Recent questions tagged q10

The position $x$ of a particle at time $t$ is given by $x=\large\frac{v_0}{a} $$(1-e^{-at})$ where $v_0$ is constant and $a >0$ find the dimensions of $v_0$ and $a$

asked Jun 17, 2013 by meena.p

1 answer

The angle between the curves $\large\frac{x^{2}}{25}+\frac{y^{2}}{9}=$$1$ and $\large\frac{x^{2}}{8}-\frac{y^{2}}{8}=$$1$ is

asked May 15, 2013 by poojasapani_1

1 answer

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

asked May 7, 2013 by poojasapani_1

1 answer

Show that the equation of the normal to the curve $x=a\cos^{3}\theta ; y=a\sin^{3}\theta$ at $\;'\theta'$ is$\; x\cos\theta-y\cos\theta=a\cos 2\theta.$

asked May 3, 2013 by poojasapani_1

1 answer

Find the angle between the pairs of lines: $ \overrightarrow r = 3\hat i + \hat j - 2\hat k + \lambda (\hat i - \hat j - 2\hat k)\: and \: \overrightarrow r = 2\hat i - \hat j - 56\hat k + \mu (3\hat i - 5\hat j - 4\hat k) $

asked Apr 30, 2013 by rvidyagovindarajan_1

1 answer

Find the area of the circle whose radius is $a$ .

asked Apr 28, 2013 by poojasapani_1

1 answer

Evaluate the following problems using properties of integration: $\int\limits_{\large\frac{\pi}{6}}^{\large\frac{\pi}{3}}\large\frac{dx}{1+\sqrt{\tan x}}$

asked Apr 27, 2013 by poojasapani_1

1 answer

Evaluate the following problems using second fundamental theorem: $\int\limits_{0}^{1} x^{2} e^{x} dx$

asked Apr 27, 2013 by poojasapani_1

1 answer

Prove that every element a in Boolean algebra has a unique inverse.

asked Apr 22, 2013 by sreemathi.v

0 answers

$x,y$ and $z$ represent three switches in an position and $x^1,y^1$ and $z^1$ represent the three switches in an off position.Construct a switching circuit representing the polynomial $(x^1+y^1)(x+z^1)+y^1(y+z)$.Using the laws of Boolean algebra,show that the above polynomial is equivalent to $x^1z^1+y^1$ and construct an equivalent switching circuit.

asked Apr 22, 2013 by sreemathi.v

0 answers

If $a \; =\; cos \; 2\alpha \; + \; i \; sin \; 2\alpha , \; b \; =\; cos\; 2\beta + i\; sin\; 2\beta\; $ and $\;c\; = \; cos \; 2\gamma\; + \; i sin\; 2\gamma$ prove that $\frac{a^{2}b^{2}+c^{2}}{abc}\; = \; 2\; cos \; 2\left ( \alpha \;+\;\beta \;+\;\gamma \right )$

asked Apr 19, 2013 by geethradh

0 answers

If $a \; =\; cos \; 2\alpha \; + \; i \; sin \; 2\alpha , \; b \; =\; cos\; 2\beta + i\; sin\; 2\beta\; $ and $\;c\; = \; cos \; 2\gamma\; + \; i sin\; 2\gamma$ prove that $\sqrt{abc}\; + \; \frac{1}{\sqrt{abc}}\; = \; 2\; cos\left ( \alpha \;+\;\beta \;+\;\gamma \right )$

asked Apr 19, 2013 by geethradh

0 answers

A random variable $x$ has a probability density function $f(x) = \left\{ \begin{array}{l l} k & \quad \text{0<x<2n}\\ 0 & \quad \text{elsewhere} \end{array} \right.$ Find $p(\large\frac{\pi}{2}<x<\frac{3\pi}{2})$

asked Apr 19, 2013 by poojasapani_1

1 answer

A random variable $x$ has a probability density function $f(x) = \left\{ \begin{array}{l l} k & \quad \text{0<x<2n}\\ 0 & \quad \text{elsewhere} \end{array} \right.$ Find $p(0<x<\large\frac{\pi}{2})$

asked Apr 19, 2013 by poojasapani_1

1 answer

A random variable $x$ has a probability density function $f(x) = \left\{ \begin{array}{1 1} k & \quad 0 < x < 2n \\ 0 & \quad \text{else where} \end{array} \right.$ Find $k$

asked Apr 19, 2013 by poojasapani_1

1 answer

If a,b,c are elements of Boolean Algebra,prove that $ab+c(a'+b')=ab+c$.

