Recent questions tagged sec-c

Suppose 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

If a,b,c are positive and unequal, show that the following determinant is negative. $ \Delta = \begin{bmatrix} a & b & c \\ b & c & a \\ c & a & b \end{bmatrix} $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

using matrices, solve the following system of equations $ x+2y-3z=-4;2x+3y+2z=2 ; 3x-3y-4z=11 $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Show that the volume of the greatest cylinder that can be inscribed in a cone of height 'h' and semi-vertical angle $ \alpha $ is $ \large\frac{4}{27}\pi h^3\tan^2 \alpha $.

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Evaluate the following $ \int_{-1}^{\large\frac{3}{2}} |x\sin \: \pi \: x |dx $

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Sketch the graph of $ f(x) = \left\{ \begin{array}{l l}|x-2|+2, & \quad { x \leq 2} \\ x^2-2, & \quad { x > 2} \end{array} \right. $ Evaluate $ \int_0^4 f(x) dx $ What does the value of this integral represent on the graph?

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Find the equation of the plane passing through the point P(1,1,1) and containing the line $ \overrightarrow r = (-3\hat i + \hat j + 5\hat k)+ \lambda (3\hat i - \hat j - 5\hat k).$. Also show that the plane contains the line $ \overrightarrow r = (-\hat i + 2\hat j + 5\hat k)+ H (\hat i - 2\hat j - 5\hat k).$

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Two bags A and B contain 4 white and 3 black balls and 2 white,2 black balls respectively. From bag A, two balls are transferred to bag B. Find the probability of drawing (a) 2 white balls from Bag B? (b) 2 black balls from bag B? (c) 1 white and 1 black ball from bag B?

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Every gram of wheat provides 0.1 g of proteins and 0.25 g of carbohydrates. The corresponding values for rice are 0.05 g and .5 g respectively. Wheat costs Rs.4 per kg and rice Rs.6 per kg. The minimum daily requirements of proteins and carbohydrates for an average child are 5 g and 200 g respectively. In what qualities should wheat and rice be mixed in the daily diet to provide minimum daily requirements of protiens and carbohydrates at minimum cost. Form a L.P.P and solve it graphically.

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Using matrices, solve the following system, of equations : $ \large\frac{1}{x}-\frac{1}{y}+\frac{1}{z}$$=4: \: \large\frac{2}{x}+\frac{1}{y}-\frac{3}{z}$$=0: \: \large\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$$=2 \qquad x \neq 0, y \neq 0, z \neq 0 $

asked Feb 3, 2013 by thanvigandhi_1

1 answer

Show that the volume of the greatest cylinder which can be inscribed in a cone of height h and semivertical angle $ \alpha, \: is \: \large\frac{4}{27}$$ \pi \: h^3\: tan^2\: \alpha $

asked Feb 3, 2013 by thanvigandhi_1

1 answer

Show that the normal at any point $ \theta $ to the curve $ x=a\cos\theta+a\theta\: \sin\theta$ and $ y=a\sin\theta-a\theta \cos\theta$ is at a constant distance from the origin.

asked Feb 3, 2013 by thanvigandhi_1

0 answers

Find the area of the region: $ {(x,y): 0 \leq y \leq x^2,0 \leq y \leq x+2:0 \leq x \leq 3}. $

asked Feb 3, 2013 by thanvigandhi_1

0 answers

Find the particular solution of the differential equation $(xdy-ydx)y.\sin \bigg(\large\frac{y}{x} \bigg)$$=(ydx+xdy)x \cos\large\frac{y}{x},$ given that $ y=\pi$ when $x = 3$.

asked Feb 3, 2013 by thanvigandhi_1

0 answers

Find the equation of the plane passing through the point (1,1,1) and containing the line $ \overrightarrow r = (3\hat i + \hat j + 5\hat k) + \lambda (3\hat i - \hat j - 5\hat k)$. Also, show that the plane contains the line $ \overrightarrow r = (-\hat i + 2\hat j + 5\hat k) + \lambda (\hat i - 2\hat j - 5\hat k)$.

asked Feb 3, 2013 by thanvigandhi_1

0 answers

A company sells two different products A and B. The products are produced in a common production process which has 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 demand in the market shows that the maximum number of units of A that can sold is 70 and that of B is 125. Profit on each unit of A is Rs. 20 and on B is Rs.15. How many units of A and B should be produced to maximise the profit? Form an L.P.P and solve it graphically.

asked Feb 3, 2013 by thanvigandhi_1

1 answer

In an examination, 10 questions of true-false type are asked. A student toses a fair coin to determine his answer to each question. If the coin falls heads, he answers 'true' and if it falls tails, he answers 'false'. Show that the probability that he answers at most 7 questions correctly is $ \frac{121}{128} $.

