Recent questions in Mathematics

If $\omega$ is a complex root of unity, one root of the equation $\begin{vmatrix}x+1 &\omega&\omega^2\\\omega&x+\omega^2&1\\\omega^2&1&x+\omega\end{vmatrix}=0$ is

asked Apr 9, 2014 by sreemathi.v

1 answer

The ratio in which the line segment joining the points $(4,-6)$ and $(3,1)$ is divided by the parabola $y^2=4ax$ is

asked Apr 9, 2014 by meena.p

1 answer

$z=\large\frac{1}{1-\cos \theta+i\sin \theta}$ .Re(z) is equal to

asked Apr 9, 2014 by sreemathi.v

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Given $x=2+5i$ , the value of $x^3-5x^2+33x-19$ is

asked Apr 9, 2014 by sreemathi.v

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Find the points of the conic $y=x^2+7x+2$ which is nearest to the line $3x-y-3=0$

asked Apr 9, 2014 by meena.p

1 answer

If $\omega=\large\frac{z-\perp}{z+1}$ $\quad (z\neq -\perp)$ and $\mid z\mid =\perp$ then $Re(\omega)$ equals

asked Apr 9, 2014 by sreemathi.v

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Find the equation of the chord of the parabola $y^2=12x$ which is bisected at $(5,-7)$

asked Apr 9, 2014 by meena.p

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$z$ and $\omega$ are two non zero complex numbers such that $\mid z\mid=\mid \omega\mid$ and $arg(z)+arg(\omega)=\pi$ .Then $z$ equals

asked Apr 9, 2014 by sreemathi.v

1 answer

If $z\neq 0$ is a complex no having arg= $\large\frac{\pi}{4}$ ,then

asked Apr 9, 2014 by sreemathi.v

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The radius of the circle passing through the foci of the ellipse $\large\frac{x^2}{16}+\frac{y^2}{9}$ $=1$ and having its center at $(0,3)$ is

asked Apr 9, 2014 by meena.p

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Let $a,b$ be real numbers between $0\; and\; 1$ such that $z_1=1+bi,z_2=a+i$ and $z_3=0$ forms an equilateral triangle then

asked Apr 9, 2014 by sreemathi.v

1 answer

The equation $2x^2+3y^2-8x-18y+35=k$ represents

asked Apr 9, 2014 by meena.p

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The complex numbers $\sin x+i\cos 2x$ and $\cos x-i\sin 2x$ are conjugate for

asked Apr 9, 2014 by sreemathi.v

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If complex numbers $z_1,z_2,z_3$ represents vertices of an equilateral triangle and $\mid z_1\mid=\mid z_2\mid=\mid z_3\mid$ then

asked Apr 9, 2014 by sreemathi.v

1 answer

The circle passing through $(1,-2)$ and touching the axis of x at $(3,0)$ also passes through the point.

asked Apr 9, 2014 by meena.p

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The length of the diameter of the circle which touches the x-axis at the point $(1,0)$ and passes through the point $(2,3)$ is

asked Apr 9, 2014 by meena.p

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The circle $x^2+y^2=4x+8y+5$ intersects the line $3x-4y=m$ at the two distinct points if

asked Apr 9, 2014 by meena.p

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If a circle passes through the points $(a,b)$ and cuts the circle $x^2+y^2=4$ orthogonally, then the locus of its centre is

asked Apr 9, 2014 by meena.p

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The two circles $x^2+y^2=ax$ and $x^2+y^2=c^2\; (c > 0)$ touch each other if

asked Apr 9, 2014 by meena.p

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Intercept on the line $y=x$ by the circle $x^2+y^2-2x=0$ is $AB$ equation of the circle on AB as a diameter is :

asked Apr 9, 2014 by meena.p

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If the lines $2x+3y+1=0,\qquad 3x-y-4=0$ lie along diameter of a circle of circumference $10\pi$ then the equation of the circle is :

asked Apr 8, 2014 by meena.p

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The lines $2x-3y=5$ and $3x-4y=7$ are diameters of a circle having area as $154$ sq.units. The equation of the circle is .

asked Apr 8, 2014 by meena.p

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If the two circles $(x-1)^2+(y-3)^2=r^2$ and $x^2+y^2-8x+2y+8=0$ intersect in two distinct point then

asked Apr 8, 2014 by meena.p

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The centre of the circle passes through $(0,0)$ and $(1,0)$ and touching the circle $x^2+y^2=9$ is

asked Apr 8, 2014 by meena.p

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If the chord $y=mx+1$ of the circle $x^2+y^2=1$ substance on angle of measures $45^{\circ}$ at the major segment of the circle then value of m is

asked Apr 8, 2014 by meena.p

1 answer

The number of common tangent to the circle $x^2+y^2=4$ and $x^2+y^2-6x-8y=24$

asked Apr 8, 2014 by meena.p

1 answer

The circle passing through the point $(-1,0)$ and touching the y-axis at $(0,2)$ also passes through the point .

