right )=\mathit{x+iy}$, show that 2.5.10 ... $\left ( 1+n^{2} \right )$ = $ x^{2}+y^{2}$

asked Apr 2, 2013 by geethradh

1 answer

For what values of $\mathit{x}$ and $\mathit{y}$, the numbers $-3+\mathit{ix^{2}y}$ and $\mathit{x^{2}}+y+4\mathit{i}$ are complex conjugate of each other$?$

asked Apr 1, 2013 by geethradh

1 answer

Find the real values of $\mathit{x}$ and $\mathit{y}$ for which the following equation: $\sqrt{x^{2}+3x+8} + \left ( x+4 \right )\mathit{i} = \mathit{y}\left (2 + \mathit{i} \right )$

asked Apr 1, 2013 by geethradh

1 answer

Find the real values of $\mathit{x}$ and $\mathit{y}$ for which the following equation: $\large\frac{\left ( 1+\mathit{i} \right )\mathit{x}-2\mathit{i}}{3+\mathit{i}} + \frac{\left ( 2-3\mathit{i} \right )\mathit{y}+\mathit{i}}{3-\mathit{i}} = $$\mathit{i}$

asked Apr 1, 2013 by geethradh

1 answer

Find the real values of $\mathit{x}$ and $\mathit{y}$ for which the following equation: $\left ( 1-\mathit{i} \right )\mathit{x} + \left ( 1+\mathit{i} \right )\mathit{y} = 1-3\mathit{i}$

asked Apr 1, 2013 by geethradh

1 answer

Find the least positive integer $\mathit{n}$ such that $\left ( \large\frac{1+\mathit{i}}{1-\mathit{i}} \right )^{\mathit{n}}$$ = 1$

asked Apr 1, 2013 by geethradh

1 answer

Page:

« prev
1
...
21
22
23
24
25
26
27
...
32
next »

Feedback Terms Facebook Twitter About Us

Your payment for is successful.

...