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Recent questions tagged short-answer

Find the co-ordinates of the point on the curve $\sqrt x\quad \sqrt y=4$ at which tangent is equally inclined to the axes.

asked Jan 11, 2013 by sreemathi.v

1 answer

Prove that the curves $xy=4$ and $x^2+y^2=8$ touch each other.

asked Jan 11, 2013 by sreemathi.v

1 answer

Find the condition that the curves $2x=y^2$ and $2xy=k$ intersect orthogonally.

asked Jan 11, 2013 by sreemathi.v

1 answer

x and y are the sides of two squares such that $y=x-x^2$.Find the rate of change of the area of second square with respect to the area of first square.

asked Jan 11, 2013 by sreemathi.v

1 answer

The volume of a cube increases at a constant rate.Prove that the increase in its surface area varies inversely as the length of the side.

asked Jan 11, 2013 by sreemathi.v

1 answer

A swimming pool is to be drained for cleaning .If L represents the number of litres of water in the pool seconds after the pool has been plugged off to drain and $L=200(10-t)^2$.How fast is the water running out at the end of 5 seconds?What is the average rate at which the water flows out during the first 5 seconds?

asked Jan 11, 2013 by sreemathi.v

1 answer

A man, 2m tall, walks at the rate of $1\frac{2}{3}m/s$ towards a street light which is $5\frac{1}{3}m$ above the ground.At what rate is the tip of his shadow moving?At what rate is the length of the shadow changing when he is $3\frac{1}{3}m$ from the base of the light?

asked Jan 11, 2013 by sreemathi.v

1 answer

Find the approximate volume of metal in a hollow spherical shell whose internal and external radii are 3cm and 3.0005cm,respectively.

asked Jan 11, 2013 by sreemathi.v

1 answer

FInd the approximate value of $(1.999)^5$.

asked Jan 11, 2013 by sreemathi.v

1 answer

Find an angle $\theta$,$0$ <$\;\theta<\Large \frac{1}{2}$,which increases twice as fast as its sine.

asked Jan 11, 2013 by sreemathi.v

1 answer

Two men A and B start with velocities v at the same time from the junction of two roads inclined at $45^\circ$ to each other.If they travel by different roads,find the rate at which they are being separated.

asked Jan 10, 2013 by sreemathi.v

1 answer

A kite is moving horizontally at a height of 151.5 meters If the speed of kite is 10m/s,how fast is the string being let out,when the kite is 250m away from the boy who is flying the kite?The height of boy is 1.5m

asked Jan 10, 2013 by sreemathi.v

1 answer

If the area of a circle increases at a uniform rate,then prove that perimeter varies inversely as the radius.

asked Jan 10, 2013 by sreemathi.v

1 answer

A spherical ball of salt is dissolving in water in such a manner that the rate of decrease of the surface.Prove that the radius is decreasing at a constant rate.

asked Jan 10, 2013 by sreemathi.v

1 answer

An urn contains m white and n black balls,A ball is drawn at random and is put back into the urn along with k additional balls of the same color as that of the ball drawn,A ball is again drawn at random.Show that the probability of drawing a white ball now does not depend on k.

asked Jan 9, 2013 by sreemathi.v

1 answer

Two dice are tossed.Find whether the following two events A and B are independent.\[A=(x,y):x+y=11\quad B=(x,y):x=5\]where (x,y) denotes a typical sample point.

asked Jan 9, 2013 by sreemathi.v

1 answer

A and B throw pair of dice alternately.A wins the game if he gets a total of 6 and B wins if she gets a total of 7.It A starts the game,find the probability of winning the game by A in third throw of the pair of dice.

asked Jan 9, 2013 by sreemathi.v

1 answer

Find the variance of the distribution.

asked Jan 9, 2013 by sreemathi.v

1 answer

The random variable X can take only the values 0,1,2.Given that P(x=0)=P(X=1)=P and that E($X^2$)=E[X],find the value of p.

asked Jan 9, 2013 by sreemathi.v

1 answer

Find the probability distribution of the maximum of two scores obtained when a die is thrown twice .Determine also the mean of the distribution.

asked Jan 9, 2013 by sreemathi.v

1 answer

Two natural numbers r,s are drawn one at a time,without replacement from the set S=1,2,3,......,n.Find $P[r\leq p|s\leq p],where \;p\in S$

asked Jan 9, 2013 by sreemathi.v

1 answer

Suppose that 6% of the people with blood group O are left handed and 10% of those with other blood groups are left handed 30% of the people have blood group O.If a left handed person is selected at random,what is the probability that he/she will have blood group O?

asked Jan 9, 2013 by sreemathi.v

1 answer

Suppose you have two coins which appear identical in your pocket.you know that one is fair and one is 2 headed.If you take one out,toss it and get a head,what is the probability that it was a fair coin?

asked Jan 9, 2013 by sreemathi.v

1 answer

A factory produces bulbs,The probability that any one bulb is defective is $\Large \frac{1}{50}$ and they are packed in boxes of 10.From a single box,find the probability that\begin{array}{1 1}(i)\;none\;of\;the\;bulbs\;is \;defective.\\(ii)\;exactly\;two\;bulbs\;are\;defective\\(iii)\;more\;than\;8\;bulbs\;work\;properly\end{array}

asked Jan 9, 2013 by sreemathi.v

1 answer

Two probability distributions of the discrete random variable X and Y are given below.

