Recent questions tagged 2010

If the lines $2x+3y+12=0,x-y+k=0$ are conjugate with respect to the parabola $y^2=8x,$ then $k=$

asked Sep 27, 2013 by meena.p

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The product of the perpendicular distances from any point on the hyperbola $\large\frac{x^2}{a^2}-\frac{y^2}{b^2}$$=1$ to its asymptotes is :

asked Sep 27, 2013 by meena.p

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The equation of the hyperbola which passes through the point $(2,3)$ and has the asymptotes $4x+3y-7=0$ and $x-2y-1=0$ is :

asked Sep 27, 2013 by meena.p

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Let M be the foot of the perpendicular from a point P on the parabola $y^2=8(x-3)$ onto its directrix and let S be the focus of the parabola. If $\Delta SPM$ is an equilateral triangle, then $P=$

asked Sep 27, 2013 by meena.p

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The length of the common chord of the circles of radii 15 and 20 whose centers are 25 units of distance apart, is :

asked Sep 27, 2013 by meena.p

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If the circle $x^2+y^2+2x+3y+1=0$ cuts another circle $x^2+y^2+4x+3y+2=0$ in A and B, then the equation of the circle with AB as a diameter is :

asked Sep 27, 2013 by meena.p

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The equation of the circle concentric with the circle $x^2+y^2-6x+12y+15=0$ and of double its area is :

asked Sep 27, 2013 by meena.p

1 answer

If the lengths of tangents drawn to the circles :$x^2+y^2-8x+40=0; 5x^2+5y^2-25x+80=0;x^2+y^2-8x+16y+160=0$ from the point P are equal, then P=

asked Sep 27, 2013 by meena.p

1 answer

The equation of the radical axis of the pair of circles $7x^2+7y^2-7x+14y+18=0$ and $4x^2+4y^2-7x+8y+20=0$ is :

asked Sep 27, 2013 by meena.p

1 answer

If $3x^2-11xy+10y^2-7x+13y +k=0$ denotes a pair of straight lines, then the point of intersection of the lines is :

asked Sep 27, 2013 by meena.p

1 answer

A pair of perpendicular lines passes through the origin and also through the points of intersection of the curve $x^2+y^2 =4$ with $x+y=a,$ where $a > 0$. Then $a=$

asked Sep 27, 2013 by meena.p

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The distance between the two lines represents by $8x^2-24 xy +18 y^2-6x+9y-5=0$

asked Sep 27, 2013 by meena.p

1 answer

A straight line which makes equal intercepts on positive X and Y axes and which is at a distance 1 unit from the origin intersects the straight line $y=2x+3+\sqrt 2 $ at $(x_0,y_0).$ Then $ 2x_0+y_0=$

asked Sep 27, 2013 by meena.p

1 answer

The image of the line $x+y-2=0$ in the $Y-axis$ is :

asked Sep 27, 2013 by meena.p

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The image of point $(4,-13) $ with respect to the line $5x+y+6=0$ is :

asked Sep 27, 2013 by meena.p

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If a straight line L is perpendicular to the line $4x-2y=1$ and forms a triangle of area 4 square units with the coordinate axes, then an equation of the line L is :

asked Sep 27, 2013 by meena.p

1 answer

If the mean and variance of a binomial variable X are 2 and 1 respectively, the $P(X \geq 1)=$

asked Sep 27, 2013 by meena.p

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Suppose that a random variable X follows Poisson distribution. If $P(X=1)=P(X=2)$ then $P(X=5)=$

asked Sep 27, 2013 by meena.p

1 answer

Suppose A and B are two events such that $P(A \cap B)=\large\frac{3}{25}$ and $P(B-A)=\large\frac{8}{25}$. Then $ P(B)=$

asked Sep 27, 2013 by meena.p

1 answer

If $A_i (i =1,2,3..........,n)$ are $n$ independent events with $ P(A_i)=\large\frac{1}{1+i}$ for each i, then the probability that none of $A_i$ occurs is :

