Recent questions tagged mar-2008

Find all the values of $\bigg(\large\frac{1}{2}$$-i\large\frac{\sqrt 3}{2}\bigg)^{\Large\frac{3}{4}}$ and hence prove that the product of the values is 1.

asked Jun 13, 2013 by sreemathi.v

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The distribution function $F(X)$ of a random variable $X$ is

asked Jun 3, 2013 by poojasapani_1

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Var $(4X+3)$ is

asked May 28, 2013 by poojasapani_1

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In the multiplicative group of $n{ th } $ roots of unity, the inverse of $\omega^{k}$ is $(k<n)$

asked May 27, 2013 by poojasapani_1

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A monoid becomes a group if it also satisfies the

asked May 24, 2013 by poojasapani_1

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Which of the following is a tautology?

asked May 24, 2013 by poojasapani_1

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The integrating factor of the differential equation $\large\frac{dy}{dx}$$-y\tan x=\cos x $ is

asked May 24, 2013 by poojasapani_1

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If $\large\frac{dy}{dx}=\frac{x-y}{x+y}$ then

asked May 23, 2013 by poojasapani_1

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Solution of $\large\frac{dx}{dy}$$+mx=0,$where $m<0$ is

asked May 22, 2013 by poojasapani_1

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The length of the are of the curve $x^{2/3}+y^{2/3}=4$ is

asked May 22, 2013 by poojasapani_1

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The area bounded by the parabola $y^{2}=x $ and its latus rectum is

asked May 22, 2013 by poojasapani_1

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The value of $\int\limits_{0}^{\pi/4}\cos^{3}2x dx$ is

asked May 21, 2013 by poojasapani_1

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The curve $ay^{2}=x^{2}(3a-x)$ cuts the $y$-axis at

asked May 21, 2013 by poojasapani_1

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If $u=\large\frac{1}{\sqrt{x^{2}+y^{2}}},$ then $x\large\frac{\partial u}{\partial x}$$+y\large\frac{\partial u}{\partial y}$ is equal to

asked May 20, 2013 by poojasapani_1

1 answer

Which of the following curves is concave down ?

asked May 20, 2013 by poojasapani_1

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The value of $c$ in Rolle's Theorem for the function $f(x)=\cos\large\frac{x}{2}$ on $[\pi,3]$ is

asked May 17, 2013 by poojasapani_1

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The equation of the tangent to the curve $y=\large\frac{x^{3}}{5}$ at the point $(-1,-1/5)$ is

asked May 15, 2013 by poojasapani_1

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The length of the latus rectum of the rectangular hyperbola $xy=32$ is

asked May 14, 2013 by poojasapani_1

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The angle between the asymptotes to the hyperbola $\large\frac{x^{2}}{16}-\frac{y^{2}}{9}=$$1 $ is

asked May 14, 2013 by poojasapani_1

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The point of intersection of the tangents at $t_{1}=t $ and $t_{2}=3t$ to the parabola $y^{2}=8x $ is

asked May 13, 2013 by poojasapani_1

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If $-i+2 $ is one root of the equation $ax^{2}-bx+c=0$, then the other root is

asked May 13, 2013 by poojasapani_1

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If $x=\cos\theta+i\sin\theta $ the value of $x^{n}+\large\frac{1}{x^{n}}$ is

asked May 12, 2013 by poojasapani_1

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The modulus and amplitude of the complex number $[e^{3-i \pi/4}]^{3}$ is respectively

asked May 11, 2013 by poojasapani_1

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The shortest distance of the point $(2 , 10 ,1 )$ from the plane $\overrightarrow{r}.(\overrightarrow{3i}-\overrightarrow{j}+\overrightarrow{4k})=2\sqrt{26}$ is

asked May 10, 2013 by poojasapani_1

1 answer

If$[\overrightarrow{a}\times\overrightarrow{b},\overrightarrow{b}\times\overrightarrow{c},\overrightarrow{c}\times\overrightarrow{a}]=64$ then $[\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}]$ is

asked May 10, 2013 by poojasapani_1

1 answer

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 $\overrightarrow{a}$ 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

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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

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

asked May 6, 2013 by poojasapani_1

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

asked May 4, 2013 by poojasapani_1

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

asked May 4, 2013 by poojasapani_1

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Find$C$. $\mu$ and $c^{2}$ of the normal distribution whose probability function is given by $f{x}$=$C$$e^{\large -x^2+3x}$$,-\infty<$X$<\infty$.

asked Apr 23, 2013 by poojasapani_1

1 answer

Four coins are tossed simultaneously .what is the probability of getting at most two heads

asked Apr 21, 2013 by poojasapani_1

1 answer

Four coins are tossed simultaneously.what is the probability of getting at least two heads

asked Apr 21, 2013 by poojasapani_1

1 answer

Four coins are tossed simultaneously .what is the probability of getting exactly $2$ heads

asked Apr 21, 2013 by poojasapani_1

1 answer

Find the mean and variance for the following probability density functions $f(x) = \left\{ \begin{array}{l l} xe^{-x}, & \quad \text{if $x$$>$0}\\ 0, & \quad \text{otherwise} \end{array} \right.$

asked Apr 20, 2013 by poojasapani_1

1 answer

Solve the following differential equation;$\large\frac{d^{2}y}{dx^{2}}$$-3\large\frac{dy}{dx}$$+2y=2e^{3x}$ when $x =\log$$2$,$y=0,$ and when $x=0,y=0$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following. $\large\frac{dy}{dx}$$+y\;=\;x$

asked Apr 16, 2013 by poojasapani_1

1 answer

Find the equation of rectangular hyperbola which has for one of its asymptotes the line $x+2y-5=0 $ and passes through the point $(6 , 0 ) $ and $(-3 , 0 )$ find its equation and asymptotes

asked Apr 13, 2013 by poojasapani_1

1 answer

Find the equation of the hyperbola if the asymptotes are $2x+3y-8=0$ and $3x-2y+1=0$ and $ (5 , 3 ) $ is a point on the hyperbola.

asked Apr 13, 2013 by poojasapani_1

1 answer

Find the eccentricity, centre , foci , and vertices of the following hyperbolas and draw their diagrams: $x^{2}-3y^{2}+6x+6y+18=0$

asked Apr 11, 2013 by poojasapani_1

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if $\ \overrightarrow{a}= \overrightarrow{2i}+ \overrightarrow{3j}- \overrightarrow{k} , \overrightarrow{b}= -\overrightarrow{2i}+ \overrightarrow{5k}, \overrightarrow{c}= \overrightarrow{j}- \overrightarrow{3k}. $ Verify that $ \overrightarrow{a}\times ( \overrightarrow{b}\times \overrightarrow{c})= (\overrightarrow{a}. \overrightarrow{c}) \overrightarrow{b}- (\overrightarrow{a}. \overrightarrow{b})c$

asked Apr 5, 2013 by poojasapani_1

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Prove by the vector method , cos$(A+B)=$ cos$A$ cos$B$ - sin$A$ sin$B$

asked Apr 3, 2013 by poojasapani_1

1 answer

Show that the adjoint of $A=\begin{bmatrix} -4 & -3 & -3 \\1 & 0 & 1 \\4 & 4 & 3 \end{bmatrix}$ is$\;A\;$ it self

asked Mar 28, 2013 by poojasapani_1

1 answer

Show that the set of all matrices of the form $\bigl(\begin{smallmatrix} a & 0 \\ 0 & 0 \end{smallmatrix} \bigr) $, $a \in R$ − {0} forms an abelian group under matrix multiplication.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

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