asked Apr 19, 2013 by sreemathi.v

0 answers

Write the Boolean expression for the following circuit :

asked Apr 19, 2013 by sreemathi.v

0 answers

A discrete random variable $x$ has the following probability distributioxs. Find$ p(3$$<$$x$$<$$7)$\[\]$\begin{array} {llllllll} X:& 0& 1& 2& 3& 4& 5& 6& 7& 8 &\\ {P(X):}& a& 3a &5a& 7a& 9a &11a &13a &15a&17a \end{array}$

asked Apr 18, 2013 by poojasapani_1

1 answer

Find the least distance of the plane $12x+4y+3z=327$ from the sphere $x^2+y^2+z^2+4x-2y-6z=155.$

asked Apr 17, 2013 by sreemathi.v

0 answers

A plane passes through the point (4,2,4) and is perpendicular to the planes $2x+5y+4z+1=0$ and $4x+7y+6z+2=0$.Find the equation of the plane.

asked Apr 17, 2013 by sreemathi.v

1 answer

Show that the equation to a sphere passing through three points (2,0,0),(0,2,0) and (0,0,2) and having its centre on the plane $2x+3y+4z=27$ is $x^2+y^2+z^2-6x-6y-6z+8=0.$

asked Apr 17, 2013 by sreemathi.v

0 answers

Find the equations to be two planes passing through the points (0,4,-3) and (6,-4,3),if the sum of their intercepts on the three axes is zero.

asked Apr 17, 2013 by sreemathi.v

0 answers

Solve the following differential equation;$(D^{2}-6D+9)$$y=x+e^{2x}$

asked Apr 16, 2013 by poojasapani_1

1 answer

Prove that the plane $x+2y-z=4$ cuts the sphere $x^2+y^2+z^2-x+z-2=0$ in a circle whose radius is unity.

asked Apr 16, 2013 by sreemathi.v

0 answers

Find the equation of the plane through the point (1,2,3) and perpendicular to the planes $x+y+2z=3$ and $3x+2y+z=4$.

asked Apr 16, 2013 by sreemathi.v

0 answers

If $A(-1,4,-3)$ is one end of a diameter $AB$ of the sphere $x^2+y^2+z^2-2y+2z-15=0$ then find the coordinates of the other end point B.

asked Apr 15, 2013 by sreemathi.v

0 answers

Find the coordinates of the point where the line joining the points (1,-2,3) and (2,-1,5) cuts the plane $x-2y+3z=19$.Hence,find the distance of this point from the point (5,4,1).

asked Apr 15, 2013 by sreemathi.v

0 answers

Find the equation of the sphere which passes through the circle $x^2+y^2-6z-4=0,x+2y+2z=0$ and whose centre lies on the plane $2x-y+z=1.$

asked Apr 12, 2013 by sreemathi.v

0 answers

Find the equation of the plane which contains the line $\large\frac{x-1}{2}=\large\frac{y+1}{-1}=\large\frac{z-3}{4}$ and is perpendicular to the plane $x+2y+z=12.$

asked Apr 12, 2013 by sreemathi.v

0 answers

In any $\Delta ABC$,prove by vector method that $\cos B=\large\frac{c^2+a^2-b^2}{2ca}$.

asked Apr 12, 2013 by sreemathi.v

0 answers

Find the value of $\lambda$ for which the four points with position vectors $2\hat{i}+5\hat{j}+\hat{k},-\hat{j}-4\hat{k},3\hat{i}+\lambda\hat{j}+8\hat{k}$ and $-4\hat{i}+3\hat{j}+4\hat{k}$ are coplanar.

asked Apr 12, 2013 by sreemathi.v

2 answers

If D,E,F are mid-points of the sides of a triangle ABC,Prove by vector method that : Area of ADEF=$\frac{1}{4}$(Area of $\Delta$ABC).

asked Apr 11, 2013 by sreemathi.v

0 answers

Prove that : $\begin{bmatrix}\overrightarrow{a}+\overrightarrow{b}& \overrightarrow{b}+\overrightarrow{c}&\overrightarrow{c} +\overrightarrow{a}\end{bmatrix}=2\begin{bmatrix}\overrightarrow{a}&\overrightarrow{b}&\overrightarrow{c}\end{bmatrix}$

asked Apr 11, 2013 by sreemathi.v

0 answers

The arch of a bridge is in the shape of a semi-ellipse having a horizontal span of $40ft$ and $16ft$ high at the centre. How high is the arch $9ft$ from the right or left of the centre .