asked Sep 27, 2013 by meena.p

1 answer

An urn A contains 3 white and 5 black balls. Another urn B contains 6 white and 8 black balls. A ball is picked from A at random and then transferred to B. Then a ball is picked at random from B. The probability that it is a white ball is :

asked Sep 26, 2013 by meena.p

1 answer

Let $ OA,OB,OC$ be the co-terminal edges of a rectangular parallelopiped of volume V and let P be the vertex opposite to O. Then $[\overrightarrow{AP} \overrightarrow {BP} \overrightarrow {CP} ]=$

asked Sep 26, 2013 by meena.p

1 answer

If the angle $\theta$ between the vectors $\overrightarrow {a}=2x^2 \overrightarrow {i}+ 4x \overrightarrow {j}+ \overrightarrow {k}$ and $\overrightarrow {b}=7 \overrightarrow{i}-2 \overrightarrow {j}+x \overrightarrow {k}$ is such that $90^{\circ} < \theta <180^{\circ}$ then $x$ lies in the interval ::

asked Sep 26, 2013 by meena.p

1 answer

$\overrightarrow {u}=\overrightarrow {a}-\overrightarrow {b},\overrightarrow {v}=\overrightarrow {a}+\overrightarrow {b},| \overrightarrow {a} | =| \overrightarrow {b} |=2 => | \overrightarrow {u} \times \overrightarrow {v} |=$

asked Sep 26, 2013 by meena.p

1 answer

$\bigg[ \overrightarrow {a}+ 2 \overrightarrow {b}- \overrightarrow {c}\bigg].\bigg[\overrightarrow {a}- \overrightarrow {b}\bigg] \times \bigg[\overrightarrow {a}-\overrightarrow {b}-\overrightarrow {c}\bigg]=$

asked Sep 26, 2013 by meena.p

1 answer

If three unit vectors $\overrightarrow {a},\overrightarrow {b},\overrightarrow {c}$ satisfy $\overrightarrow {a}+\overrightarrow {b}+\overrightarrow {c}=\overrightarrow {0}$ then the angle between $\overrightarrow {a}$ and $\overrightarrow {b}$ is :

asked Sep 26, 2013 by meena.p

1 answer

Let $\overrightarrow {a}=\overrightarrow {i}- 2 \overrightarrow {j}+ 3 \overrightarrow {k},\; \overrightarrow {b}=2 \overrightarrow {i}+3 \overrightarrow {j}-\overrightarrow {k}$ and $\overrightarrow {c}= \lambda \overrightarrow {i}+\overrightarrow {j}+(2 \lambda -1) \overrightarrow {k}.$ If $\overrightarrow {c}$ is parallel to the plane containing $\overrightarrow {a},\overrightarrow {b} $ then $\lambda=$

asked Sep 26, 2013 by meena.p

1 answer

The sum of angles of elevation of the top of tower from two points distant a and b from the base and in the same straight line with it is $90^{\circ}$. Then the height of the tower is :

asked Sep 26, 2013 by meena.p

1 answer

In a triangle $ABC,C=90^{\circ}$.Then $\large\frac{a^2-b^2}{a^2+b^2}=$

asked Sep 26, 2013 by meena.p

1 answer

If $\Delta =a^2-(b-c)^2, $ is the area of the triangle ABC, then $\tan A=$

asked Sep 26, 2013 by meena.p

1 answer

$\tan h^{-1}x = a\log \bigg(\large\frac{1+x}{1-x}\bigg),| x | < 1 =>a=$

asked Sep 26, 2013 by meena.p

1 answer

$\tan ^{-1}x +\tan ^{-1} y +\tan ^{-1} z= \large\frac{\pi}{2}$$=>1-xy-yz-zx=$

asked Sep 26, 2013 by meena.p

1 answer

The set of solution of the equation $(\sqrt 3-1) \sin \theta+(\sqrt 3+1) \cos \theta=2$ is :

