Recent questions tagged sec-c

From the point P(1, 2, 4 ) a perpendicular is drawn on the plane $ 2x+y-2z+3 = 0 $. Find the equation of the length and coordinates of the foot of the $ \bot $

asked Jan 2, 2013 by thanvigandhi_1

1 answer

A farmer mixes two brands P and Q of cattle feed. Brand P costing Rs. 200 per bag contains 1.5 units of nutritional element A, 11.25 units of element B and 3 units of element C . The minimum requirements of nutrients A, B and C are 18 units, 45 units and 24 units, respectively. Determine the number of bags of each brand which should be mixed in order to produce a mixture having a minimum cost per bag? What is the minimum cost of the mixture per bag?

asked Jan 2, 2013 by thanvigandhi_1

0 answers

Suppose, we have four boxes A, B, C and D containing coloured marbles as given below : One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A? box B? and box C?

asked Jan 2, 2013 by thanvigandhi_1

0 answers

Show that the height of the cylinder of maximum volume that can be inscribed in a cone of height h is $ \large\frac{1}{3} $ h.

asked Dec 29, 2012 by thanvigandhi_1

0 answers

A manufacturer can sell x items at a price of Rs. $ \bigg( 5 - \large \frac{x}{100} \bigg) $ each. The cost price of x items is Rs. $ \bigg( \large\frac{x}{5}$$ + 500 \bigg) $. Find the number of items he should sell to earn the maximum profit.

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Prove that the curves $ y^2 = 4x$ and $ x^2 = 4y$ divide the area of the square bounded by $ x = 0, x = 4, y = 4$ and $y = 0$ into three equal parts.

asked Dec 29, 2012 by thanvigandhi_1

0 answers

An open box is to be constructed by removing equal squares from each corner of a 3 metre by 8 metre rectangular sheet of aluminium and folding up the sides. Find the volume of the largest such box.

asked Dec 29, 2012 by thanvigandhi_1

1 answer

If $ A = \begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end {bmatrix} $, find $ A^{-1} $ . Using $ A^{-1} $ , solve the system of equations : $ 2x – 3y + 5z = 11 ,3x + 2y – 4z = –5 ,x + y – 2x = –3. $

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Evaluate : $ \int\: \large\frac{dx}{(x^2-3x+2) \sqrt {x-1}} $

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Using elementary transformation, find the inverse of $\begin{bmatrix} 1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0 \end{bmatrix} $

asked Dec 29, 2012 by thanvigandhi_1

1 answer

Evaluate : $ \int_0^1 \: \sin^{-1} (x \sqrt{1-x} - \sqrt x \sqrt {1-x^2} ) dx, 0 \leq \: x \leq \: 1. $

asked Dec 29, 2012 by thanvigandhi_1

0 answers

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

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Evaluate :$ \int \: \sqrt {\large\frac{1- \sqrt x}{1+ \sqrt x}}$$ dx $

asked Dec 29, 2012 by thanvigandhi_1

0 answers

A helicopter is flying along the curve $ y = x^2 + 2$. A soldier is placed at the point (3, 2) . Find the nearest distance between the soldier and the helicopter.

asked Dec 29, 2012 by thanvigandhi_1

0 answers

A manufacturer can sell x items at a price of Rs. $ \bigg( 5-\large\frac{x}{100} \bigg) $ each. The cost price of x items is Rs. $ \bigg( \large\frac{x}{5} - \normalsize 500 \bigg) $. Find the number of items he should sell to earn maximum profit.

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Using matrices, solve the following system of equations : $ \begin{array} xx+y+z=6 & x+2z=7 & 3x+y+z = 12 \end{array} $

asked Dec 29, 2012 by thanvigandhi_1

0 answers

If the sum of the lengths of the hypotenuse and a side of a right angled triangle is given, show that the area of traingle is maximum when the angle between them is $ \large\frac{\pi}{3} $.

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Find the area of the smaller region bounded by the ellipse $ \large\frac{x^2}{9} + \frac{y^2}{4} = $$1$ and the straight line $ \large\frac{x}{2}+\frac{y}{2} = 1. $

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Show that the general solution of the differential equation $\large \frac{dy}{dx}+\frac{y^2+y+1}{x^2+x+1}\normalsize=0$ is given by $ x+y+1 = A(1-x-y-2xy)$, where A is parameter.

