Recent questions in Mathematics

The points in the set $\bigg\{z \in C: Arg \bigg(\large\frac{Z-2}{Z-6i}\bigg)-\frac{\pi}{2}\bigg\}$ lie on the curve which is (Where C denotes the set of all complex numbers )

asked Oct 17, 2013 by meena.p

1 answer

$\begin {bmatrix} a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b \end{bmatrix}$

asked Oct 17, 2013 by meena.p

1 answer

The inverse of the matrix $\begin {bmatrix} 7 & -3 & -3 \\ -1 & 1 & 0 \\ -1 & 0 & 1 \end{bmatrix} $ is :

asked Oct 17, 2013 by meena.p

1 answer

If $A=\begin {bmatrix} 1 & -2 \\ 4 & 5 \end{bmatrix}$ and $f(t)=t^2-3t+7$, then $f(A)+ \begin {bmatrix} 3 & 6 \\ 12 & -9 \end{bmatrix} = $

asked Oct 17, 2013 by meena.p

0 answers

The sum of the fourth powers of the of the equation $x^3+x+1=0$ is

asked Oct 17, 2013 by meena.p

1 answer

The cubic equation whose roots are thrice to each of the roots of $x^3+2x^2-4x+1=0$ is

asked Oct 16, 2013 by meena.p

1 answer

If $ \alpha+\beta=-2$ and $\alpha^3+\beta^3=-56$, then the quadratic equation whose roots are $\alpha$ and $\beta$ is

asked Oct 16, 2013 by meena.p

1 answer

Let $\alpha$ and $\beta$ be the roots of the quadratic equation $ax^2+bx+c=0$. Observe the lists given below:

asked Oct 16, 2013 by meena.p

1 answer

$\large\frac{1}{1.3}+\frac{1}{2.5}+\frac{1}{3.7}+\frac{1}{4.9}+....=$

asked Oct 16, 2013 by meena.p

1 answer

$\sum\limits _{k=1} ^{\infty}$ $\large\frac{1}{k !} \bigg(\sum \limits _{n=1}^k 2^{n-1} \bigg)=$

asked Oct 16, 2013 by meena.p

1 answer

If $\large\frac{x^2+x+1}{x^2+2x+1}$$=A+\large\frac{B}{x+1}+\frac{C}{(x+1)^2}$ then $A-B=$

asked Oct 16, 2013 by meena.p

1 answer

If $\alpha=\large\frac{5}{2 ! 3}+\frac{5.7}{3 ! 3^2}+ \frac{5.7.9}{4 ! 3^3}+........,$ then $ \alpha^2+4 \alpha=$

asked Oct 16, 2013 by meena.p

1 answer

If $(1+x+x^2+x^3)^5= \sum \limits_{k=0} ^{15} a_k x^k$ then $ \sum \limits_{k=0}^7 a_{2k}=$

asked Oct 16, 2013 by meena.p

1 answer

If $^n P_r=30240$ and $^n C_r=252$ then the ordered pair (n,r)=

asked Oct 16, 2013 by meena.p

1 answer

9 balls are to be placed in 9 boxes; and 5 of the balls cannot fill into 3 small boxes. The number of ways of arranging one ball in each of the boxes is

asked Oct 16, 2013 by meena.p

0 answers

For any integer $ n \leq 1$, the sum $\sum \limits _{k=1}^n$. $ k(k+2)$ is equal to

asked Oct 16, 2013 by meena.p

1 answer

If $x= \large\frac{1}{2} \bigg(\sqrt 7+\large\frac{1}{\sqrt 7}\bigg)$ then $\large\frac{\sqrt {x^2-1}}{x- \sqrt {x^2-1}}=$

asked Oct 16, 2013 by meena.p

0 answers

Given that $a,b \in \{0,1,2,.........,9\}$ with $ a+b \neq 0$ and that $\bigg(a, \large\frac{b}{10}$$ \bigg)^x=\bigg(\large\frac{a}{10},\frac{b}{100}\bigg)^y$$-1000$ Then $\large\frac{1}{x}-\frac{1}{y}=$

asked Oct 16, 2013 by meena.p

1 answer

If $f:[-6,6] \to \Re$ is defined by $f(x)=x^2-3$ for $x \in \Re$, then $(f0f0f)(-l)+(f0f0f)(0)+(f0f0f)(l)=$

asked Oct 16, 2013 by meena.p

1 answer

If $f: \Re \to \Re$ and $g: \Re \to \Re$ are defined by $f(x) - | x |$ and $g(x)=[x - 3]$ for $ x \in \Re$, then $\bigg \{ g(f(x)):-\large\frac{8}{5} $$ < x < \large\frac{8}{5} \bigg \} -$

asked Oct 16, 2013 by meena.p

1 answer

If $f: R \to C $ is defined by $f(x)=e^{2ix}$ for $x \in R$ then, f is (Where C denotes the set of all complex numbers)

asked Oct 16, 2013 by meena.p

1 answer

The differential equation of the family $y=ae^x+bx\; e^x+cx^2\;e^x$ of curves, where $a,b,c$ are arbitrary constants, is :

asked Oct 11, 2013 by meena.p

1 answer

The solution of the differential equation $\large\frac{dy}{dx}$$=\sin (x+y) \tan (x+y)-1$ is :

asked Oct 11, 2013 by meena.p

1 answer

The velocity of a particle which starts from rest is given by the following table :

