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Recent questions tagged short-answer

A bag contains 5 red marbles and 3 black marbles.Three marbles are drawn one by one with out replacement.What is the probability that at least one of the three marbles drawn be black,if the first marble is red?

asked Jan 8, 2013 by sreemathi.v

1 answer

The probability that at least one of the two events A and B occurs is 0.6.If A and B occur simultaneously with probability 0.3,evaluate $P(\bar{A})+P(\bar{B})$.

asked Jan 8, 2013 by sreemathi.v

1 answer

For a loaded die,the probabilities of outcomes are given as under P(1)=P(2)=0.2,P(3)=P(5)=P(6)=0.1 and P(4)=0.3.The die is thrown two times.Let A and B be the events,'same number each time',and 'a total score is 10 or more',respectively.If the die were fair,determine whether or not the events A and B are independent.

asked Jan 8, 2013 by sreemathi.v

1 answer

For a loaded die,the probabilities of outcomes are given as under P(1)=P(2)=0.2,P(3)=P(5)=P(6)=0.1 and P(4)=0.3.The die is thrown two times.Let A and B be the events,'same number each time',and 'a total score is 10 or more',respectively.Determine whether or not A and B are independent.

asked Jan 8, 2013 by sreemathi.v

1 answer

A man rides his motorcycle at the speed of 50km/hour.He has to speed Rs 2 per km on petrol.If he rides it at at a faster speed of 80km/hour,the petrol cost increases to Rs 3 per km.He has at most Rs120 to spend on petrol and one hour's time.He wishes to find the maximum distance that he can travel.Express this problem as a linear programming problem.

asked Jan 7, 2013 by sreemathi.v

1 answer

A company manufactures two types of sweaters :type A sweaters type B.It costs Rs 360 to make a type A sweater and Rs 120 to make a type B sweater.The company can make at most 300 sweaters and spend at most Rs72,000 a day.The number of sweaters of type B cannot exceed the number of sweaters of type A by more than 100.The company makes a profit of Rs 200 for each sweater of type A and Rs 120 for every sweater of type B.Formulate this problem at a LPP to maximise the profit to the company.

asked Jan 7, 2013 by sreemathi.v

1 answer

A company manufactures two types of screws A and B.All the screws have to pass through a threading machine and a slotting machine.A box of type A screws requires 2 minutes on the threading machine and 3minutes on the slotting machine.A box of type B screws requires 8 minutes of threading on the threading machine and 2 minutes on the slotting machine.In a week,each machine is available for 60 hours.On selling these screws,the company gets a profit of Rs100 per box on type A screws and Rs170 per box on type B screws.

asked Jan 7, 2013 by sreemathi.v

1 answer

A firm has to transport 1200 packages using large vans which can carry 200 packages each and small vans which can take 80 packages each.The cost for engaging each large van is Rs 400 and each small van is Rs 200.Not more than Rs 3000 is to be spent on the job and the number of large vans cannot exceed the number of small vans.Formulate this problem as a LPP given that the objective is to minimize cost.

asked Jan 7, 2013 by sreemathi.v

1 answer

A manufacture of electronic circuits has a stock of 200 resistors,120 transistors and 150 capacitors and is required to produce two types of circuits A and B .Type A requires 20 resistors,10 transistors and 10 capacitors .Type B requires 10 resistors,20 transistors and 30 capacitors.If the profit on type A circuit is Rs 50 and that an type B circuit is Rs 60,formulate this problem as a LPP so that the manufacturer can maximize his profit.

asked Jan 7, 2013 by sreemathi.v

1 answer

Minimise $Z=13x-15y$ subject to the constraints: $x+y\leq 7,2x-3y+6\geq 0,x\geq 0,y\geq 0$.

asked Jan 7, 2013 by sreemathi.v

1 answer

Maximise the function $Z=11x+7y$,subject to the constraints : $x\leq 3,y\leq 2,x\geq 0,y\geq 0.$

asked Jan 7, 2013 by sreemathi.v

1 answer

Maximise $Z=3x+4y$,subject to the constraints: $x+y\leq 1,x\geq 0,y\geq 0$.

asked Jan 7, 2013 by sreemathi.v

1 answer

Determine the maximum value of $z=11x+7y$ subject to the constraints: $2x+y\leq 6,x\leq 2,y\geq 0.$

asked Jan 7, 2013 by sreemathi.v

1 answer

Using mean value theorem,prove that there is a point on the curve $y=2x^2-5x+3$ between the points $A(1,0)$ and $B(2,1)$where tangent is parallel to chord $AB$. Also find the point.

asked Jan 2, 2013 by sreemathi.v

1 answer

Find a point on the curve $y=(x-3)^2$,where the tangent is parallel to the chord joining the point (3,0) and (4,1).

