Recent questions tagged sec-c

Using the method of integration, find the area of the region bounded by the lines$ 2x+y=4, 3x-2y=6 \:and \: x-3y+5=0$

asked Feb 15, 2013 by thanvigandhi_1

0 answers

Find the equation of the plane passing through the point (-1,3,2) and perpendicular to each of the planes $ x+2y+3z=5\: and \: 3x+3y+z=0$

asked Feb 15, 2013 by thanvigandhi_1

0 answers

Find the maximum area of the 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 major axis.

asked Feb 11, 2013 by thanvigandhi_1

1 answer

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

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Using matrices, solve the following system of equation $ x+y+z=3; 2x-y+z=2 ; x-2y+3z=2$

asked Feb 11, 2013 by thanvigandhi_1

1 answer

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

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Find the area of the part of the circle $ x^2+y^2=16$ which is exterior to the parabola $y^2=6x$.

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Solve the following differential equation : $\large\frac{dy}{dx}$$+y\cot\: x = x^2\cot x+2x $

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Find the length of the perpendicular and the co-ordinates of the foot of the perpendicular from the point (2,-1,5) to the line $ \large\frac{x-11}{10}=\frac{y+2}{-4}=\frac{z+8}{-11} $.

asked Feb 11, 2013 by thanvigandhi_1

1 answer

An aerolpane can carry a maximum of 200 passengers. A profit of Rs. 400 is made on each first class ticket and a profit of Rs. 300 is made on each second class ticket. The airline reserves atleast 20 seats for the first class. However, at least 4 times as many passengers prefer to travel by second class, than by the first 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 Feb 11, 2013 by thanvigandhi_1

1 answer

A man is known to speak truth 3 out of 4 times. He throws a die and report that it is a 6. Find the probability that it is actually 6.

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Using matrices, solve the following system of equation \[ x+y-z=3\] \[ 2x+3y+z=10 \] \[ 3x-y-7z=1\]

asked Feb 11, 2013 by thanvigandhi_1

1 answer

Show that the rectangle of maximum area that can be inscribed in a circle is a square.

asked Feb 11, 2013 by thanvigandhi_1

1 answer

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

asked Feb 11, 2013 by thanvigandhi_1

0 answers

Using integration, find the area of the region bounded by the parabola $ y^2=4x$ and the circle $ 4x^2+4y^2=9$

asked Feb 10, 2013 by thanvigandhi_1

1 answer

Evaluate : \[ \int_{-a}^a \sqrt{\frac{a-x}{a+x}}dx \]

asked Feb 10, 2013 by thanvigandhi_1

1 answer

Find the equation of the plane passing through the point (-1,-1,2) and perpendicular to each of the following planes : $2x+3y-3z=2\: and \: 5x-4y+z=6 $

asked Feb 10, 2013 by thanvigandhi_1

1 answer

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

asked Feb 10, 2013 by thanvigandhi_1

1 answer

A dealer wishes to purchase a number of fans and sewing machines. He has only Rs. 5760 to invest and has space for at most 20 items. A fan costs Rs. 360 and a sewing machine cost Rs. 240. He can sell a fan at a profit of Rs. 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximise the profit? Translate the problem as an LPP and solve it graphically.

asked Feb 10, 2013 by thanvigandhi_1

1 answer

An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accident involving a scooter, a car and a truck are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver.

asked Feb 10, 2013 by thanvigandhi_1

0 answers

A small firm manufactures items A and B. The total number of items that it can manufacture in a day is at the most 24 items. A takes one hour to make while item B takes only half an hour. The maximum time available per dat is 16 hours. If the profit on one unit of item A be Rs. 300 and that of one unit of item B be Rs. 160, how many of each type of item should be produced to maximize the profit? Solve the problem graphically.

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Solve the following systems of equations using matrix method : \[ x-y=3;\: 2x+3y+4x=17; \: y+2z=7\]

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is $ \frac{2R}{\sqrt 3} $. Find the volume of the largest cylinder inscribed in a sphere of radius R.

asked Feb 9, 2013 by thanvigandhi_1

1 answer

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

asked Feb 9, 2013 by thanvigandhi_1

1 answer

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

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Find the co-ordinates of the foot of perpendicular drawn from the point $A(1,8,4)$ to the line joining the points $B(0,-1,3)$ and $C(2,-3,-1)$.

asked Feb 9, 2013 by thanvigandhi_1

1 answer