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Recent questions tagged sec-c

Solve the differential equation : $ (x+y)\large\frac{dy}{dx}$$-2e^{-y}\: where \: x=0, \: when \: y=0. $

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Solve the differential equation : $ (1+e^{\large\frac{x}{y}})dx+e^{\large\frac{x}{y}} \bigg( 1- \large\frac{x}{y} \bigg)$$ dy=0$

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Show that the lines : $\large\frac{x-5}{4} = \frac{y-7}{4}=\frac{z+3}{-5}$ and $\large \frac{x-8}{7} = \frac{y-4}{1}=\frac{z-5}{3}$ intersect.

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Kellogg is a new cereal fromed of a mixture of bran and rice that contains at least 88 g of protein and at least 36 milligram of iron. Knowing that bran contains 80 g of protein and 40 milligram of iron per kilogram, and that rice contains 100 g of protein and 30 milligrams of iron per kilogram, find the minimum cost of producing this new cereal if bran costs Rs.5 per kilogram and rice costs Rs. 4 per kilogram.

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Let X denote the number of hours you study during a randomly selected school day. The probability that X can take the values X has the following form, where k is some unknown constant. \[ p(X=x) = \left\{ \begin{array}{l l}0.1, & \quad if{ x = 0}\\ kx, & \quad if{ x = 1 \: or\: 2} \\ k(5-x), & \quad if{ x = 3 \: or\: 5} \\ 0, & \quad \: otherwise \end{array}. \right. \] (i) Find the value of K (ii) What is the probability that you study atleast two hours? Exactly two hours? Atmost two hours?

asked Jan 30, 2013 by thanvigandhi_1

1 answer

A wire of length 36 cm is cut into two pieces. One of the pieces is turned in the form of a square and the other in the form of an equilateral triangle. Find the length of each piece so that the sum of the areas of the two be minimum.

asked Jan 29, 2013 by fingeazy

1 answer

Solve the following system of equation by matrix method : $ u-2v+w=1, 2u+v+w=1 , u+v-2w=-2 $

asked Jan 29, 2013 by thanvigandhi_1

1 answer

Find the area of the smaller region bounded by the ellipse $\large\frac{x^2}{a^2}+\large\frac{y^2}{b^2}$$=1$ and the straight line $\large\frac{x}{a}+\frac{y}{b}$$=1$.

asked Jan 29, 2013 by thanvigandhi_1

0 answers

Find the area of the region $ \{(x,y); x^2+y^2 \leq 1 \leq x+y \}.$

asked Jan 28, 2013 by thanvigandhi_1

0 answers

A window is in the form of rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum sunlight through the whole opening.

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Evaluate : $\int_0^{\pi} \cos 2x\log\sin\:x\: dx $

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \large\frac{\sin x}{\sin 4x}$$dx$

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Find the equation of the line passing through the point (-1, 3, -2) and perpendicular to each of the lines $ \large\frac{x}{1} = \frac{y}{2} = \frac{z}{3}$ and $\large\frac{x+2}{-3} = \frac{y-1}{2} = \frac{z+1}{5} $. Also, find its vector equation.

asked Jan 28, 2013 by thanvigandhi_1

0 answers

A company sells two different products A and B. The two products are produced in a common production process, which has a total capacity of 500 man-hours. It takes 5 hours to produce a unit of A and 3 hours to produce a unit of B. The market has been surveyed and company officials feel that the maximum number of units of A that can be sold is 70 and that of B is 125. If the profit is Rs.20 per unit for the product A and Rs.15 per unit for the product B, how many units for each product should be sold to maximize profit.

asked Jan 28, 2013 by thanvigandhi_1

0 answers

There are 40 workers in a factory who are participating in strike for increase in wages. Out of them 5 workers are sincere to management and believe that management know each thing and do the needful. Management selects 2 workers at random out of them. Write the probability distribution for the selected worker who are sincere. Also find the mean of the distribution.

asked Jan 28, 2013 by thanvigandhi_1

0 answers

For the matrix \( A= \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & -3 \\ 2 & -1 & 3 \end{bmatrix} \), show that \( A^3-6A^2+5A+11I=0.\) Hence, find \(A^{-1}.\)

asked Jan 27, 2013 by thanvigandhi_1

0 answers

Prove that the area of a right-angled triangle of given hypotenuse is maximum when it is isosceles.