asked Apr 11, 2013 by poojasapani_1

1 answer

In any triangle ABC,prove by vector method : $\large \frac{a}{sin\;A}=\frac{b}{sin\;B}=\frac{c}{sin\;C}$

asked Apr 10, 2013 by sreemathi.v

0 answers

For any three vectors $\overline{a},\overline{b},\overline{c}$ prove :$[\;\overline{a}-\overline{b}\;\overline{b}-\overline{c}\;\overline{c}-\overline{a}\;]=0.$

asked Apr 10, 2013 by sreemathi.v

0 answers

Find the vector and cartesian equations of the plane passing through the points $ A(1 , -2 , 3 )$ and $B(-1 , 2 , -1 )$ and is parallel to the line $ \large\frac{x-2}{2}=\frac{y+1}{3}=\frac{z-1}{4}.$

asked Apr 8, 2013 by poojasapani_1

1 answer

Prove that $(\overrightarrow{a}\times\overrightarrow{b}) . (\overrightarrow{c}\times\overrightarrow{d}) + (\overrightarrow{b}\times\overrightarrow{c}) . (\overrightarrow{a}\times\overrightarrow{d}) + (\overrightarrow{c}\times\overrightarrow{a}) . (\overrightarrow{b}\times\overrightarrow{d})=0$

asked Apr 6, 2013 by poojasapani_1

1 answer

Find the magnitude and direction cosines of the moment about the point $(1, -2 ,3)$ of a force $\overrightarrow{2i}+\overrightarrow{3j}+\overrightarrow{6k}$ Whose line of action passes through the origin.

asked Apr 5, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}\times \overrightarrow{b}= \overrightarrow{C}\times \overrightarrow{d}$ and $\overrightarrow{a}\times \overrightarrow{c}=\overrightarrow{b}\times\overrightarrow{d},$ show that $\overrightarrow{a}- \overrightarrow{d}$ and $\overrightarrow{b}-\overrightarrow{c}$ are parallel.

asked Apr 4, 2013 by poojasapani_1

1 answer

If$|\overrightarrow{a}+\overrightarrow{b}|=60, |\overrightarrow{a}-\overrightarrow{b}|=40$ and $|\overrightarrow{b}|=46$ find$|\overrightarrow{a}|.$

asked Apr 3, 2013 by poojasapani_1

1 answer

A small seminar hall can hold 100 chairs.Three different colours(red,blue and green) of chairs are available. The cost of a red chair is Rs.240, cost of a blue chair is Rs.260, and the cost of a green chair is Rs.300. The total cost of chair is Rs.25,000. Find atleast 3 different solution of the number of chairs in each colour to be purchased.

asked Mar 29, 2013 by poojasapani_1

1 answer

For $A=\begin{bmatrix} -1 & 2 & -2 \\4 & -3 & 4 \\4 & -4 & 5 \end{bmatrix}$ show that $A=A^{-1}$

asked Mar 29, 2013 by poojasapani_1

1 answer

L and M are two points with position vectors $2\overrightarrow{a}-\overrightarrow{b}$ and $\overrightarrow{a}+2\overrightarrow{b}$ respectively.Write the position vector of a point N which divides the line segment LM in the ratio 2 : 1 externally.

asked Mar 22, 2013 by sreemathi.v

1 answer

A and B are two points with position vectors $2\overrightarrow{a}-3\overrightarrow{b}$ and $6\overrightarrow{b}-\overrightarrow{a}$ respectively.Write the position vector of a point P which divides the line segment AB internally in the ratio 1 : 2.

asked Mar 22, 2013 by sreemathi.v

1 answer

The money to be spent for the welfare of the employees of a firm is proportional to the rate of change of its total revenue (marginal revenue).If the total revenue(in rupees) received from the sale of Xunits of a product is given by R(x)=$3x^2+36x+5$,find the marginal revenue,when x=5,and write which value does the question indicate.

asked Mar 20, 2013 by sreemathi.v

1 answer

Find which of the operations given below has identity:$(vi)\;\; a \ast b = ab^2$

asked Mar 19, 2013 by meena.p

1 answer

Find which of the operations given below has identity:$(v)\;\; a \ast b = \large\frac {ab} {4}$

asked Mar 19, 2013 by meena.p

1 answer

Find which of the operations given below has identity: $(iv)\;\; a \ast b = (a-b)^2$

asked Mar 19, 2013 by meena.p

1 answer

Find which of the operations given below has identity: $(iii)\;\; a \ast b = a+ab$

asked Mar 19, 2013 by meena.p

1 answer

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