Recent questions tagged medium

Solve the equation : $\;x^{2}-2x+\large\frac{3}{2}=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;3x^{2}-4x+\large\frac{20}{3}=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Convert the following in the polar form : $\;\large\frac{1+3i}{1-2i}$

asked Apr 11, 2014 by yamini.v

1 answer

Convert the following in the polar form : $\;\large\frac{1+7i}{(2-i)^{2}}$

asked Apr 11, 2014 by yamini.v

1 answer

If $\;x-iy=\sqrt{\large\frac{a-ib}{c-id}}\;$ what is the value of $\;(x^{2}+y^{2})^{2}$?

asked Apr 11, 2014 by yamini.v

1 answer

Reduce $\;(\large\frac{1}{1-4i}- \large\frac{2}{1+i})\;(\large\frac{3 -4i}{5+i})\;$ to the standard form

asked Apr 11, 2014 by yamini.v

1 answer

For any two complex numbers $\;z_{1}\;$ and $\;z_{2}\;$, what is the value of $\; Re(z_{1} z_{2}) $?

asked Apr 11, 2014 by yamini.v

1 answer

Evaluate : $\;[i^{18} +(\large\frac{1}{i})^{25}]^{3}$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;x^{2}+\large\frac{x}{\sqrt{2}}+1=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;x^{2}+x+\large\frac{1}{\sqrt{2}}=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

Solve the equation : $\;\sqrt{3}x^{2}-\sqrt{2}x+3\sqrt{3}=0\;$

asked Apr 11, 2014 by yamini.v

1 answer

The vertices of the hyperbola $9x^2-16y^2-36x+96y-252=0$ are

asked Apr 11, 2014 by meena.p

1 answer

Find the asymptotes of the hyperbola. $xy=4x+3y$

asked Apr 11, 2014 by meena.p

1 answer

Convert the given complex number in polar form :$\;i\;$

asked Apr 10, 2014 by yamini.v

1 answer

Find the equation of the hyperbola with focus $(2,2) \; e=2$ and directrise $x+y=9$

asked Apr 10, 2014 by meena.p

1 answer

Convert the given complex number in polar form :$\;\sqrt{3}+i\;$

asked Apr 10, 2014 by yamini.v

1 answer

The minimum area of triangle formed by the tangents to the ellipse $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ coordinate axes is :

asked Apr 10, 2014 by meena.p

1 answer

The locus of the mid- points of the portion of the tangents to the ellipse intercepted between the axis is :

asked Apr 10, 2014 by meena.p

1 answer

Convert the given complex number in polar form :$\;-3$

asked Apr 10, 2014 by yamini.v

1 answer

Equation of the director circle of the ellipse $x^2+2y^2+2x-12y+15=0$ is

asked Apr 10, 2014 by meena.p

1 answer

Convert the given complex number in polar form :$\;-1-i\;$

asked Apr 10, 2014 by yamini.v

1 answer

Convert the given complex number in polar form :$\;-1+i\;$

asked Apr 10, 2014 by yamini.v

1 answer

Show that $9^{n+1} – 8n – 9$ is divisible by $64$, whenever $n$ is a positive integer.

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Find $(x+1)^6 + (x – 1)^6$. Hence, evaluate $( \sqrt2 + 1)^6+(\sqrt 2 –1)^6$.

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Convert the given complex number in polar form :$\;1-i\;$

asked Apr 10, 2014 by yamini.v

1 answer

Find $ (a + b)^4 - (a - b)^4.$ Hence, evaluate $( \sqrt3 + \sqrt2)^4 - (\sqrt 3 - \sqrt 2)^4$.

