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The point of intersection of the line $\overrightarrow{r}=(\overrightarrow{i}-\overrightarrow{k}) + t(\overrightarrow{3i}+\overrightarrow{2j}+\overrightarrow{7k})$ and the plane $\overrightarrow{r}. (\overrightarrow{i}+\overrightarrow{j}-\overrightarrow{k})=8 $ is

asked May 10, 2013 by poojasapani_1

1 answer

If $\overrightarrow{PR}=2\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}, \;\overrightarrow{QS}=-\overrightarrow{i}+\overrightarrow{3j}+\overrightarrow {2k},$ then the area of the quadrilateral $PQRS$ is

asked May 9, 2013 by poojasapani_1

0 answers

If $\overrightarrow{p} ,\overrightarrow{q}$ and $\overrightarrow{p}+\overrightarrow{q}$ are vectors of magnitude $\lambda$ than the magnitude of $|\overrightarrow{p}-\overrightarrow{q}|$ is

asked May 9, 2013 by poojasapani_1

1 answer

If $|\overrightarrow{a+b}|=|\overrightarrow{a-b}|$ then

asked May 9, 2013 by poojasapani_1

1 answer

The area of the parallelogram having a diagonal $\overrightarrow{3i}+\overrightarrow{j}-\overrightarrow{k}$ and a side $\overrightarrow{i}-\overrightarrow{3j}+\overrightarrow{4k} $ is

asked May 9, 2013 by poojasapani_1

1 answer

The vectors $\overrightarrow{2i}+\overrightarrow{3j}+\overrightarrow{4k} $ and $\overrightarrow{ai}+\overrightarrow{bj}+\overrightarrow{ck}$ are perpendicular when

asked May 9, 2013 by poojasapani_1

1 answer

If $A=\large\frac{1}{3}$$\begin{bmatrix} 2 & 2 & 1 \\-2 & 1 & 2 \\1 & -2 & 2 \end{bmatrix}$ prove that $A^{-1}=A^T$.

asked May 8, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}$ and $\overrightarrow{b} $ include an angle $120^{\circ}$ and their magnitude are $2$ and $\sqrt{3}$ then $\overrightarrow{a} .\overrightarrow{b} $ is equal to

asked May 8, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two unit vectors and $\theta $is the angle between them, then $(\overrightarrow{a}+\overrightarrow{b})$ is a unit vector if

asked May 8, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}$ is a non-zero vector and $m$ is a non-zero scalar then $m\overrightarrow{a} $ is a unit vector if

asked May 8, 2013 by poojasapani_1

1 answer

If the equation $-2x+y+z=i\;;x-2y+z=m\;;x+y-2z=n$ such that $i+m+n=0,$ then the system has

asked May 8, 2013 by poojasapani_1

1 answer

The system of equations $ax+y+z=0; x+by+z=0; x+y+cz=0 $ has a non-trivial solution then $\large\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}=$

asked May 7, 2013 by poojasapani_1

1 answer

In a system of $3$ linear non-homogeneous equation with three unknowns,if $\bigtriangleup=0\;$ and $\;\bigtriangleup_{x}=0 ,\bigtriangleup_y\neq 0 $ and $ \bigtriangleup_z=0$ then the system has

asked May 7, 2013 by poojasapani_1

1 answer

Inverse of $\begin{bmatrix}2& -1 \\-5 & 3 \end{bmatrix}$ is

asked May 7, 2013 by poojasapani_1

1 answer

If $A$=$\begin{bmatrix} 0 & 0 \\0 & 5 \end{bmatrix}$, then $A^{12}$ is

asked May 7, 2013 by poojasapani_1

1 answer

If $A$ and $B$ are any two matrices such that $AB=O$ and $A$ is non-singular, then

asked May 7, 2013 by poojasapani_1

1 answer

If $A$ is a matrix of order $3$, then det($kA$)

asked May 7, 2013 by poojasapani_1

1 answer

If $A$ is a square matrix of order $n$ then |adj$A$| is

asked May 7, 2013 by poojasapani_1

1 answer

If $A$=$\begin{bmatrix} 2 & 1 \\3 & 4 \end{bmatrix}$, than (adj $A)A$=

asked May 7, 2013 by poojasapani_1

1 answer

If the matrix $\begin{bmatrix} -1 & 3 & 2 \\1 & k & -3 \\1 & 4 & 5 \end{bmatrix}$ has an inverse than the value of $k$

asked May 7, 2013 by poojasapani_1

1 answer

If $A$ is a scalar matrix with scalar $k \neq 0$ of order $3$ than $A^{-1}$ is

asked May 7, 2013 by poojasapani_1

1 answer

If the rank of the matrix$\begin{bmatrix} \lambda & -1 & 0 \\0 & \lambda & -1 \\-1 & 0 & \lambda \end{bmatrix}$ is $2$, than $\lambda$ is

asked May 7, 2013 by poojasapani_1

1 answer

If A=$\begin{bmatrix} 2& 0& 1 \end{bmatrix}$ than the rank of $AA^{T}$is

asked May 6, 2013 by poojasapani_1

1 answer

If A=$\begin{bmatrix} 1\\ 2 \\ 3 \end{bmatrix}$ than the rank of $AA^{T}$is

asked May 6, 2013 by poojasapani_1

1 answer

The rank of the diagonal matrix $\begin{bmatrix} -1 & & \\ & -2 & \\ & & 0\\& & &-4\\ & & & &0 \end{bmatrix}$

