Recent questions tagged sec-c

If $A=\begin{bmatrix}3 & -5\\-4 & 2\end{bmatrix},$ then find $A^2-5A-14I.$Hence,obtain $A^3$.

asked Dec 23, 2012 by sreemathi.v

1 answer

Does $A=\begin{bmatrix}5 & 3\\1 & 2\end{bmatrix}$ satisfy the equation $\;A^2-3A-7I=0$ and hence find $\;A^{-1}$

asked Dec 22, 2012 by sreemathi.v

1 answer

Show that the function f given by $ f (x) = tan^{–1} (sinx + cosx), x > 0$ is always an strictly increasing function in $ \bigg(0,\frac{\pi}{4} \bigg) $

asked Dec 22, 2012 by thanvigandhi_1

0 answers

Find the area of the region enclosed between the two circles $x^2+ y^2 = 4$ and $(x – 2)^2 + y^2 = 4$.

asked Dec 22, 2012 by thanvigandhi_1

0 answers

A dietician has to develop a special diet using two foods P and Q. Each packet (containing 30g) of food P contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Q contains 3 units of calcium, 20 units of iron, 4 units of cholesterol, and 3 units of vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of iron and atmost 300 units of cholesterol. How many packets of each food should be used to minimize the amount of vitamin A in the diet? What is the minimum amount of vitamin A?

asked Dec 22, 2012 by thanvigandhi_1

0 answers

Let a pair of dice be thrown and the random variable X be the sum of the numbers that appear on the two dice. Find the mean or expectation of X.

asked Dec 21, 2012 by balaji.thirumalai

0 answers

A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, scooter or by any other means of transport are respectively $\frac{3}{10}, \frac{1}{5}, \frac{1}{10} $ and $ \frac{2}{5} $ . The probabilities that he will be late are $ \frac{1}{4}, \frac{1}{3} $ and $ \frac{1}{12} $ if he comes by train, bus and scooter respectively, but if he comes by other means of transport, then he will not be late. When he arrives, he is late. What is the probability that he comes by train.

asked Dec 21, 2012 by thanvigandhi_1

1 answer

Find the distance between the point P (6, 5, 9) and the plane determined by points A (3, –1, 2), B (5, 2, 4) and C (–1, –1, 6).

asked Dec 21, 2012 by thanvigandhi_1

0 answers

Find the equation of the 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 20, 2012 by thanvigandhi_1

0 answers

Find the area of the region included between the parabola $ y^2 = x $ and the line $ x + y = 2$.

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Evaluate : $ \int_0^{\pi} \mathrm \:\large \frac{x \: dx}{a^2 \cos^2 \: x + b^2 \sin^2 \: x} $

asked Dec 20, 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 20, 2012 by thanvigandhi_1

0 answers

Coloured balls are distributed in three bags as shown in the table below, a bag is selected at random and then two balls are randomly drawn from the selected bag. They happen to be black and red. what is the probability that they came from bag 1 ?

asked Dec 20, 2012 by thanvigandhi_1

1 answer

If $a_1,a_2,a_3,......a_n$ is an arithmetic progression with common difference d,then evaluate the following expression $\tan \bigg( \tan^{-1}\bigg(\frac{d}{1+a_1a_2}\bigg)+\tan^{-1}\bigg(\frac{d}{1+a_2a_3}\bigg)+\tan^{-1}\bigg(\frac{d}{1+a_3a_4}\bigg)+........+\tan^{-1}\bigg(\frac{d}{1+a_{n-1}a_n}\bigg) \bigg) $

asked Dec 20, 2012 by sreemathi.v

1 answer

A dealer wishes to purchase a number of fans and sewing machines. He has only Rs. 5,760, to invest and has a space for at most 20 items. A fan cost him Rs.360 and a sewing machine Rs.240. His expectation is that he can sell a fan at a profit of Rs. 22 and a sewing machine 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 his profit ? Formulate this as a linear programming problem and solve it graphically.

asked Dec 20, 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 the triangle is maximum when the angle between them is $ \frac{\pi}{3} $

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Find the value of $4\tan^{-1}{\large \frac{1}{5}}$$-\tan^{-1}{\large\frac{1}{239}}$

asked Dec 20, 2012 by sreemathi.v

1 answer

Using properties of determinants, prove the following : $ \begin{bmatrix} \alpha & \beta & \gamma \\[0.3em] \alpha^2 & \beta^2 & \gamma^2 \\[0.3em] \beta + \gamma & \gamma + \alpha & \alpha + \beta \end{bmatrix} = ( \alpha - \beta ) (\beta - \gamma) (\gamma - \alpha) ( \alpha + \beta + \gamma ) $

asked Dec 19, 2012 by thanvigandhi_1

0 answers

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

asked Dec 19, 2012 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 Dec 19, 2012 by thanvigandhi_1

0 answers

Evaluate : $ \int_{-a}^a \: \sqrt {\large\frac{a-x}{a+x}} dx $

asked Dec 19, 2012 by thanvigandhi_1

0 answers

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 Dec 19, 2012 by thanvigandhi_1

0 answers

A factory owner purchases two types of machines, A and B for his factory. The requirements and the limitations for the machines are listed below. He has maximum area of 9000 $ m^2 $ available, and 72 skilled labourers who can operate both the machines. How many machines of each type should he buy to maximise the daily output.

asked Dec 19, 2012 by thanvigandhi_1

0 answers

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 truckare 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 Dec 19, 2012 by thanvigandhi_1

0 answers

Find the shortest distance between the lines whose vector equations are $ \overrightarrow r = ( \hat i + 2\hat j + 3\hat k) + \lambda ( \hat i - 3\hat j + 2\hat k )$ and $ \overrightarrow r = 4 \hat i + 5\hat j + 6\hat k + \mu (2\hat i + 3\hat j + \hat k )$

asked Dec 14, 2012 by thanvigandhi_1

1 answer