Recent questions tagged q3

Find the angle between the asymptotes of hyperbola $4x^{2}-5y^{2}-16x+10y+31=0$

asked Apr 13, 2013 by poojasapani_1

1 answer

Find the angle between the asymptotes of hyperbola $9(x-2)^{2}-4(y+3)^{2}=36$

asked Apr 13, 2013 by poojasapani_1

1 answer

Find the angle between the asymptotes of hyperbola $24x^{2}-8y^{2}=27$

asked Apr 13, 2013 by poojasapani_1

1 answer

Find the equation of the tangent and normal to the hyperbola $4x^{2}-y^{2}=64 $ ,which are parallel to $10x-3y+9=0$

asked Apr 13, 2013 by poojasapani_1

1 answer

Find the equation of the tangent and normal to the ellipse $\large\frac{x^{2}}{20}+\frac{y^{2}}{5}$$=1,$ Which are perpendicular to $ x+y+z=0$

asked Apr 13, 2013 by poojasapani_1

1 answer

Find the equation of the tangent to the parabola $y^{2}=16x,$ perpendicular to the line $3x-y+8=0$

asked Apr 13, 2013 by poojasapani_1

1 answer

Find the equation of the tangents to the parabola $y^{2}=6x,$ parallel to $3x-2y+5=0$

asked Apr 13, 2013 by poojasapani_1

1 answer

$P$ , $Q$ and $R$ represent switches in 'on' positions and P',Q' and R' represent switches in 'off' positions.Construct a switching circuit representing the polynomial $PR+Q(Q'+R)(P+QR).$Use Boolean algebra to prove that the above circuit can be simplified to an expression in which,when $P$ and $R$ are 'on' or $Q$ and $R$ are 'on',the light is on.Construct an equivalent circuit.

asked Apr 12, 2013 by sreemathi.v

0 answers

Prove that the following equation represents a pair of straight lines.Find their point of intersection and the angle between them :$2x^2+7xy+3y^2+2(4x+7y+4)=0.$

asked Apr 12, 2013 by sreemathi.v

0 answers

Find the equation of the parabola whose focus is (-1,-2) and the equation of the directrix is given by $4x-3y+2=0$.Also find the equation of the axis.

asked Apr 12, 2013 by sreemathi.v

0 answers

Using Rolle's theorem,find a point on the curve $y=\sin x+\cos x-1,x\in \begin{bmatrix}0,\large\frac{\pi}{2}\end{bmatrix}$ where the tangent is parallel to the x-axis.

asked Apr 11, 2013 by sreemathi.v

2 answers

Find the equations of directrices ,latus rectums and length of latus rectum of the following hyperbolas:$9x^{2}-4y^{2}-36x+32y+8=0$

asked Apr 11, 2013 by poojasapani_1

1 answer

Find the equations of directrices ,latus rectums and length of latus rectum of the following hyperbolas: $4x^{2}-9y^{2}=576$

asked Apr 11, 2013 by poojasapani_1

1 answer

P,Q and R represent switches in 'ON position' and $P^1,Q^1$ and $R^1$ represent switches in 'OFF position'.Construct a switching circuit representing the polynomial : $P(P+Q)Q(Q+R^1$)

asked Apr 11, 2013 by sreemathi.v

0 answers

Prove that : $2Tan^{-1}\large\frac{1}{5}\normalsize+Cos^{-1}\large\frac{7}{5\sqrt 2}\normalsize+2Tan^{-1}\large\frac{1}{8}=\large \frac{\pi}{4}$

asked Apr 11, 2013 by sreemathi.v

0 answers

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

Find the locus of the point which moves so that the sum of its distances from $(3 , 0 )$ and $(-3 , 0 ) $ is $ 9.$

asked Apr 10, 2013 by poojasapani_1

1 answer

$\begin{array}{1 1}(i)\text{ Write the Boolean expression corresponding to the circuit given below} : \\(ii) \text{ Simplify the expression using laws of Boolean Algebra and constract the simplified circuit.}\end{array}$

asked Apr 10, 2013 by sreemathi.v

0 answers

Prove that : $cos^{-1}\frac{63}{65}+2tan^{-1}\frac{1}{5}=sin^{-1}\frac{3}{5}$

asked Apr 10, 2013 by sreemathi.v

0 answers

If a parabolic reflector is $20cm$ in diameter and $5cm$ deep, find the distance of the focus from the centre of the reflector.

asked Apr 9, 2013 by poojasapani_1

1 answer

Obtain the vector and cartesian equation of thesphere whose centre is $(1 , -1 , 1 )$ and radius is the same as that of the sphere $|\overrightarrow{r}-(\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{2k})|=5.$

asked Apr 9, 2013 by poojasapani_1

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

The planes $\overrightarrow{r} .(\overrightarrow{2i}+\lambda\overrightarrow{j}-\overrightarrow{3k})=10 $and $ \overrightarrow{r}. (\lambda\overrightarrow{i}+\overrightarrow{3j}+\overrightarrow{k})=5$ are perpendiculare find $\lambda$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the point of intersection of the line $\overrightarrow{r}=(\overrightarrow{j}-\overrightarrow{k})+s(\overrightarrow{2i}-\overrightarrow{j}+\overrightarrow{k})$ and $x z$ - plane.