asked May 6, 2013 by poojasapani_1

1 answer

Evaluate the limit for the following if exists. $\;\lim \limits_{x \to 1 } x^{\large\frac{1}{x-1}}$

asked May 6, 2013 by poojasapani_1

1 answer

Find the intervals of concavity and the points of inflection of the following functions: $y=12x^{2}-2x^{3}-x^{4}$

asked May 6, 2013 by poojasapani_1

1 answer

Find the intervals of concavity and the points of inflection of the following functions: $f(x)=x^{4}-6x^{2}$

asked May 6, 2013 by poojasapani_1

1 answer

Find the intervals of concavity and the points of inflection of the following functions: $f(x)=2x^{3}+5x^{2}-4x$

asked May 6, 2013 by poojasapani_1

1 answer

Find two numbers whose sum is $100 $ and whose product is a maximum.

asked May 5, 2013 by poojasapani_1

1 answer

Find the intervals on which $f$ is increasing or decreasing. $f(x)= x^{3}-3x+1$

asked May 4, 2013 by poojasapani_1

1 answer

Find the intervals on which $f$ is increasing or decreasing. $f(x)=20-x-x^{2}$

asked May 4, 2013 by poojasapani_1

1 answer

Obtain the Maclaurin's series expansion for:$\;\tan x,- \large\frac{\pi}{2} \lt \normalsize x \lt \large\frac{\pi}{2}$

asked May 4, 2013 by poojasapani_1

1 answer

Obtain the Maclaurin's series expansion for:$\;\large\frac{1}{1+x}$

asked May 4, 2013 by poojasapani_1

1 answer

Verify Lagrange's theorem for the following function;\[\]$f(x)=x^{3}-5x^{2}-3x\;[1,3]$

asked May 3, 2013 by poojasapani_1

1 answer

Verify Lagrange's theorem for the following function;\[\]$f(x)=x^{\large\frac{2}{3}}[-2,2]$

asked May 3, 2013 by poojasapani_1

1 answer

Verify Rolle's theorem for the following function; $f(x)=\sin x, 0\leq x\leq\pi$.

asked May 3, 2013 by poojasapani_1

1 answer

If the curve $ y^{2}=x$ and $xy=k$ are orthogonal than prove that $8k^{2}=1.$

asked May 3, 2013 by poojasapani_1

1 answer

Show that the equation of the normal to the curve $x=a\cos^{3}\theta ; y=a\sin^{3}\theta$ at $\;'\theta'$ is$\; x\cos\theta-y\cos\theta=a\cos 2\theta.$

asked May 3, 2013 by poojasapani_1

1 answer

Prove that the curve $2x^{2}+4y^{2}=1$ and $6x^{2}-12y^{2}=1$ cut each other at right angles.

asked May 3, 2013 by poojasapani_1

1 answer

Let $P$ be a point on the curve $y=x^{3}$ and suppose that the tangent line at $P$ intersects the curve again at $Q$. Prove that the slope at $Q$ is four times the slope at $P$.

asked May 3, 2013 by poojasapani_1

1 answer

A particle of unit mass moves so that displacement after $t$ secs is given by $x=3\cos(2t-4).$ Find the acceleration and kinetic energy at the end of $2 \;secs.[ K.E =\large\frac{1}{2}$$mv^{2}\quad m $ is mass]

asked Apr 30, 2013 by poojasapani_1

1 answer

Prove that the curved surface area of a sphere of radius $r$ intercepted between two parallel planes at a distance $a$ and $b$ from the centre of the sphere is $\;2\pi r(b-a)$ and hence deduct the surface area of the sphere,$(b>a)$

asked Apr 30, 2013 by poojasapani_1

1 answer

Find the surface area of the solid generated by revolving the arc of the parabola$\;y^{2}=4ax$, bounded by its latus rectum about $x$- axis.

asked Apr 30, 2013 by poojasapani_1

1 answer

Find the length of the curve $x=a(t-\sin t),y=a(1-\cos t)$ between $t=0$and $\pi$.

asked Apr 30, 2013 by poojasapani_1

1 answer

Find the perimeter of the circle with radius $a$.

asked Apr 30, 2013 by poojasapani_1

1 answer

Find the volume of the solid that results when the region enclosed by the given curve: $(11$$to14)$$\large\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ is revolved about major axis $a>b>0.$

asked Apr 30, 2013 by poojasapani_1

1 answer

Find the common area enclosed by the parabolas $4y^{2}=9x$ and $3x^{2}=16y$

asked Apr 28, 2013 by poojasapani_1

1 answer

Find the area of the region bounded by the ellipse $\large\frac{x^{2}}{9}+\frac{y^{2}}{5}$$=1$ between the two latus rectums.

asked Apr 27, 2013 by poojasapani_1

1 answer

Find the area of the region bounded by the curve $y=3x^{2}-x$ and the $x$-axis between $x=-1$ and $x=1$

asked Apr 27, 2013 by poojasapani_1

1 answer

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