asked Apr 8, 2014 by meena.p

1 answer

The center of circle inscribed in square formed by the lines $x^2-8x+12=0$ and $y^2-14\;y+45=0$ is

asked Apr 8, 2014 by meena.p

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If the tangent at the point P on the circle $x^2+y^2+6x=2$ meets a straight line $5x-2y+6=0$ at a point Q on the y-axis , then the length of $PQ$ is

asked Apr 8, 2014 by meena.p

1 answer

Find the point of intersection of the line $4x-3y-10=b$ and circle $x^2+y^2-2x+4y-20=0$

asked Apr 8, 2014 by meena.p

1 answer

There are 10 points in a plane out of these 6 are collinear. If N is the number of triangle formed by joining these points. Then

asked Apr 8, 2014 by meena.p

1 answer

The line $p(p^2+1)x-y+q=0$ and $(p^2+1)^2x +(p^2+1)y+2q=0$ are perpendicular to a common line for

asked Apr 8, 2014 by meena.p

1 answer

The shortest distance between the line $y-x=1$ and the curve $x=y^2$ is

asked Apr 8, 2014 by meena.p

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The perpendicular bisector of the line segment joining $P(1,4)$ and $Q(K,3)$ has y-intercept $-4$ , Then a possible value of $k$ is

asked Apr 8, 2014 by meena.p

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A straight line through the point $A(3,4)$ is such that its intercept between the axis is bisected at A. Its equation is

asked Apr 8, 2014 by meena.p

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If one of the lines given by $6x^2-xy+4cy^2=0$ is $3x+4y=0$ then c equals

asked Apr 8, 2014 by meena.p

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If the sum of the slopes of the lines given by $x^2-2cxy-7y^2=0$ is four times their product c has the value.

asked Apr 8, 2014 by meena.p

1 answer

Let $A(2,3)$ and $B(-2,3)$ be vertices of a triangle ABC. If the centriod of this triangle moves on the line $2x+3y=1$ then the locus of the vertex C is the line .

asked Apr 8, 2014 by meena.p

1 answer

Locus of centriod of the triangle whose vertices are $(a \cos t, a \sin t),(b \sin t,-b \cos t)$ and $(1,0)$ where t is a parameter is

asked Apr 8, 2014 by meena.p

1 answer

If the pair of straight lines $x^2-2pxy-y^2=0$ and $x^2-2qxy-y^2=0$ be such that each pair bisects the angle between the other pair then,

asked Apr 8, 2014 by meena.p

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The pair of lines represented by $3ax^2+5xy+(a^2-2)y^2=0$ are perpendicular to each other for

asked Apr 8, 2014 by meena.p

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If the pair of lines $ax^2+2hxy +by^2+2gx+ 2fy+c=0$ intersect on the y-axis then

asked Apr 8, 2014 by meena.p

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A triangle with vertices $(4,0),(-1,-1),(3,5)$ is

asked Apr 8, 2014 by meena.p

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If a,b and c are in A.P thin the straight line $ax+by+c=0$ will always pass through line $ax+by+c=0$ will always pass through a fixed point whose coordinates are

asked Apr 8, 2014 by meena.p

1 answer

Given the points $A(0,4)$ and $B(0,-4)$ the equation of the locus of the point $P(x,y)$ such that $|AP-BP|=6$ is

asked Apr 8, 2014 by meena.p

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The set of lines $ax+by+c=0$ where $3a+2b+4c=0$ is concurrent at the point.

asked Apr 8, 2014 by meena.p

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The area enclosed within the curve $|x|+|y|=1$ is

asked Apr 8, 2014 by meena.p

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If $f_k(x) = \large\frac{1}{k}$ $(\sin^k x + \cos^k x)$ , where $x\in R$ and $k \geq 1$ . The $f_4(x) - f_6(x)$ equals

asked Apr 6, 2014 by balaji.thirumalai

1 answer

If $\alpha, \beta \neq 0$ , and $f(n) = \alpha^n+\beta^n$ and $\begin{vmatrix} 3 & 1+f(1) & 1+f(2)\\ 1+f(1)& 1+f(2) &1+f(3) \\ 1+f(2)&1+f(3) & 1+f(4) \end{vmatrix}$ $=K(1-\alpha)^2\;(1-\beta)^2\;(\alpha-\beta)^2$ , then $K$ is equal to

asked Apr 6, 2014 by balaji.thirumalai

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If $z$ is a complex number such that $\left|\; z \;\right| \geq 2$ then the minimum value of $\large\left|\normalsize z \normalsize + \large\frac{1}{2} \right |$

asked Apr 6, 2014 by balaji.thirumalai

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