asked Sep 26, 2013 by meena.p

1 answer

If $\cos (x-y), \cos x, \cos (x+y)$ are three distinct numbers which are in harmonic progression and $\cos x \neq \cos y,$ then $1+\cos y=$

asked Sep 26, 2013 by meena.p

1 answer

$a \sin ^2 \theta+ b \cos ^2 \theta=c=>\tan ^2 \theta=$

asked Sep 26, 2013 by meena.p

1 answer

The period of $\bigg(\tan \theta -\large\frac{1}{3}$$ \tan ^3 \theta\bigg)\bigg(\large\frac{1}{3}$$-\tan ^2 \theta\bigg)^{-1},$ Where $\tan ^{2} \theta \neq \large\frac{1}{3}$ is :

asked Sep 26, 2013 by meena.p

1 answer

$(\sqrt 3+i)^7+(\sqrt 3-i)^7=$

asked Sep 26, 2013 by meena.p

1 answer

If $\omega$ is a complex cube root of unity, then $(x+1)(x+ \omega)(x-\omega-1)=$

asked Sep 26, 2013 by meena.p

1 answer

$z=1+i \sqrt 3=>|Arg z|+|Arg \bar {z}|=$

asked Sep 26, 2013 by meena.p

1 answer

If A is a nonzero square matrix of order $n$ with det $(I+A) \neq 0$ and $A^3=0$, Where $I,O$ are unit and null matrices of order $n \times n $ respectively the $(1+A^{-1})=$

asked Sep 26, 2013 by meena.p

1 answer

If the system of equations :$(k+1)^3x+(k+2)^3y=(k+3)^3 \;;\;(k+1)x+(k+2)y=k+3\;;\;x+y=1$ is consistent, then the value of $k$ is :

asked Sep 26, 2013 by meena.p

1 answer

$\begin {vmatrix} x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3 \end {vmatrix}=0,x \neq y \neq z=>1+xyz=$

asked Sep 26, 2013 by meena.p

1 answer

$f(x)=\begin {vmatrix} 2 \cos x & 1 & 0 \\ x-\frac{\pi}{2} & 2 \cos x & 1 \\ 0 & 1 & 2 \cos x \end {vmatrix}=>f'(\pi)=$

asked Sep 26, 2013 by meena.p

1 answer

Let $\alpha \neq 1$ be a real root of the equation $x^3-ax^2+ax-1=0,$ where $a \neq -1 $ is a real number. Then a root of this equation, among the following, is :

asked Sep 26, 2013 by meena.p

1 answer

The condition that the roots of $x^3-bx^2+cx-d=0$ are in geometric progression is :

asked Sep 26, 2013 by meena.p

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$\bigg \{ x \in R: \large\frac{14 x}{x+1}-\frac{9x-30}{x-4} $$<0 \bigg\}=$

asked Sep 26, 2013 by meena.p

1 answer

For $x \in R$, the least value of $\large\frac{x^2-6x+5}{x^2+2x+1}$ is :

asked Sep 26, 2013 by meena.p

1 answer

$\log _4 2-\log _g 2+\log _{16} 2-...............=$

asked Sep 26, 2013 by meena.p

1 answer

$ \large \frac{3x^2+x+1}{(x-1)^4}=\frac{a}{(x+1)}+\frac{b}{(x-1)^2}+\frac{c}{(x-1)^3}+\frac{d}{(x-1)^4} $$ => \begin{bmatrix} a & b \\ c & d \end{bmatrix} $=

asked Sep 26, 2013 by meena.p

1 answer

For $| x | < \large\frac{1}{5}$, the coefficient of $x^3$ in the expansion of $\large\frac{1}{(1-5x)(1-4x)}$ is :

asked Sep 26, 2013 by meena.p

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