asked Feb 3, 2013 by thanvigandhi_1

0 answers

Two bags A and B contain 4 white and 3 black balls and 2 white and 2 black balls respectively. From bag A, two balls are drawn at random and then transferred to bag B, A ball is then drawn from bag B and is found to be a black ball. What is the probability that the transferred balls were 1 white and 1 black?

asked Feb 3, 2013 by thanvigandhi_1

0 answers

Use product $ \begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{bmatrix} $ $ \begin{bmatrix} -2 & 0 & 1 \\ 9 & 2 & -3 \\ 6 & 1 & -2 \end{bmatrix} $ to solve the system of equations: $ x-y+2z=1, \: 2y-3z=1, \: 3x-2y+4z=2 $

asked Feb 2, 2013 by thanvigandhi_1

0 answers

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

asked Feb 2, 2013 by thanvigandhi_1

0 answers

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 Feb 2, 2013 by thanvigandhi_1

1 answer

Use definite integration, find the area of triangle whose vertices are (-1,6),(1,2) and (5,4).

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Find the area of the smaller region boundary by the ellipse $ \large\frac{x^2}{9}+\large\frac{y^2}{4}=1$ and the straight line $\large \frac{x}{3}+\frac{y}{2}=1 $.

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Solve the differential equation : $(x+y)dy + (x-y) dx=0$

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Find the equation of the plane passing through the line intersection of the plane $ x-2y+z=1$ and $ 2x+y+z=8$ and parallel to the line with direction ratios 1,2,1. Also, find the perpendicular distance of the point P(3,1,2) from this plane.

asked Feb 2, 2013 by thanvigandhi_1

0 answers

A retired person has 70000 to invest and two types of bonds are available in the market for investment. First type of bond yields an annual income of 8% on the amount invested and the second type of bond yields 10% per annum. As per norms, he has to invest minimum of 10000 in the first type and not more than 30000 in the second type. How should he plan his investment, so as to get maximum return after one year of investment. Make it an L.P.P. and solve the above problem.

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Probability of solving a mathematical problem by A, B, and C respectively are $ \frac{1}{3}, \frac{1}{2} \: and \: \frac{1}{4}$. If they try to solve the problem indepently. Find the probability that : (i) The problem is solved. (ii) exactly one of them solve the problem (iii) exactly two of them solve the problem.

asked Feb 2, 2013 by thanvigandhi_1

0 answers

A company has two plants to manufacture bicycles. Plant I manufactures 70% of the bicycles and plant II manufactures 30%. At plant I 80% of the bicycles are rated as of standard quality and a plant II 90% of the bicycles are rated as of standard quality. A bicycle is choosen at random and is found to be of standard quality. What is the probability that it has come from plant II?

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Let A = N x N and * be a binary operation on A defined by (a,b)(c,d)=(ac,bd), show that : (i) (A) is commutative. (ii) (A*) is associative (iii) Find the identity element, if any, in A.

asked Jan 31, 2013 by thanvigandhi_1

1 answer

Show that volume of the greatest cylinder which can inscribed in a cone of height h and semi-vertical angle $ 30^{\circ} \: is \: \large\frac{4}{81} $$\: \pi h^3.$

asked Jan 31, 2013 by thanvigandhi_1

1 answer

Find the area of greatest rectangle which can be inscribed in a circle of radius 10 cm.

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Use definite integration, find the area of triangle whose vertices are (-1,6), (1,2) and (5,4).

asked Jan 31, 2013 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 $\large \frac{x}{3}+\frac{y}{2}=1$.

asked Jan 31, 2013 by thanvigandhi_1

0 answers

A farmer has a supply of chemical fertilizer of type A which contains 10% nitrogen and 5% phosphoric acid, and type B which contains 6% nitrogen and 10% phosphoric acid. After testing the soil conditions of the field, it was found that atleast 14 kg of nitrogen and 14 kg of phosphoric acid is required for producing a good crop. The fertilizer of type A costs Rs.5 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 possible cost? Using L.P.P. solve the above problem graphically.

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Solve by matrix method : $ x+y+z=20, \: 2x+y-z=23, \: 3x+y+z=46 $

asked Jan 31, 2013 by thanvigandhi_1

1 answer

Show that line whose vector equation is $ \overrightarrow r = 2\hat i - 2\hat j + 3\hat k + \lambda (\hat i - \hat j + 4\hat k)$ is parallel to the plane $ \overrightarrow r .(\hat i + 5\hat j + \hat k)=5$ and find the distance between them.

asked Jan 31, 2013 by thanvigandhi_1

0 answers

An insurance company insured 2000 scooters and 3000 motor cycles. The probability of an accident involving a scooter is 0.01 and that of a motor cycle is 0.02. An insured vehicle met with an accident. Find the probability that the accidental vehicle was a motor cycle.

asked Jan 31, 2013 by thanvigandhi_1

0 answers