asked Jan 9, 2013 by sreemathi.v

1 answer

Two biased dice are thrown together.For the first die $P(6)=\Large \frac{1}{2}$,the other scores being equally likely while for the second die,$P(1)=\Large \frac{2}{5}$ and the other scores are equally likely.Find the probability distribution of 'the number of ones seen'.

asked Jan 9, 2013 by sreemathi.v

1 answer

A die is thrown three times.Let X be 'the number of twos seen'.Find the expectation of X.

asked Jan 9, 2013 by sreemathi.v

1 answer

A biased die is such that $P(4)=\Large \frac{1}{10}$ and other scores being equally likely.The die is tossed twice.If X is the number of fours seen',find the variance of the random variable X.

asked Jan 9, 2013 by sreemathi.v

1 answer

For the following probability distribution determine standard deviation of the random variable X.

asked Jan 9, 2013 by sreemathi.v

1 answer

The probability distribution of a random variable X is given below:

asked Jan 9, 2013 by sreemathi.v

0 answers

Consider the probability distribution of a random variable X.

asked Jan 9, 2013 by sreemathi.v

1 answer

A lot of 100 watches is known to have 10 defective watches.If 8 watches are selected(one by one with replacement) at random,what is the probability that there will be at least one defective watch?

asked Jan 9, 2013 by sreemathi.v

1 answer

The probability of a man hitting a target is 0.25.He shoots 7 times.What is the probability of his hitting at least twice?

asked Jan 9, 2013 by sreemathi.v

1 answer

Ten coins are tossed.What is the probability of getting at least 8 heads?

asked Jan 9, 2013 by sreemathi.v

1 answer

A die is thrown 5 times.Find the probability that an odd number will come up exactly three times.

asked Jan 9, 2013 by sreemathi.v

1 answer

Four cards are successively drawn with out replacement from a deck of 52 playing cards.What is the probability that all the four cards are kings?

asked Jan 9, 2013 by sreemathi.v

1 answer

A box has 5 blue and red balls.One ball is drawn at random and not replaced.Its colour is also not noted .The another ball is drawn at random.what is the probability of second ball being blue?

asked Jan 9, 2013 by sreemathi.v

1 answer

Bag I contains 3 black and 2 white balls,Bag II contains 2 black and 4 white balls.A bag and a ball is selected at random .Determine the probability of selecting a black ball.

asked Jan 9, 2013 by sreemathi.v

1 answer

A bag contains 4 white and 5 black balls.Another bag contains 9 white and 7 black balls.A ball is transferred from the first bag to the second and then a ball is drawn at random from the second bag.Find the probability that the ball drawn is white.

asked Jan 9, 2013 by sreemathi.v

1 answer

Suppose 10,000 tickets are sold in a lottery each for Re1.First prize is of Rs 3000 and the second prize is of Rs 2000.There are three third prizes of Rs 500 each.If you buy one ticket,what is your expectation.

asked Jan 8, 2013 by sreemathi.v

1 answer

Three dice are thrown at the same time.Find the probability of getting three two's,if it is known that the sum of the numbers on the dice was six.

asked Jan 8, 2013 by sreemathi.v

1 answer

In a dice game, a player pays a stake of Re1 for each throw of a die.She receives Rs 5 if the die shows a 3,Rs 2 if the die shows a 1 or 6,and nothing otherwise.What is the player's expected profit per throw over a long series of throws?

asked Jan 8, 2013 by sreemathi.v

1 answer

If X is the number of tails in three tosses of a coin ,determine the standard deviation of X.

asked Jan 8, 2013 by sreemathi.v

1 answer

Prove that\begin{array}{1 1}(i)\;P(A)+P(A\cap B)+P(A\cap \bar{B})\\(ii)\;P(A\cup B)=P(A\cap B)+P(A\cap\bar{B})+P(\bar{A}\cap\bar{B})\end{array}

asked Jan 8, 2013 by sreemathi.v

1 answer

A discrete random variable X has the probability distribution given as below:

asked Jan 8, 2013 by sreemathi.v

1 answer

Let $E_1$ and $E_2$ be the two independent events.Such that $P(E_1)=p_1$ and $P(E_2)=p_2$.

asked Jan 8, 2013 by sreemathi.v

1 answer

Three events A,B and C have probabilities $\Large \frac{2}{5},\frac{1}{3}$ and $\Large \frac{1}{2}$,respectively.Given that $P(A\cap C)=\frac{1}{5}\;and\;P(B\cap C)=\frac{1}{4}$,find the value of $P(C|B)\; and \;P(A'\cap C').$

asked Jan 8, 2013 by sreemathi.v

1 answer

A and B are two events such that $P(A)=\frac{1}{2},P(B)=\frac{1}{3} and\; P(A\cap B)=\frac{1}{4}$.Find:\[(i)\;P(A|B)\quad(ii)\;P(B|A)\quad(iii)\;P(A'|B)\quad(iv)\;P(A'|B')\]

asked Jan 8, 2013 by sreemathi.v

1 answer

Explain why the experiment of tossing a coin three times is said to have binomial distribution.

asked Jan 8, 2013 by sreemathi.v

1 answer

Two dice are thrown together and the total score is noted.The events E,F and G are 'a total of 4','a total of 9 or more',and 'a total divisible by 5'respectively.Calculate P(E),P(F) and P(G) and decide which pairs of events,if any, are independent.

asked Jan 8, 2013 by sreemathi.v

1 answer

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