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the length of the perpendicular frome the origin to the plane$\overrightarrow{r} . (\overrightarrow{3i}+\overrightarrow{4j}+\overrightarrow{12k})=26$.

asked Apr 7, 2013 by poojasapani_1

1 answer

Show that the lines $\large \frac{x-1}{1}=\frac{y+1}{-1}=\frac{z}{3}$ and $\large\frac{x-2}{1}=\frac{y-1}{2}=\frac{-z-1}{1}$ intersect and find their point of intersection.

asked Apr 7, 2013 by poojasapani_1

1 answer

What are the d . c . s of the vector equally inclined to the axes?

asked Apr 6, 2013 by poojasapani_1

1 answer

Prove that $\mid[\overrightarrow{a} \overrightarrow{b} \overrightarrow{c}]\mid=a b c $ if and only if $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are mutually perpendicular.

asked Apr 5, 2013 by poojasapani_1

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 = 0$

asked Apr 5, 2013 by geethradh

0 answers

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

asked Apr 5, 2013 by geethradh

0 answers

Find the area of the parallelogram determined by the sides $\overrightarrow{i}+\overrightarrow{2j}+\overrightarrow{3k}$ and $-\overrightarrow{3i}-\overrightarrow{2j}+\overrightarrow{k}$

asked Apr 5, 2013 by poojasapani_1

1 answer

Differentiate the following functions with respect to $x:\; sinx(ax+b)$

asked Apr 4, 2013 by balaji.thirumalai

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

Find the unit vectors perpendicular to the plane containing the vectors $\overrightarrow{2i}+\overrightarrow{j}+\overrightarrow{k}$ and $\overrightarrow{i}+\overrightarrow{2j}+\overrightarrow{k}$

asked Apr 4, 2013 by poojasapani_1

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

Prove by vector method , The sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of the sides.

asked Apr 3, 2013 by poojasapani_1

1 answer

Find $\lambda $ so that the vectors $\overrightarrow{2i}+\overrightarrow{\lambda\;j}+\overrightarrow{k}$ and $\overrightarrow{i}- \overrightarrow{2j} +\overrightarrow{k}$ are perpendicular to each other.

asked Apr 2, 2013 by poojasapani_1

1 answer

For what valus of $k$, the system of equations $kx+y+z=1\;,x+ky+z=1\;,x+y+kz=1\;,$have (i) unique solution (ii) more than one solution (iii) no solution.

asked Apr 2, 2013 by poojasapani_1

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

Solve the following non-homogeneous system of linear equation by determinant method : $4x+5y=9\;,8x+10y=18 $

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the rank of the following matrix :$\begin{bmatrix} 3 & 1 & 2 &0 \\1 & 0 & -1 &0 \\2 & 1 & 3 &0 \end{bmatrix}$

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve by matrix inversion method following system of linear equation $\;x+y+z=9\;,\;2x+5y+7z=52\;,2x+y-z=0$

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the adjoint of matrix A=$\begin{bmatrix} 3 & -3 & 4 \\2 & -3 & 4 \\0 & -1 & 1 \end{bmatrix}$ and verify the result $A\;(adj A)=(adj A)\;A=$|$A$|$.I$

asked Mar 28, 2013 by poojasapani_1

1 answer

The money to be spent for the welfare of the employees of a firm is proportional to the rate of change of its total revenue (marginal revenue).If the total revenue(in rupees) received from the sale of Xunits of a product is given by R(x)=$3x^2+36x+5$,find the marginal revenue,when x=5,and write which value does the question indicate.

asked Mar 20, 2013 by sreemathi.v

1 answer

For what value of x, is the matrix A=$\begin{bmatrix}0 & 1 & -2\\-1 & 0 & 3\\x & -3 & 0\end{bmatrix}$ a skew-symmetric matrix?

asked Mar 20, 2013 by sreemathi.v

1 answer

Write the value of $\tan^{-1}\begin{bmatrix}2\sin\bigg(2\cos^{-1}\frac{\sqrt 3}{2}\bigg)\end{bmatrix}$

asked Mar 20, 2013 by sreemathi.v

1 answer

Find $ gof$ and $fog$, if $f(x) = 8x^3$ and $g(x)=x^\frac{1}{3}$

asked Mar 13, 2013 by sreemathi.v

1 answer

Find $ gof$ and $fog$, if (ii) $ f(x) = 8x^3$ and $ g(x) = x ^ \frac { 1} {3} $

asked Mar 7, 2013 by meena.p

1 answer

Find $ gof$ and $fog$, if $ f(x) = |\;x\;|$ , and $ g(x) = |\;5x-2\;| $

asked Mar 7, 2013 by meena.p

1 answer

Show that the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\lambda \;and\;\frac{x-4}{5}=\frac{y-1}{2}=z=\mu\;$intersect. Also,find thier point of intersection.

asked Mar 7, 2013 by sreemathi.v

1 answer

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