Recent questions tagged sec1

Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event - the coin shows a tail, given that - at least one die shows a 3.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Given that the two numbers appearing on throwing two dice are different. Find the probability of the event - the sum of numbers on the dice is 4.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

An instructor has a question bank consisting of 300 easy True / False questions, 200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl, (ii) at least one is a girl?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A black and a red dice are rolled. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Determine P(E|F) . Mother, father and son line up at random for a family picture E : son on one end, F : father in middle

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Determine P(E|F) . A die is thrown three times, E : 4 appears on the third toss, F : 6 and 5 appears respectively on first two tosses

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Determine P(E|F) when Two coins are tossed once, where E : tail appears on one coin, F : one coin shows head

asked Nov 27, 2012 by balaji.thirumalai

1 answer

If P(A) =6 / 11 , P(B) = 5 / 11 and P(A ∪ B)= 7 /11 find (i) P(A∩B) (ii) P(A|B) (iii) P(B|A)

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Evaluate P(A ∪ B), if 2P(A) = P(B) =5/13 and P(A|B) =2/5

asked Nov 27, 2012 by balaji.thirumalai

1 answer

If P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find i) P(A ∩ B), (ii) P(A|B) and (iii) P(A ∪ B)

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Compute P(A|B), if P(B) = 0.5 and P (A $\cap$ B) = 0.32

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Choose the correct answer in the total revenue in Rupees received from the sale of $x$ units of a product is given by $Rx = 3x^2 +36x + 5$. The marginal revenue, when $x = 15$ is

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the rate of change of the area of a circle with respect to its radius $r$ at $r = 6$ cm is

asked Nov 23, 2012 by thanvigandhi_1

1 answer

The total revenue in Rupees received from the sale of $x$ units of a product is given by $ R(x) = 13x^2 + 26x + 15.$ Find the marginal revenue when $x = 7$.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

The total cost $C(x)$ in Rupees associated with the production of $x$ units of an item is given by $ C(x) = 0.007x^3 - 0.003x^2 + 15x + 4000.$ Find the marginal cost when 17 units are produced.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Sand is pouring from a pipe at the rate of $12 cm^3/s$. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?

asked Nov 23, 2012 by thanvigandhi_1

1 answer

A balloon, which always remains spherical, has a variable diameter $\large\frac{3}{2}$$(2x+1)$. Find the rate of change of its volume with respect to $x.$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

The radius of an air bubble is increasing at the rate of $ \large\frac{1}{2}$ cm/s. At what rate is the volume of the bubble increasing when the radius is $1\; cm$?

asked Nov 23, 2012 by thanvigandhi_1

1 answer

A particle moves along the curve $ 6y = x^3 +2$. Find the points on the curve at which the $y$-coordinate is changing $8$ times as fast as the $x$-coordinate.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall ?

asked Nov 23, 2012 by thanvigandhi_1

1 answer

A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is $10\; cm$.

asked Nov 22, 2012 by thanvigandhi_1

1 answer

A balloon, which always remains spherical on inflation, is being inflated by pumping in $900$ cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is $15\; cm$.

asked Nov 22, 2012 by thanvigandhi_1

1 answer

The length $x$ of a rectangle is decreasing at the rate of $5\; cm/minute$ and the width y is increasing at the rate of $4\; cm/minute$. When $x = 8$ cm and $y = 6$ cm, find the rates of change of (a) the perimeter

asked Nov 22, 2012 by thanvigandhi_1

1 answer

The radius of a circle is increasing at the rate of $0.7\; cm/s$. What is the rate of increase of its circumference?

asked Nov 22, 2012 by thanvigandhi_1

1 answer

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

asked Nov 22, 2012 by thanvigandhi_1

1 answer

An edge of a variable cube is increasing at the rate of $3\; cm/s$. How fast is the volume of the cube increasing when the edge is $10\; cm$ long?

asked Nov 22, 2012 by thanvigandhi_1

1 answer

The radius of a circle is increasing uniformly at the rate of $3\; cm/s.$ Find the rate at which the area of the circle is increasing when the radius is $10\; cm$.

asked Nov 22, 2012 by thanvigandhi_1

1 answer

If a matrix has 24 elements, what are the possible orders it can have? What if it has 13 elements?

asked Nov 16, 2012 by mahuya_bh

0 answers

The volume of a cube is increasing at the rate of $ 8\;cm^ 3/s$ . How fast is the volume of a cube is increasing at the rate of $8\;cm^ 3 /s$ . How fast is the surface area increasing when the length of an edge is $12 cm$?