asked Jan 27, 2013 by thanvigandhi_1

0 answers

Find the maximum area of an isosceles triangle inscribed in the ellipse $ \large\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ with its vertex at one end of the major axis.

asked Jan 27, 2013 by thanvigandhi_1

0 answers

Find the area of the region bounded by the parabola \( y=x^2+1\) and the lines \( y=x,x=0 \: and \: x=2.\)

asked Jan 27, 2013 by thanvigandhi_1

0 answers

Prove that $ \int_0^{\large\frac{\pi}{2}} ( \sqrt{\tan\:x}+ \sqrt{\cot\:x})dx= \sqrt2 \pi $

asked Jan 27, 2013 by thanvigandhi_1

0 answers

Find the equation of plane through the intersection of the plane \( x+y+z=9 \: and \: 2x+3y+4z+5=0 \) and passing through the point (1,1,1).

asked Jan 27, 2013 by thanvigandhi_1

0 answers

Find the shortest distance between the lines $\large \frac{x-8}{3} = \frac{y+9}{-16}=\frac{z-10}{7}$ and $\large\frac{x-15}{3}=\frac{y-29}{8}=\frac{z-5}{-5} $ Also, find equation of the line of shortest distance.

asked Jan 27, 2013 by thanvigandhi_1

0 answers

If a young man rides his motorcycle at 25 km/hour, he had to spend Rs.2 per km on petrol. If he rides at a faster speed of 40 km/hour, the petrol cost increases at Rs.5 per km. He has Rs.100 to spend on petrol and wishes to find what is the maximum distance he can travel within one hour. Express this as L.P.P. and solve it graphically.

asked Jan 27, 2013 by thanvigandhi_1

1 answer

Assume that the chances of a patient having a heart attack is 40%. It is assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chance by 25%. At a time, a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?

asked Jan 27, 2013 by thanvigandhi_1

1 answer

If \( A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \\ \end{bmatrix} \), prove that $A^n = \begin{bmatrix} 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \\ \end{bmatrix} $, for \( n \in N.\)

asked Jan 27, 2013 by thanvigandhi_1

1 answer

The sum of three numbers is -1. If we multiply second number by 2, third number by 3 and add them, we get 5. If we subtract third number from the sum of first and second number, we get -1. Represent the information by the system of equation and find the number using inverse of a matrix.

asked Jan 26, 2013 by thanvigandhi_1

0 answers

A point on the hypotenuse of a right-angled triangle is at distances a and b from the sides. Show that length of the hypotenuse is at least \( (a^{\large\frac{2}{3}}+b^{\large\frac{2}{3}})^{\large\frac{3}{2}} \)

asked Jan 26, 2013 by thanvigandhi_1

0 answers

Show that semi-vertical angle of the right circular cone of given total surface area and maximum volume is \( sin^{-1}\frac{1}{3} \)

asked Jan 26, 2013 by thanvigandhi_1

0 answers

Find the area enclosed between the parabolas \( y^2=4ax\: and \: x^2=4ay\)

asked Jan 26, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_0^{\Large\frac{\pi}{4}} \large\frac{\sin x \: \cos x}{\cos^4x+sin^4x}$$dx $

asked Jan 26, 2013 by thanvigandhi_1

0 answers

From the distance of the point (2,3,4) from the line \( \large\frac{x+3}{3} = \frac{y-2}{6} = \frac{z}{2} \) measured parallel to the plane $3x+2y+2z+5=0.$

asked Jan 26, 2013 by thanvigandhi_1

0 answers

A company makes two kinds of belts, belt A is of pure leather and belt B is macro based. The respective profits are Rs.40 and Rs.30 per belt. Each belt of type A requires twice as much time as a belt of type B and if all the belts were of type B a company could make 1000 belts per day. The supply of leather and macro is sufficient for only 8000 belts per day (both A and B combined). Belt A requires a fancy buckle and only 4000 buckles are available. There are only 7000 buckles per day available for belt B. What should be the daily production of each belt to have maximum profit?

asked Jan 26, 2013 by thanvigandhi_1

1 answer

A card from a pack of 52 playing cards is lost. Two cards are drawn from the remaining cards and found to be both spade. (i) Find the probability of lost card being a spade card.(ii)While playing in ground you found a purse containing rupees and some other documents,what will you do?