asked Oct 10, 2013 by meena.p

1 answer

The line $x= \large\frac{\pi}{4}$ divides the area of the region bounded by $y=\sin x, y= \cos x$ and x-axis $\bigg(0 \leq x \leq \large\frac{\pi}{2}\bigg)$ into two regions of areas $A_1$ and $A_2$. Then $A_1 : A_2=$

asked Oct 10, 2013 by meena.p

0 answers

$\int \limits_0^\pi \large\frac{1}{1+\sin x}$$dx$

asked Oct 10, 2013 by meena.p

1 answer

If $I_n=\int \sin ^n x dx $, then $n\; I_n-(n-1)I_{n-2}$=

asked Oct 10, 2013 by meena.p

1 answer

$\int \bigg(\large\frac{2 -\sin 2x}{1-\cos 2x}\bigg)$$e^x dx=$

asked Oct 10, 2013 by meena.p

1 answer

$\int \large\frac{dx}{(x+1)\sqrt {4x+3}}=$

asked Oct 10, 2013 by meena.p

1 answer

$z=\tan (y+ax)+\sqrt {y-ax}=> z_{xx}-a^2z_{yy}=$

asked Oct 10, 2013 by meena.p

1 answer

The maximum value of $\large\frac{\log x}{x}$$,0 < x < \infty$ is :

asked Oct 10, 2013 by meena.p

1 answer

The function $f(x) =x^3+ax^2+bx+x, a^2 \leq 3b$ has:

asked Oct 10, 2013 by meena.p

1 answer

There is an error of $\pm 0.04\;cm$ in the measurement of the diameter of a sphere. When the radius is $10\;cm$, the percentage error in the volume of the sphere is :

asked Oct 10, 2013 by meena.p

1 answer

$y=e^{a \sin ^{-1}x}=>(1-x^2)y_{n+2}-(2n+1)xy_{n+1}=$

asked Oct 10, 2013 by meena.p

1 answer

$\large\frac{d}{dx}$$ \bigg[a \tan ^{-1} + b \log \bigg(\large\frac{x-1}{x+1}\bigg)\bigg]=\frac{1}{x^4-1}$$=>a-2b=$

asked Oct 10, 2013 by meena.p

1 answer

$x= \cos ^{-1} \bigg(\large\frac{1}{\sqrt {1+t^2}}\bigg),$$y= \sin ^{-1} \bigg(\large\frac{t}{\sqrt {1+t^2}}\bigg)=>\frac{dy}{dx}=$

asked Oct 10, 2013 by meena.p

1 answer

$x= \large\frac{1-\sqrt y}{1+\sqrt y}=>\large\frac{dy}{dx}=$

asked Oct 10, 2013 by meena.p

0 answers

If $f:R \to R$ is defined by $f(x) = \left\{ \begin{array}{l l} \frac{2 sin x-\sin 2x}{2x \cos x}, & \quad if \;x \neq 0 \\ a, & \quad if \; x =0 \end{array} \right. $ then the value of $a$ so that f is continuous at 0 is :

asked Oct 10, 2013 by meena.p

1 answer

$\lim \limits _{x \to \infty} \bigg(\large\frac{x+5}{x+2}\bigg)^{x+3}=$

asked Oct 10, 2013 by meena.p

1 answer

The radius of the sphere $x^2+y^2+z^2=12 x +4y+3z$ is :

asked Oct 10, 2013 by meena.p

1 answer

The image of the point $(3,2,1)$ in the plane $2x-y+3z=7$ is :

asked Oct 10, 2013 by meena.p

1 answer

If a line in the space makes angles $\alpha, \beta$ and $\gamma$ with the coordinate axes, then $ \cos 2 \alpha+ \cos 2 \beta+\cos 2 \gamma +\sin ^2 \alpha +\sin ^2 \beta+\sin ^2 \gamma=$

asked Oct 10, 2013 by meena.p

1 answer

The perimeter of the triangle with vertices at $(1,0,0),(0,1,0)$ and $(0,0,1)$ is :

asked Oct 10, 2013 by meena.p

1 answer

The eccentricity of the conic $\large\frac{5}{r}$$=2 + 3 \cos \theta+ 4 \sin \theta$ is :

asked Oct 10, 2013 by meena.p

1 answer

The mid point of the chord $4x-3y=5$ of the hyperbola $2x^2-3y^2=12$ is :

asked Oct 10, 2013 by meena.p

1 answer

If the circle $x^2+y^2=a^2$ intersects the hyperbola $xy=c^2$ in four points $(x_i,y_i),$ for $i=1,2,3$ and $4$, then $y_1+y_2+y_3+y_4=$

asked Oct 10, 2013 by meena.p

1 answer

If the distance between the foci of an ellipse is 6 and the length of the minor axis is 8, then the eccentricity is :

asked Oct 10, 2013 by meena.p

1 answer

The number of normals drawn to the parabola $y^2=4x$ from the point (1,0) is :

asked Oct 10, 2013 by meena.p

1 answer

The equation of the circle which passes through the origin and cuts orthogonally each of the circles $x^2+y^2-6x+8=0$ and $x^2+y^2-2x-2y=7$ is :

asked Oct 10, 2013 by meena.p

1 answer

The points (3,-4) lies on both the cirlces $x^2+y^2-2x+8y+13=0$ and $x^2+y^2-4x+6y+11=0.$ Then the angle between the circles is :

asked Oct 10, 2013 by meena.p

1 answer

Ask Questions, Get Answers