Recent questions tagged 2013

The management committee of a residential colony decided to award some of its members (say x) for honesty,some (say y) for helping others and some others (say z) for supervising the workers to keep the colony neat and clean . The sum of all the awardees is 12. Three times the sum of awardees for cooperation and supervision added in two times the number of awardees for honesty is 33. If the sum of the number of awardees for honesty and supervision is twice the number of awardees for helping others, using matrix method, find the number of awardees of each category. Apart from these values, namely, honesty, cooperation and supervision, suggest one more value which the management of the colony must include for awards.

asked Mar 20, 2013 by sreemathi.v

1 answer

If Matrix A = $\begin{bmatrix} 1 &-1 \\ -1 & 1 \end{bmatrix}$, and $A^2=kA$, then write the value of $k$.

asked Mar 20, 2013 by balaji.thirumalai

1 answer

A manufacturer considers that man and women workers are equally efficient and so he pays them at the same rate.He has 30 and 17 units of workers(male and female) and capital respectively,which he uses to produce two types of goods A and B.To produce 1 unit of A,2 workers and 3 units of capital are required while 3 workers and 1 unit of capital is required to produce 1 unit of B.If A and B are priced at Rs100 and 120 per unit respectively,how should he use his resources to maximize the total revenue?Form the above as an LPP and solve graphically.Do you agree with this view of the manufacturer that men and women workers are equally efficient and so should be paid at the same rate?

asked Mar 20, 2013 by sreemathi.v

0 answers

In a hockey match,both teams A and B scored same number of goals up to the end of the game,so to decide the winner ,the referee asked both the captains to throw a die alternately and decided that the team,whose captain gets a six first,will be declared the winner.If the captain of team A was asked to start,find their respective probabilities of winning the match and state whether the decision of the referee was fair or not.

asked Mar 20, 2013 by sreemathi.v

1 answer

Find the vector equation of the line passing through the point (1,2,3) and parallel to the planes $\overrightarrow{r}.(\hat{i}-\hat{j}+2\hat{k})=5$ and $\overrightarrow{r}.(3\hat{i}+\hat{j}+\hat{k})=6.$

asked Mar 20, 2013 by sreemathi.v

1 answer

Find the equation of the plane passing through the line of intersection of the planes $\overrightarrow{r}.(\hat{i}+3\hat{j})-6=0$ and $\overrightarrow{r}.(3\hat{i}-\hat{j}-4\hat{k})=0$,whose perpendicular distance from origin is unity.

asked Mar 20, 2013 by sreemathi.v

1 answer

Find the particular solution of the differential equation $(\tan^{-1}y-x)dy=(1+y^2)dx$,given that when x=0,y=0.

asked Mar 20, 2013 by sreemathi.v

1 answer

Find the area of the region bounded by the parabola $y=x^2$ and y=| x |.

asked Mar 20, 2013 by sreemathi.v

1 answer

Find the equations of tangents to the curve $3x^2-y^2=8$,which pass through the point$\big(\frac{4}{3},0\big)$. (Note: This question has been split into 2 questions)

asked Mar 20, 2013 by sreemathi.v

1 answer

Find the area of the greatest rectangle that can be inscribed in an ellipse $\Large \frac{x^2}{a^2}+\frac{y^2}{b^2}\normalsize = 1.$

asked Mar 20, 2013 by sreemathi.v

1 answer

The probabilities of two students A and B coming to the school in time are $\frac{3}{7}$ and $\frac{5}{7}$ respectively.Assuming that the events,'A coming in time' and 'B coming in time' are independent ,find the probability of only one of them coming to the school in time.Write at least one advantage of coming to school in time.

asked Mar 20, 2013 by sreemathi.v

1 answer

Find the vector equation of the plane through the points (2,1,-1) and (-1,3,4) and perpendicular to the plane x-2y+4z=10.

asked Mar 20, 2013 by sreemathi.v

1 answer

Show that the lines $\begin{array}{1 1}\overrightarrow{r}=3\hat{i}+2\hat{j}-4\hat{k}+\lambda(\hat{i}+2\hat{j}+2\hat{k});\\\overrightarrow{r}=5\hat{i}-2\hat{j}+\mu(3\hat{i}+2\hat{j}+6\hat{k})\end{array} $ are intersecting. Hence find their point of intersection.

asked Mar 20, 2013 by sreemathi.v

1 answer

If $\overrightarrow{a}=\hat{i}-\hat{j}+7\hat{k}$ and $\overrightarrow{b}=5\hat{i}-\hat{j}+\lambda\hat{k}$,then find the value of $\lambda$,so that $\overrightarrow{a}+\overrightarrow{b}$ and $\overrightarrow{a}-\overrightarrow{b}$ are perpendicular vectors.