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Find the equation of plane determined by the points A(3, -1, 2), B(5, 2, 4) and C(-1, -1, 6). Also find the distance of the point P(6, 5, 9) from the plane.

asked Dec 29, 2012 by thanvigandhi_1

1 answer

A merchant plans to sell two types of personal computer - a desk top model and a portable model that will cost Rs. 25,000 and Rs. 40,000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get a maximum profit if he does not want to invest more than 70 lakh and if his profit on the desktop model is Rs. 4,500 and the portable is Rs. 5,000.

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Assume that the chance of a patient having a heart attack 40%. It is also assumed that a meditation and yoga course reduces the risk of heart attack by 30% and prescription of a certain drug reduces its chance by 25%. At a time a patient can choose any one of the two option 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 Dec 29, 2012 by thanvigandhi_1

0 answers

Using properties of determinants, show that $ \Delta = \begin{bmatrix} (a+b)^2 & ab & ca \\ ab & (a+b)^2 & bc \\ ac & bc & (a+b)^2 \end{bmatrix} = 2abc\: (a + b + c )^3 $

asked Dec 28, 2012 by thanvigandhi_1

0 answers

The sum of the perimeter of a circle and a square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.

asked Dec 28, 2012 by thanvigandhi_1

0 answers

Given $A=\begin{bmatrix}2 & 2 & 4\\4 & 2 & 4\\2 & 1 & 5\end{bmatrix},B=\begin{bmatrix}1 & 1 & 0\\2 & 3 & 4\\0 & 1 & 2\end{bmatrix}$,find BA and use this to solve the system of equations y+2z=7,x-y=3,2x+3y+4z=17

asked Dec 26, 2012 by sreemathi.v

1 answer

Using matrix method ,solve the system of equations 3x+2y-2z=3,x+2y+3z=6,2x-y+z=2.

asked Dec 26, 2012 by sreemathi.v

1 answer

If $A=\begin{bmatrix}1 & 2 & 0\\-2 & -1 & -2\\0 & -1 & 1\end{bmatrix},find\;A^{-1}.$\[Using\;A^{-1}, solve\; the\; system\; of\; linear\; equations\; x-2y=10,2x-y-z=8,-2y+Z=7.\]

asked Dec 26, 2012 by sreemathi.v

1 answer

Find $A^{-1}$ if $A=\begin{bmatrix}0 & 1 & 1\\1 & 0 & 1\\1 & 1 & 0\end{bmatrix}$ and show that $ A^{-1}=\Large \frac{A^2-3I}{2}$

asked Dec 26, 2012 by sreemathi.v

1 answer

show that the $\Delta$ABC is an isosceles triangle if the determinant\[\Delta=\begin{bmatrix}1 & 1& 1\\1+\cos A & 1+\cos B & 1+\cos C\\\cos^2A+\cos A & \cos^2B+\cos B & \cos^2C+\cos C\end{bmatrix}=0\]

asked Dec 26, 2012 by sreemathi.v

1 answer

Evaluate : $\int \large\frac{1}{\sin x (5-4\cos x )}$$ dx$

asked Dec 26, 2012 by thanvigandhi_1

0 answers

Using integration, find the area of the region $ \{ (x,y) : | x - 1 | \leq y \leq \sqrt {5-x^2} \} $

asked Dec 26, 2012 by thanvigandhi_1

0 answers

Show that the lines $ \large\frac{x+3}{-3} = \frac{y-1}{1} = \frac{z-5}{5} $ and $\large \frac{x+1}{-1} = \frac{y-2}{2} = \frac{z-5}{5} $ are coplanar. Also find the equation of the plane.

asked Dec 26, 2012 by thanvigandhi_1

1 answer

From a pack of 52 cards, a card is lost. Fro the remaining 51 cards, two cards are drawn at random ( without replacement ) and are found to be both diamonds. What is the probability that the lost card was a card of heart?

asked Dec 26, 2012 by thanvigandhi_1

0 answers

A diet for a sick person must contain at least 4000 units of vitamins, 50 units of minerals and 1400 calories. Two foods X and Y are available at a cost of Rs.4 and Rs.3 per unit respectively. One unit of food X contains 200 units of vitamins, 1 unit of minerals and 40 calories, whereas 1 unit of food Y contains 100 units of vitamins, 2 units of minerals and 40 calories. Find what combination of foods X and Y should be used to have atleast cost, satisfying the requirements. Make it an LPPand solve it graphically.