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Using Binomial Theorem, indicate which number is larger $(1.1)^{10000}$ or $1000$.

asked Apr 10, 2014 by balaji.thirumalai

1 answer

If $3x+2y=0$ and $5x-12y=0$ are the equation of the pour of conjugates diameters, then value of eccentricity e is

asked Apr 10, 2014 by meena.p

1 answer

The lengths of the axes of the conic $9x^2+4y^2-6x+4y+1=0$ are

asked Apr 10, 2014 by meena.p

1 answer

Find the modulus and the argument of the complex number $\;z=-\normalsize \sqrt{3} + \normalsize i$

asked Apr 10, 2014 by yamini.v

1 answer

Length of latus rectum is one third of major axis:

asked Apr 10, 2014 by meena.p

1 answer

Find the modulus and the argument of the complex number $\;z=-\normalsize 1- \normalsize i\sqrt{3}$

asked Apr 10, 2014 by yamini.v

1 answer

Express the following expression in the form $\;\normalsize a + \normalsize ib : \large\frac{(\normalsize 3 + \normalsize i \sqrt{5})(\normalsize 3 - \normalsize i \sqrt{5})}{(\normalsize \sqrt{3} + \normalsize i \sqrt{2})-(\normalsize \sqrt{3} - \normalsize i \sqrt{2})}$

asked Apr 10, 2014 by yamini.v

1 answer

If the polar of $y^2=4ax$ is always touching the ellipse $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}$$=1$ then locus of the pole is :

asked Apr 10, 2014 by meena.p

1 answer

A man deposited $Rs. 10,000$ in a bank at the rate of $5\%$ simple interest annually. Find the amount in $15^{th}$ year since he deposited the amount and also find the total amount after $20$ ears.

asked Apr 10, 2014 by rvidyagovindarajan_1

1 answer

If $y=mx+c$ is a tangent to the ellipse $x^2+2y^2=6$ then $c^2$ is equal to

asked Apr 10, 2014 by meena.p

1 answer

Find the multiplicative inverse of the complex number $\;\normalsize -i\;$

asked Apr 10, 2014 by yamini.v

1 answer

The line $x \cos \alpha + y \sin \alpha =p$ is a tangent to the ellipse. $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}$$=1$ if

asked Apr 10, 2014 by meena.p

1 answer

The eccentric angle of a point on the ellipse $\large\frac{x^2}{6} +\frac{y^2}{2}$$=1$ Whose distance from the centre of ellipse is 2 is

asked Apr 10, 2014 by meena.p

1 answer

Find the equation of tangent to the ellipse $3x^2+4y^2=12$ which are parallel to the line $y+2x=4$

asked Apr 10, 2014 by meena.p

1 answer

P is a point, two tangents are drawn from it to the parabola $y^2=4x$ such that the slope of one tangent is three times the slope of the other. The locus of P is

asked Apr 10, 2014 by meena.p

1 answer

If $x+y=k$ is the normal to $y^2=12x$ then k is

asked Apr 10, 2014 by meena.p

1 answer

If the line $x-1=0$ is the directrix of parabola $y^2-kx+8=0$ then one of the value of k is

asked Apr 10, 2014 by meena.p

1 answer

The equation of the directrise of the parabola $y^2+4y+4x+2=0$ is

asked Apr 10, 2014 by meena.p

1 answer

The angle between the tangents draw from the origin to the parabola $y^2=4a(x-a)$ is

asked Apr 10, 2014 by meena.p

1 answer

The equation of common tangent to the curves $y^2=8x$ and $xy=-1$ is

asked Apr 10, 2014 by meena.p

1 answer

If $\omega=\cos\large\frac{\pi}{n}$$+i\sin\large\frac{\pi}{n}$,then the value of $1+\omega+\omega^2+.....+\omega^{n-1}$ is :

asked Apr 10, 2014 by sreemathi.v

1 answer

If $(x+iy)^{\large\frac{1}{3}}=a+ib$ then $\large\frac{x}{a}+\frac{y}{b}$ equals

asked Apr 10, 2014 by sreemathi.v

1 answer

If $z_k=\cos\big(\large\frac{k\pi}{10})$$+i\sin(\large\frac{k\pi}{10})$,then $z_1z_2z_3z_4$ equals

asked Apr 10, 2014 by sreemathi.v

1 answer

$z=x+iy$ and $\omega=\large\frac{1-iz}{z-i}$ then $|\omega|=1$ implies that in complex plane

asked Apr 10, 2014 by sreemathi.v

1 answer

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