asked Mar 20, 2013 by sreemathi.v

1 answer

Evaluate :$\int\limits_0^{2{\pi}}\large\frac{1}{1+e^{sin x}}$$dx$

asked Mar 20, 2013 by sreemathi.v

1 answer

Evaluate :$\int \large \frac{dx}{x(x^5+3)}$

asked Mar 20, 2013 by sreemathi.v

1 answer

Evaluate:$\large \int\frac{x+2}{\sqrt{x^2+2x+3}}$dx

asked Mar 20, 2013 by sreemathi.v

1 answer

Evaluate: $\int\large \frac{cos 2x-cos 2\alpha}{cos x-cos\alpha}$$dx$

asked Mar 20, 2013 by sreemathi.v

1 answer

If x=$acos^3\theta$ and y=$asin^3\theta,$then find the value of $\Large \frac{d^2y}{dx^2}$ at $ \theta=\Large \frac{\pi}{6}$.

asked Mar 20, 2013 by sreemathi.v

1 answer

Find the value of k, for which $f(x) =\left\{\begin{array}{1 1}\frac{\sqrt{1+kx}-\sqrt{1-kx}}{x}, & if\;-1\leq x<0\\\frac{2x+1}{x-1}, & if\;0\leq x<1\end{array}\right.$ is continuous at x=0.

asked Mar 20, 2013 by sreemathi.v

1 answer

Differentiate the following with respect to $x: \sin^{-1}\bigg(\large \frac{2^{x+1}.3^x}{1+(36)^x}\bigg)$

asked Mar 20, 2013 by sreemathi.v

1 answer

If $y^x=e^{y-x}$,prove that $\large \frac{dy}{dx}=\frac{(1+log y)^2}{log y}$

asked Mar 20, 2013 by sreemathi.v

1 answer

Using properties of determinants,prove the following $\begin{vmatrix}x& x+y & x+2y\\x+2y & x & x+y\\x+y & x+2y & x\end{vmatrix}=9y^2(x+y)$

asked Mar 20, 2013 by sreemathi.v

1 answer

Solve the following equation :$\cos\big(tan^{-1}x\big)=sin\bigg(cot^{-1}\frac{3}{4}\bigg)$

asked Mar 20, 2013 by sreemathi.v

1 answer

Show that: $tan\bigg(\frac{1}{2}sin^{-1}\frac{3}{4}\bigg)=\frac{4-\sqrt 7}{3}$

asked Mar 20, 2013 by sreemathi.v

1 answer

Consider $( f:R_+ \to [4,\infty)$ given by $(f(x)=x^2 +4)$. Show that $(f)$ is invertible with the inverse $(f^{-1})$ of $(f)$ given by $(f^{-1}(y) = \sqrt {y-4})$,where $R_+$ is the set of all non-negative real numbers.

asked Mar 20, 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 the length of the perpendicular drawn from the origin to the plane 2X-3Y+6Z+21=0.

asked Mar 20, 2013 by sreemathi.v

1 answer

Find $\mid\overrightarrow{x}\mid$,if for a unit vector $\overrightarrow{a},(\overrightarrow{x}-\overrightarrow{a}).(\overrightarrow{x}+\overrightarrow{a})=15.$

asked Mar 20, 2013 by sreemathi.v

1 answer

P and Q are two points with position vectors $3\overrightarrow{a}-2\overrightarrow{b}$ and $\overrightarrow{a}+\overrightarrow{b}$ respectively.Write the position vector of a point R which divides the line segment PQ in the ratio 2 : 1 externally.

asked Mar 20, 2013 by sreemathi.v

1 answer

If $A_{ij}$ is the cofactor of the element $a_{ij}$ of the determinant $\begin{vmatrix}2 & -3 & 5\\6 & 0 & 4\\1 & 5 & -7\end{vmatrix}$,then write the value of $a_{32}.A_{32}$.

asked Mar 20, 2013 by sreemathi.v

1 answer

Write the differential equation representing the family of curves y=mx,where m is an arbitrary constant.

asked Mar 20, 2013 by sreemathi.v

1 answer

For what value of x, is the matrix A=$\begin{bmatrix}0 & 1 & -2\\-1 & 0 & 3\\x & -3 & 0\end{bmatrix}$ a skew-symmetric matrix?

asked Mar 20, 2013 by sreemathi.v

1 answer

Write the value of $\tan^{-1}\begin{bmatrix}2\sin\bigg(2\cos^{-1}\frac{\sqrt 3}{2}\bigg)\end{bmatrix}$

asked Mar 20, 2013 by sreemathi.v

1 answer

Write the principal value of $\tan^{-1}(\sqrt 3)-cot^{-1}(-\sqrt 3).$

asked Mar 20, 2013 by sreemathi.v

1 answer

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