Recent questions in Mathematics

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

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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

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

asked Sep 26, 2013 by meena.p

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$\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

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

asked Sep 26, 2013 by meena.p

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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

1 answer

$\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

1 answer

$(1+2x+3x^2)^{10}=a_0+a_1x+a_2x^2+..........+a_{20}x^{20}=>\large\frac{a_2}{a_1}$=

asked Sep 26, 2013 by meena.p

1 answer

A polygon has 54 diagonals. Then the number of its sides is :

asked Sep 26, 2013 by meena.p

2 answers

Let $a_n=\large\frac{10^n}{n !}$ for $n=1,2,3.......$ Then the greatest value of $n$ for which $a_n$ is the greatest is :

asked Sep 26, 2013 by meena.p

1 answer

Let $n= 1 !+ 4 !+7 !+.............+400 !$. Then ten's digits of $n$ is :

asked Sep 26, 2013 by meena.p

1 answer

The numbers $a_n=6^n-5n$ for $n=1,2,3,.....$ when divided by 25 leave the remainder:

asked Sep 26, 2013 by meena.p

1 answer

Let R denotes the set of all real numbers and $R^{+}$ denote the set of all positive real numbers. For the subsets $A$ and $B$ of R define $f:A \to B$ by $f(x)=x^2$ for $x \in A$. Observe the two lists given below:

asked Sep 26, 2013 by meena.p

1 answer

If $f(0),f(1)=1,f(2)=2$ and $f(x)=f(x-2)+f(x-3)$ for $x=3,4,5,........$ then $f(9)=$

asked Sep 26, 2013 by meena.p

1 answer

A police party is moving in a jeep at a constant speed $v$. They saw a theif at a distance x on a motorcycle which is at rest. The moment the police saw the thief, the thief started at constant acceleration $\alpha$. Which of the following relations is true if the police is able to catch the thief?

asked Sep 23, 2013 by meena.p

1 answer

A certain vector in the $xy$ plane has an $x$ component of 4 m and any component of 10 m. It is then rotated in the $xy$ plane so that its $x-$ component is doubled. Then its new y component is (approximately):

asked Sep 23, 2013 by meena.p

1 answer

The dimensional formula of $\large\frac{1}{2}$$\mu_0H^2(\mu_0$- Permeability of free space and H-magnetic field intensity ) is :

asked Sep 23, 2013 by meena.p

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In a $p-n$ junction diode the thickness of depletion layer is $2 \times 10^{-6}\;m$ and barrier potential is $0.3\;V$. the intensity of the electric field at the junction is :

asked Sep 23, 2013 by meena.p

1 answer

If $200 \;MeV$ of energy is released in the fission of one nucleus of $^{235}_{92} U$, the number of nuclei that must undergo fission to release an energy of $1000\;J$ is :

asked Sep 23, 2013 by meena.p

1 answer

The radius of the circle given by $x^2+y^2+z^2+2x-2y-4z-19=0=x+2y+2z+7,$ is

asked Sep 23, 2013 by meena.p

1 answer

A plane passes through $(2,3,1)$ and is perpendicular to the line having direction ratios $3,-4,7$.The perpendicular distance from the origin to this plane is

asked Sep 23, 2013 by meena.p

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If the angles made by a straight line with the coordinate axes are $\alpha,\large\frac{\pi}{2},$$ -\alpha, \beta$ then $\beta=$

asked Sep 23, 2013 by meena.p

1 answer

The ratio in which the line joining $(2,-4,3)$ and $(-4,5,-6)$ is divided by the plane $3x+2y+z-4$ is

asked Sep 23, 2013 by meena.p

1 answer

The polar equation of the line perpendicular to the line $\sin \theta- \cos \theta=\large\frac{1}{r}$ and passing through the point $\bigg(2, \large\frac{\pi}{6}\bigg)$ is

asked Sep 23, 2013 by meena.p

1 answer

The angle between the asymptotes of the hyperbola $x^2-3y^2=3$ is

asked Sep 23, 2013 by meena.p

1 answer

The eccentricity of the ellipse $x^2+4y^2+2x+16y+13=0$ is

asked Sep 23, 2013 by meena.p

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If the straight line $y=mx+c$ is parallel to the axis of the parabola $y^2=lx$ and intersects the parabola at $\bigg ( \large\frac{c^2}{8}$$,c\bigg)$ then the length of the latus rectum is

asked Sep 23, 2013 by meena.p

1 answer

If a chord of the parabola $y^2=4x$ passes through its focus and makes an angle $\theta$ with the $X-axis,$ then its length is

asked Sep 23, 2013 by meena.p

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The point of contact the circles $x^2+y^2+2x+2y+1=0$ and $x^2+y^2-2x+2y+1=0$ is

asked Sep 23, 2013 by meena.p

1 answer

If the circle $x^2+y^2+8x-4y+c=0$ touches the circle $x^2 +y^2+2x+4y-11=0$ externally and cuts the circle $x^2+y^2-6x+8y+k=0$ orthogonally then $k=$

asked Sep 23, 2013 by meena.p

1 answer

If the lines $3x+4y-14=0$ and $6x+8y+7=0$ are both tangents to a circle, then its radius is

asked Sep 23, 2013 by meena.p

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Aline segment $AM=a$ moves in the $XOY$ plane such that $AM$ is parallel to the $x-axis$. If A moves along the circle $x^2+y^2=a^2$, then the locus of M is

asked Sep 23, 2013 by meena.p

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