asked Dec 26, 2012 by thanvigandhi_1

0 answers

A fair die is rolled up. If 1 turns up, a ball is picked up at random from bag A. If 2 0r 3 turns up, a ball is picked up at random from bag B, otherwise a ball is picked up from bag C. Bag A contains 3 red and 2 white balls, bag B contains 3 red and 5 white balls and bag C contains 4 red and 5 white balls. The die is rolled, a bag is picked up and a ball is drawn from it. If the ball drawn is red, what is the probability that bag B was picked up?

asked Dec 26, 2012 by thanvigandhi_1

1 answer

If $ A = \begin{bmatrix} 2 & 1 & 3 \\ 4 & -1 & 0 \\ -7 & 2 & 1 \end{bmatrix} $, find $ A^{-1} $ and hence solve the following system of equations : $\begin{array} 2x+y+3z=3 \\ 4x-y =3 \\ -7x+2y+z=2 \end{array} $

asked Dec 25, 2012 by thanvigandhi_1

0 answers

If the length of three sides of a trapezium, other tan the base are equal to 10 cm each, then find the area of trapezium when it is maximum.

asked Dec 25, 2012 by thanvigandhi_1

0 answers

Draw a rough sketch of the region enclosed between the circles $ x^2 + y^2 = 4 $ and $ (x-2)^2 + y^2 = 1$ . Using integration, find the area of the enclosed region.

asked Dec 25, 2012 by thanvigandhi_1

0 answers

Evaluate : $ \int_1^2 \: (x^2 + x + 2 )dx$ as a limit of sums

asked Dec 25, 2012 by thanvigandhi_1

0 answers

Find the coordinates of the foot of the perpendicular distance of the poit (1, 3, 4) from the plane $ 2x - y + z + 3 = 0 $. Find also, the image of the point in the plane.

asked Dec 25, 2012 by thanvigandhi_1

0 answers

An aerolpane can carry a maximum of 200 passengers. A profit of Rs. 1000 is made on each executive class ticket and a profit of Rs. 600 is made on each economy class ticket. The airline reserves atleast 20 seats for the executive class. However, at least 4 times as many passengers prefer to travel by ecenomy class, than by the executive class. Determine how many tickets of each type must be sold, inorder to maximise the profit for the airline. What is the maximum profit? Make an L.P.P. and solve it graphically.

asked Dec 25, 2012 by thanvigandhi_1

0 answers

Using matrices, solve the following system of linear equations : $ \begin{array} xx + 2y - 3z = -4 \\ 2x + 3y + 2z = 2 \\ 3x - 3y - 4z = 11 \end{array} $

asked Dec 24, 2012 by thanvigandhi_1

0 answers

The probability that a person will get an electric contract is $\large \frac{2}{5}$ and the probability that he will not get plumbing contract is $ \frac{4}{7} $ . If the probability of getting atleast one contract is $ \large\frac{2}{3} $ . What is the probability that he will get both?

asked Dec 24, 2012 by thanvigandhi_1

0 answers

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

asked Dec 24, 2012 by thanvigandhi_1

0 answers

A point on the hypotenuse of a triangle is at distance 'a' and 'b' fro the sides of the triangle. Show that the minimum length of the hypotenuse is $ \bigg( a^{\large\frac{2}{3}} + b^{\large\frac{2}{3}} \bigg)^{\frac{2}{3}}. $

asked Dec 24, 2012 by thanvigandhi_1

0 answers

Evaluate : $ \int \:\large \frac{2\sin2\theta -\cos \theta}{6-\cos^\theta - 4\sin\theta}$$d\theta$

asked Dec 24, 2012 by thanvigandhi_1

0 answers

Find the foot of the perpendicular from ( 0, 2, 3 ) on the line $\large \frac{x+3}{5} = \frac{y-1}{2} = \frac{z+4}{3}$. Also find the length of perpendicular.

asked Dec 24, 2012 by thanvigandhi_1

0 answers

If possible,using elementary row transformations,find the inverse of the following matrices $\quad\begin{bmatrix}2 & -1 & 3\\-5 & 3 & 1\\-3 & 2 & 3\end{bmatrix}$

asked Dec 23, 2012 by sreemathi.v

1 answer

Find x,y,z if $A=\begin{bmatrix}0 & 2y & z\\x & y & -z\\x & -y & z\end{bmatrix}\;satisfies\;A'=A^{-1}$.

asked Dec 23, 2012 by sreemathi.v

1 answer

If AB=BA for any two square matrices,prove by mathematical induction that $(AB)^n=A^nB^n$.

asked Dec 23, 2012 by sreemathi.v

1 answer

Ask Questions, Get Answers