Recent questions tagged sec-c

The probability of student E passing an examination is 0.6 and of student F is 0.2. Assuming that the two events 'E passes' and 'F passes' are independent. Find the probability of : (i) both the students passing the examination (ii) Only E passing the examination.

asked Jan 24, 2013 by thanvigandhi_1

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Solve the following linear programming problem graphically: Maximize z = 60 + 15y Subject to constraints $$x + y \le 50$$ $$3x + y \le 90$$ $$x , y \ge 0 $$

asked Jan 24, 2013 by fingeazy

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Two tailors A and B earn Rs.150 and Rs.200 per day respectively. A can stitch 6 shirts and 4 plants per day while B can stitch 10 shirts and 4 pants per day. Form a linear programming problem to minimize the labour cost to produce at lest 60 shirts and 32 pants.

asked Jan 24, 2013 by fingeazy

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A company has two plants to manufacture motor cycled. 70% motor cycles are manufactured at the first plant, while 30% are manufactured at the second plant. At the first plant, 80% motor cycles are rated of the standard quality while at the second plant, 90% are rated of standard quality. A motor cycle, randomly picked up, is found to be of standard quality. Find the probability that it has come out from the second plant.

asked Jan 24, 2013 by fingeazy

1 answer

The probability that student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university: • None will graduate, • Only one will graduate, • All will graduate.

asked Jan 24, 2013 by fingeazy

1 answer

In a book of 200 pages, 200 misprints are randomly distributed. Using Poisson's distribution calculate the probability that a randomly observed page of the book will be found to have atlest 3 errors. [Use: e -1 =0.3679]

asked Jan 24, 2013 by fingeazy

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A, B and C are engaged in a printing business. A being the working partner, receives 10% of the net profit as salary. The remaining profit is divided among themselves in the ratio 4:5:9. If A gets in total Rs. 3,00,000, find the total profit in the business and the shares of B and C in it.

asked Jan 24, 2013 by fingeazy

1 answer

A and B are partners in a business sharing profits and losses equality. They admit a new partner C and it is agreed that now the profit and losses will be shared amongst A, B and C in the ratio 9 : 8 : 7 respectively. If C paid Rs. 2.10 lakh as premium for the good will, find the shares of A and B in the premium.

asked Jan 24, 2013 by fingeazy

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Find the present worth of an ordinary annuity of Rs. 1,200 per annum for 10 years at 12% per annum, compounded annually. [Use (1.12) -10 =0.3221]

asked Jan 24, 2013 by fingeazy

1 answer

A calculator manufacturing company finds that the daily cost of producing calculators is given by C(x) = 200x + 7500. • If each calculator is sold for Rs. 350, find the minimum number of calculators that must be produced daily and sold to ensure no loss. • If the selling price is increased by Rs. 150, what would be the break-even point?

asked Jan 24, 2013 by fingeazy

1 answer

A bill was drawn on April 4, 2004 at 8 months after date and was discounted on July 14, 2004 at 5% per annum. If the Banker's gain is Rs.200, find the face value of the bill.

asked Jan 24, 2013 by fingeazy

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Prove that $ \tan^{-1}\large\frac{yz}{xr}+ \tan^{-1}\frac{zx}{yr}+ \tan^{-1}\frac{xy}{zr}=\frac{\pi}{2}\;where\;x^2+y^2+z^2=r^2$

asked Jan 24, 2013 by meena.p

1 answer

If $ x= cosec \lfloor\tan^{-1}\{\cos(\cot^{-1}(\sec(\sin^{-1}a)))\}\rfloor\; $ and $ y=\sec\lfloor\cot^{-1}\{\sin(\tan^{-1}(cosec(\cos^{-1}a)))\}\rfloor\;$ where $\;a\;\in [0,1]$ Find the relationship between $x$ and $y$ in terms of $a$

asked Jan 24, 2013 by meena.p

1 answer

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

asked Jan 23, 2013 by thanvigandhi_1

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If $ \sin^{-1}x+\sin^{-1}y+\sin^{-1}z=\pi,$ prove that $x\sqrt{1-x^2}+y\sqrt{1-y^2}+z\sqrt{1-z^2}=2xyz$

asked Jan 23, 2013 by meena.p

1 answer

A toy company manufactures two types of dolls, A and B. Each doll of type B takes twice as long as to produce as one of type A. If the company produces only type A. It can make a maximum of 2000 dolls per day. The supply of plastic is sufficient to produce 1500 dolls per day. Type B requires a fancy dress which cannot be available for more than 600 per day. If the company makes profit of Rs.3 and Rs.5 per doll respectively on doll A and doll B, how many of each should be produced per day in order to maximise the profit?

asked Jan 23, 2013 by thanvigandhi_1

1 answer

Compute the area bounded by the lines $ x+2y=2, y-x+ 1 \: and \: 2x+y=7.$

asked Jan 23, 2013 by thanvigandhi_1

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Using integration, find the area of the triangle ABC. Coordinates of whose vertices are A(2, 0), B(4, 5) and C(6 ; 3).

asked Jan 23, 2013 by thanvigandhi_1

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Evaluate : $\int_0^{\pi} \large\frac{x\: \sin x}{1+\cos^2x}$$dx $

asked Jan 23, 2013 by thanvigandhi_1

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Evaluate : $ \int_0^3 (x^2+2x) dx$ as limit of sum.