asked Jan 25, 2013 by thanvigandhi_1

1 answer

A one hour routine check was made by security staff of MNC from \(\large \frac{1}{2} \) hour before office opening time. Total 80 cars are checked and result was 9 cars carrierd no official, 20 cars carried one official, 16 cars carried 2 officials, 20 cars carried 3 officials and 15 cars carried 4 officials. (i) Using this information, write down a row matrix and a column whose product gives us the total number of official carried by the 80 cars. (ii) What was the average number of official per car?

asked Jan 25, 2013 by thanvigandhi_1

0 answers

A wire of length 30 cm is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What could be the lengths of two peices, so that the combined area of the square and the circle is minimum?

asked Jan 25, 2013 by thanvigandhi_1

0 answers

An open box with a square base is to be made out of given quantity of sheet of area \( a^2 \). Show that maximum volume of the box is \( \large\frac{a^3}{6\sqrt3}.\)

asked Jan 25, 2013 by thanvigandhi_1

0 answers

Evalaute : $ \int \sqrt{\large\frac{sin(x-\alpha)}{sin(x+\alpha)}}$$dx $

asked Jan 25, 2013 by thanvigandhi_1

0 answers

Evalaute : $\int \large\frac{1}{\sin^2x+\sin2x}$$dx. $

asked Jan 25, 2013 by thanvigandhi_1

0 answers

Find the area of the circle \( 4x^2+4y^2\) which is interior to the parabola \( x^2=4y \).

asked Jan 25, 2013 by thanvigandhi_1

0 answers

Find the image of (1, 6, 3) in the line \( \large\frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}. \)

asked Jan 25, 2013 by thanvigandhi_1

0 answers

Akshay throw a die again and again until three fours are obtained. Find the probability of obtaining the third four in the sixth throw of die by Akshay.

asked Jan 25, 2013 by thanvigandhi_1

0 answers

A diet is to contain at least 80 units of minerals. Two foods \( F_1 \: and F_2\)are available. Food \( F_1 \) costs Rs.4 per unit food and \( F_2 \) costs Rs.6 per unit. A unit of food \( F_1 \) contains atleast 3 units of vitamin A and 4 units of minerals. A unit of food \( F_2 \)contains atleast 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find the minimum cost for diet that consists of mixture of these two foods, and also meets the minimal nutritional requirements.

asked Jan 25, 2013 by thanvigandhi_1

0 answers

Using elementary transformations, find the inverse of the matrix : $\begin{bmatrix} 2 & -1 & 4 \\ 4 & 0 & 2 \\ 3 & -2 & 7 \end{bmatrix}$

asked Jan 24, 2013 by thanvigandhi_1

0 answers

Using matrices, solve the following system of linear equations : $ 2x+y+z=2,x+3y-z=5, 3x+y-2z=6$

asked Jan 24, 2013 by thanvigandhi_1

1 answer

A window is in the form of rectangle above which there is a semi circle. If the perimeter of window is p units, show that the window will allow maximum light, when radius of the semicircle is \( \large\frac{p}{\pi + 4} \) units.

asked Jan 24, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_0^{\Large\frac{\pi}{2}}\large \frac{dx}{5+4\sin x} $

asked Jan 24, 2013 by thanvigandhi_1

0 answers

Find the equation of the plane passing through the points (1,2,3) and (0,-1,0) and parallel to the line $\large \frac{x-1}{2} = \frac{y+2}{3} = \frac{z}{-32}.$

asked Jan 24, 2013 by thanvigandhi_1

0 answers

Using integration, find the area of triangle PQR, whose vertices are P(3, 0)Q(4, 5) and R(5, 1).

asked Jan 24, 2013 by thanvigandhi_1

0 answers

A farmer has a supply of chemical fertilizer of type A which contains 10% nitrogen and 6% phosphoric acid, and type B which contains 5% nitrogen and 10% phosphoric acid. After testing the soil conditions of the field, it was found that ateast 14 kg of nitrogen and 14 kg of phosphoric acid is required for producing a good crop. The fertilizer of type A costs Rs. 2 per kg and the type B costs Rs.3 per kg. How many kg of each type of the fertilizer should be used to meet the requirement at the minimum problem graphically.

asked Jan 24, 2013 by thanvigandhi_1

0 answers

There are 20% chances for a worker of an industry to suffer from an occupational disease, 50 workers were selected at random and examined for the ocupational disease. Find the probabilty that (i) None is suffering from the disease. (ii) Only one is suffering from the disease.

asked Jan 24, 2013 by thanvigandhi_1

0 answers

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