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify mean value theorem for each of the function $f(x)=\sqrt {25-x^2}\;in\;[1,5].$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify mean value theorem for each of the function $f(x)=\sin x-\sin 2x\;in\;[0,\pi].$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify mean value theorem for each of the function $f(x)=x^3-2x^2-x+3\;in\;[0,1].$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify mean value theorem for each of the function $f(x)=\large\frac{1}{4x-1}$ in $[1,4].$

asked Jan 2, 2013 by sreemathi.v

1 answer

Using Rolle's theorem,find the point on the curve $y=x(x-4),x\in[0,4]$,where the tangent is parallel to $x$-axis.

asked Jan 2, 2013 by sreemathi.v

1 answer

Find the points on the curve $y=(\cos x-1)$ in [0,2$\pi$],where the tangent is parallel to $x$-axis.

asked Jan 2, 2013 by sreemathi.v

1 answer

Discuss the applicability of Rolle's theorem on the function given by $f(x)=\left \{\begin{array}{1 1}x^2+1, & if\;0\leq x\leq1\\3\;x, & if\;1<x<2\end{array}\right.$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify the Rolle's theorem for the function $f(x)=\sqrt {4-x^2}\;in\;[-2,2]$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify the Rolle's theorem for the function $f(x)=x(x+3)e^{\large-x/2}\;in\;[-3,0]$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify the Rolle's theorem for the function $log(x^2+2)-log 3\;in\;[-1,1]$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify the Rolle's theorem for the function $f(x)=\sin^4x+\cos^4x\;in\;\begin{bmatrix}0,\large\frac{\pi}{2}\end{bmatrix}$

asked Jan 2, 2013 by sreemathi.v

1 answer

Verify the Rolle's theorem for the function $f(x)=x(x-1)^2\;in\;[0,1]$

asked Jan 2, 2013 by sreemathi.v

1 answer

If $y=\tan^{-1}x$, find $\large {\frac{d^2y}{dx^2}}$ in terms of y alone.

asked Jan 2, 2013 by sreemathi.v

1 answer

If $\sqrt {1-x^2}+\sqrt {1-y^2}=a(x-y),$prove that $\large \frac{dy}{dx}=\frac{\sqrt{1-y^2}}{\sqrt{1-x^2}}$.

asked Jan 2, 2013 by sreemathi.v

1 answer

If $x\sin(a+y)+\sin a\cos(a+y)=0,prove\;that\;\large {\frac{dy}{dx}=\frac{\sin^2(a+y)}{\sin a}}$

asked Jan 2, 2013 by sreemathi.v

1 answer

If $y=(\cos x)^{\Large(\cos x)^{(\Large \cos x)..........\infty.}},$show that $\large {\frac{dy}{dx}=\frac{y^2\tan x}{ylog\cos x-1}}$

asked Jan 2, 2013 by sreemathi.v

1 answer

If $y^{\large x}=e^{\large y-x},prove\;that\;\large {\frac{dy}{dx}=\frac{(1+logy)^2}{log y}}$

asked Jan 2, 2013 by sreemathi.v

1 answer

If $x=e^{\Large \frac{x}{y}},prove\; that \; \large {\frac{dy}{dx}=\frac{x-y}{xlog x}}$

asked Jan 2, 2013 by sreemathi.v

1 answer

If $ax^2+2hxy+by^2+2gx+2fy+c=0$,then show that $\large \frac{dy}{dx}.\frac{dx}{dy}\normalsize =1$

asked Jan 2, 2013 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ when x and y are connected by the relation $(x^2+y^2)^2=xy$

asked Jan 2, 2013 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ when x and y are connected by the relation $\tan^{-1}(x^2+y^2)=a $

asked Jan 2, 2013 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ when x and y are connected by the relation $\sec(x+y)=xy$

asked Jan 2, 2013 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ when x and y are connected by the relation $\;\sin(xy)+\large\frac{x}{y}$$=x^2-y$

asked Jan 1, 2013 by sreemathi.v

1 answer

Differentiate $ tan^{-1}\bigg (\Large \frac{\sqrt {1+x^2}-1}{x}\bigg)\;\normalsize w.r.t\;\tan^{-1}x\;when\;x\neq 0$

asked Jan 1, 2013 by sreemathi.v

1 answer

Differentiate $\large \frac{x}{\sin x}\;\normalsize w.r.t\;\sin x.$

asked Dec 31, 2012 by sreemathi.v

1 answer

If $x=3\sin t-\sin 3t,y=3\cos t-\cos 3t,find \;\large \frac{dy}{dx}\;\normalsize at \;t=\large \frac{\pi}{3}$

asked Dec 31, 2012 by sreemathi.v

1 answer

If $x=a\sin 2t(1+\cos 2t)\;and\;y=b\cos 2t(1-\cos 2t),show\;that\bigg(\large \frac{dy}{dx}\bigg)_{at\;t=\frac{\pi}{4}}=\frac{-b}{a}$

asked Dec 31, 2012 by sreemathi.v

1 answer

If $x=e^{\large\cos 2t}\; and\;y=e^{\large\sin 2t},prove\;that\;\large \frac{dy}{dx}=\frac{-ylog x}{xlog y}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ of the function expressed in parametric form $x=\large\frac{1+log t}{t^2},$$y=\large\frac{3+2log t}{t}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ of the function expressed in parametric form $\sin x=\large\frac{2t}{1+t^2},$$\tan y=\large\frac{2t}{1-t^2}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ of the function expressed in parametric form $x=3\cos \theta-2\cos^3\theta,y=3\sin \theta-2\sin^3\theta$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ of the function expressed in parametric form $x=e^\theta\bigg(\theta+\frac{1}{\theta}\bigg),y=e^{-\theta}\bigg(\theta-\frac{1}{\theta}\bigg)$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ of the function expressed in parametric form $x=t+\large\frac{1}{t},$$y=t-\large\frac{1}{t}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t x: $\tan^{-1}\Large {\bigg(\frac{\sqrt {1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\bigg)},\normalsize -1 < x < 1,x\neq 0$

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$ : $\sec^{-1}\bigg(\Large \frac{1}{4x^3-3x}\bigg),\normalsize 0 < x <\Large \frac{1}{\sqrt 2}$

asked Dec 31, 2012 by sreemathi.v

1 answer

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