asked Jan 23, 2013 by thanvigandhi_1

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A variable plane, which remains at a constant distance '3p' from the origin cuts the coordinate axes at A, B and C. Show that locus of the centroid of the triangle is $\large \frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2} = \frac{1}{p^2} .$

asked Jan 23, 2013 by thanvigandhi_1

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(i) A stone is dropped into a quite lake and waves move in circles at the speed of 5 cm/s. At the instant when the radius of circular wave is 8cm, how fast is the enclosed area increasing?

asked Jan 23, 2013 by thanvigandhi_1

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Prove that $4\tan^{-1}\large\frac{1}{5}-\tan^{-1}\frac{1}{70}+\tan^{-1}\frac{1}{99}=\large\frac{\pi}{4}$

asked Jan 23, 2013 by meena.p

1 answer

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

asked Jan 23, 2013 by thanvigandhi_1

1 answer

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 Jan 22, 2013 by thanvigandhi_1

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

asked Jan 22, 2013 by thanvigandhi_1

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Show that the right circular cone of least curved surface and given volume has an altitude equal to $ \sqrt 2$ times the radius of the base.

asked Jan 22, 2013 by thanvigandhi_1

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Find the area of the circle $ 4x^2+4y^2=9$ which is interior to the parabola $ x^2 = 4y$

asked Jan 22, 2013 by thanvigandhi_1

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Find the particular solution of the differential equation $ (x^2+1)\large\frac{dy}{dx}$$-2xy=(x^4+2x^2+1)\cos \: x ; y=0, \: when\: x = 0.$

asked Jan 22, 2013 by thanvigandhi_1

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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 shortest distance

asked Jan 22, 2013 by thanvigandhi_1

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A furniture firm manufactures chairs and tables, each requiring the use of three machines A, B and C. Production of each chair requires 2 hours on machine A, 1 hour on machine B and 1 hour on machine C. Each table requires 1 hour each on machine A and B and 3 hours on machine C. The profit obtained by selling one chair is Rs. 30 while by selling one table the profit is Rs. 60. The total time available per week on machine A is 70 hours, on machine B is 40 hours and on machine C is 90 hours. How many chairs and tables should be made per week so as to maximise profit? Formulate the problem as LPP and solve it graphically.

asked Jan 22, 2013 by thanvigandhi_1

1 answer

A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both hearts. Find the probability of the lost card being a heart.

asked Jan 22, 2013 by thanvigandhi_1

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Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4 she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 or 4 with the die?

asked Jan 22, 2013 by thanvigandhi_1

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Given that $ A = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 1 & 2 \end{bmatrix}$ and $ B = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 2 -1 & 5 \end{bmatrix}$. Find AB. Hence, using this to solve the following system of linear equations. $ x-y=3;\: 2x+3y+4z=17; \: y+2z=7$

asked Jan 21, 2013 by thanvigandhi_1

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Show that semi-vertical angle of the cone of maximum volume and of given slant height is $ \tan^{-1} \sqrt 2$.

asked Jan 21, 2013 by thanvigandhi_1

1 answer

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

asked Jan 21, 2013 by thanvigandhi_1

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Calculate the area of the region enclosed between the circles $ x^2+y^2=9 \: and \: (x-3)^2+y^2=9.$

asked Jan 21, 2013 by thanvigandhi_1

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

asked Jan 21, 2013 by thanvigandhi_1

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Find the distance of the point (-2, 3, -4) from the line $ \large \frac{x+2}{3} = \frac{2y+3}{4} = \frac{3z+4}{5} $ measured parallel to the plane $ 4x+12y-3z+1=0.$

asked Jan 21, 2013 by thanvigandhi_1

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A fruit grower can use two types of fertilzer in his garden, brand P and brand Q. The amounts ( in kg ) of nitrogen , phosphoric, potash and chlorine in a bag of each brand are given in the table. Tests indicate that the garden needs atleast 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine. If the grower wants to minimise the amount of nitrogen added to the garden, how many bags of each brand should he use? What is the minimum amount of nitrogen added in the garden? What steps do you advice to a farmer to avoid overuse of fertilizers.

asked Jan 21, 2013 by thanvigandhi_1

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In a class having 70% boys, 20% of the boys, and 10% of the girls are players. A student is selected at random from the class and found to be a player. Find the probability that the selected is a girl. Explain the contribution of sports in inculcating human values.

asked Jan 21, 2013 by thanvigandhi_1

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A student is given a test with 8 questions of true-false type. If he gets 6 or more questions correct, he is declared pass, given that he guesses the answer to each question, compute the probability that student will pass in the exam. Evaluation is necessary in student learning, Explain.

asked Jan 21, 2013 by thanvigandhi_1

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Using matrices, solve the following : $2x+y-3z=13; x+y-z=6 ;2x-y+4z = -12$

asked Jan 16, 2013 by thanvigandhi_1

1 answer

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

asked Jan 16, 2013 by thanvigandhi_1

1 answer

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

asked Jan 16, 2013 by thanvigandhi_1

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

asked Jan 16, 2013 by thanvigandhi_1

1 answer

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

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_0^3 (x^2+2x)dx $ as limit of a sum.

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Find the distance of a point (1, -2, 3) from the plane x-y+z=5, measured parallel to the line $\large\frac{x}{2}=\frac{y}{3}=\frac{z}{-6} $

asked Jan 16, 2013 by thanvigandhi_1

0 answers

A housewife wishes to mix up two kind of foods X and Y in such a way that mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of 1 kg of food X and 1 kg of food Y are as given in the table : If 1 kg of food X costs Rs. 6 and 1 kg of food Y costs Rs. 10, find the least cost of the mixture which will produce the desired diet.

asked Jan 16, 2013 by thanvigandhi_1

0 answers

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