Recent questions tagged q6

Find the equation of the curve passing through $(1 , 0 )$ and which has slope $1+\large\frac{y}{x}$ at $(x , y )$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $\large\frac{dy}{dx}$$=\sin(x+y) $

asked Apr 15, 2013 by poojasapani_1

1 answer

Draw a rough sketch of the curve $y^2+1=x,x\leq 2$.Find the area enclosed by the curve and the line $x=2$.

asked Apr 15, 2013 by sreemathi.v

1 answer

Evaluate $\int_0^9f(x)$ dx,where f(x) is defined by $f(x)=\left\{\begin{array}{1 1}\sin x;if 0\leq x\leq \large\frac{\pi}{2}\\1;\large\frac{\pi}{2}\normalsize\leq x\leq 5\\e^{x-5};5\leq x\leq 9\end{array}\right.$

asked Apr 15, 2013 by sreemathi.v

0 answers

Find the equation of the asymptotes of the following rectangular hyperbola $6x^{2}+5xy-6y^{2}+12x+5y+3=0$

asked Apr 14, 2013 by poojasapani_1

1 answer

Find the equation of the asymptotes of the following rectangular hyperbola $2xy+3x+4y+1=0$

asked Apr 14, 2013 by poojasapani_1

1 answer

Find the equation of the asymptotes of the following rectangular hyperbola $xy-kx-hy=0$

asked Apr 14, 2013 by poojasapani_1

1 answer

Show that the line $x-y+4=0$ is a tangent to the ellipse $x^{2}+3y^{2}=12$ . Find the co-ordinates of the point of contact.

asked Apr 13, 2013 by poojasapani_1

1 answer

Draw a rough sketch of the curve $x^2+y=9$ and find the area enclosed by the curve,the x-axis and the lines $x+1=0$ and $x-2=0$.

asked Apr 12, 2013 by sreemathi.v

0 answers

(i) Evaluate $\int_0^{\large\frac{\pi}{2}}\log(\tan x)dx$.(ii) Evaluate $\int_0^5\big(x+\frac{1}{2}\big)dx$ as a limit of a sum.

asked Apr 12, 2013 by sreemathi.v

0 answers

Draw a rough sketch of the curve $y=x^2-5x+6$ and find the area bounded by the curve and the $x$-axis.

asked Apr 12, 2013 by sreemathi.v

1 answer

Evaluate $\large \int \frac{2\sin 2 x -\cos x }{6-\cos^2x -4\sin x }$$dx$.

asked Apr 12, 2013 by sreemathi.v

1 answer

If $y=x^x$,prove that : $\large\frac{d^2y}{dx^2}-\large\frac{1}{y}\big(\large\frac{dy}{dx}\big)^2-\large\frac{y}{x}\normalsize =0$

asked Apr 11, 2013 by sreemathi.v

0 answers

If the sum of the lengths of the hypotenuse and a side of a right angled triangle is given,show that the area of the triangle is maximum when the angle between them is $\large \frac{\pi}{3}$.

asked Apr 11, 2013 by sreemathi.v

0 answers

Find the area of the region bounded by the curves $x=4y-y^2$ and the y-axis.

asked Apr 10, 2013 by sreemathi.v

0 answers

Find the eccentricity, centre, foci, vertices of the following ellipses and draw the diagram:$ 16x^{2}+9y^{2}+32x-36y=92$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the eccentricity, centre, foci, vertices of the following ellipses and draw the diagram: $9x^{2}+4y^{2}=36$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the eccentricity, centre, foci, vertices of the following ellipses and draw the diagram:$x^{2}+4y^{2}-8x-16y-68=0$

asked Apr 10, 2013 by poojasapani_1

1 answer

Evaluate :$ \Large \int \frac{dx}{x\{6(log x)^2+7log x+2\}}$

asked Apr 10, 2013 by sreemathi.v

0 answers

Find the eccentricity, centre, foci, vertices of the following ellipses and draw the diagram: $16x^{2}+25y^{2}=400$

asked Apr 10, 2013 by poojasapani_1

1 answer

Show that diameter of a sphere subtends a right angle at a point on the surface.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the distane between the parallel planes $x-y+3z+5=0; 2x-2y+6z+7=0$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equations of the plane through the point $(2 , -1 , 4 )$ and parallel to the plane $\overrightarrow{r} . (\overrightarrow{4i}-\overrightarrow{12j}-\overrightarrow{3k})=7.$

asked Apr 7, 2013 by poojasapani_1

1 answer

If the point $(\lambda , 0 , 3 ), (1 , 3 , -1 )$ and $(-5 , -3 , 7 )$ are collinear than find $\lambda$.

asked Apr 7, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equation of the line through the point $(3 , -4 , -2 )$ and parallel to vector $\overrightarrow{9i} +\overrightarrow{6j} +\overrightarrow{2k}$.

asked Apr 6, 2013 by poojasapani_1

1 answer

Prove thet $ \overrightarrow{a}\times( \overrightarrow{b}\times \overrightarrow{c})+ \overrightarrow{b}\times( \overrightarrow{c}\times{a})+ \overrightarrow{c}\times( \overrightarrow{a}\times \overrightarrow{b})=0$

asked Apr 5, 2013 by poojasapani_1

1 answer

Prove that twice the area of parallelogram is equal to the area of another parallelogram formed by taking as its adjacent sides the diagonals of the former parallelogram.

asked Apr 5, 2013 by poojasapani_1

1 answer

If $|\overrightarrow{a}|=2, |\overrightarrow{b}|=7$ and $\overrightarrow{a}\times\overrightarrow{b}=\overrightarrow{3i}-\overrightarrow{2j}+\overrightarrow{6k}$ find the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$

asked Apr 4, 2013 by poojasapani_1

1 answer

A force magnitude $5$ units acting parallel to $\overrightarrow{2i}-\overrightarrow{2j}+ \overrightarrow{k}$ displaces the point of application from $(1,2,3)$to $(5,3,7) $ find the work done.

asked Apr 4, 2013 by poojasapani_1

1 answer

Show that the vector $\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$ is equally inclined with the coordinate axes.

asked Apr 2, 2013 by poojasapani_1

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

Solve the following non-homogeneous system of linear equation by determinant method : $3x+y-z=2\;,2x-y+2z=6\;,2x+y-2z=-2 $

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the rank of the following matrix :$\begin{bmatrix} 1 & -2 & 3 &4 \\-2 & 4 & -1 &-3 \\-1 & 2 & 7 &6 \end{bmatrix}$

asked Mar 29, 2013 by poojasapani_1

1 answer

Find the inverse of the matrix $A=\begin{bmatrix} 3 & -3 & 4 \\2 & -3 & 4 \\0 & -1 & 1 \end{bmatrix}$ and verify that $A^3=A^{-1}$

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

If $A_{ij}$ is the cofactor of the element $a_{ij}$ of the determinant $\begin{vmatrix}2 & -3 & 5\\6 & 0 & 4\\1 & 5 & -7\end{vmatrix}$,then write the value of $a_{32}.A_{32}$.

asked Mar 20, 2013 by sreemathi.v

1 answer