asked Nov 16, 2012 by kasturi.c

1 answer

Find the rate of change of the area of a circle with respect to its radius r when $(a)\; r = 3 cm$

asked Nov 16, 2012 by kasturi.c

1 answer

Find the values of $k$ so that the function $f$ is continuous at the indicated point in $ f(x) = \left\{ \begin{array} {1 1} \large\frac{k\cos x}{\pi - 2x}\normalsize,& \quad { if \; x \neq \large\frac{\pi}{2} }\\ \normalsize 3 ,& \quad { if \; x = \large\frac{\pi}{2} }\\ \end{array} \right. \qquad at \; x = \; \large\frac{\pi}{2} $

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find the values of $a$ and $b$ such that the function defined by $ f(x) = \left\{ \begin{array} {1 1} 5 ,& \quad\text{ if $ x $ $\leq 2$}\\ ax+b,& \quad \text{if $2$ < x<10}\\ 21,& \quad \text{if $ x $ $\geq 10$}\\ \end{array} \right.$ is a continuous function.

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find the values of $k$ so that the function $f$ is continuous at the indicated point in $ f(x) = \left\{ \begin{array} {1 1} kx+1 ,& \quad\text{ if $ x $ $\leq 5$}\\ 3x-5,& \quad \text{if $x$ > 5}\\ \end{array} \right.\qquad at \; x = 5 $

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find the values of $k$ so that the function $f$ is continuous at the indicated point in $f(x) = \left\{ \begin{array} {1 1} kx+1 ,& \quad\text{ if $ x $ $\leq \pi$}\\ \cos x,& \quad \text{if $x$ > $\pi$}\\ \end{array} \right.$ at $x = \pi$

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find the values of $k$ so that the function $f$ is continuous at the indicated point in $ f(x) = \left\{ \begin{array} {1 1} kx^2 ,& \quad\text{ if $ x $ $\leq 2$}\\ 3,& \quad \text{if $x$ > 2}\\ \end{array} \right. \qquad at \;x = 2 $

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Examine the continuity of $f$, where $f$ is defined by $ f(x) = \left\{ \begin{array} {1 1} \sin x - \cos x,& \quad\text{ if $x$ $\neq$ 0 }\\ -1 ,& \quad \text{if $x$ =0}\\ \end{array} \right. $

asked Nov 10, 2012 by thanvigandhi_1

1 answer

Determine if $f$ defined by $f(x) = \left\{ \begin{array} {1 1} x^2sin \large\frac{ 1 }{x},\normalsize & \quad\text{ if x $\neq$ 0 }\\ 0 ,& \quad \text{if $x$ =0}\\ \end{array} \right. $ is a continuous function?

asked Nov 10, 2012 by thanvigandhi_1

1 answer

Find all points of discontinuity of $f$, where $ f(x) = \left\{ \begin{array} {1 1} \large\frac {sinx} {x},\normalsize & \quad\text{ if $x$ < 0 }\\ x + 1 ,& \quad \text{if $x$ $ \geq 0$}\\ \end{array} \right. $

asked Nov 10, 2012 by thanvigandhi_1

1 answer

For what value of $ \lambda $ is the function defined by $f$ defined by $ f(x) = \left\{ \begin{array} {1 1} \lambda(x^2 - 2x) ,& \quad\text{ if $ x $ $\leq 0$}\\ 4x + 1,& \quad \text{if $x$ > 0}\\ \end{array} \right. $ Continuous at $x = 0$?

asked Nov 10, 2012 by thanvigandhi_1

1 answer

Find the relationship between $a$ and $b$ so that the function $f$ defined by $ f(x) = \left\{ \begin{array} {1 1} ax + 1 ,& \quad\text{ if $ x $ $\leq 3$}\\ bx + 3,& \quad \text{if $x$ > 3}\\ \end{array} \right. $ is continuous at $x = 3$.

asked Nov 10, 2012 by thanvigandhi_1

1 answer

Discuss the continuity of the function $f$, where $f$ is defined by $f(x) = \left\{ \begin{array} {1 1} -2 ,& \quad\text{ if $ x $ $\leq -1$}\\ 2x,& \quad\text{ if $ -1 $ < x $\leq1$}\\ 2 ,& \quad\text{ if $ x $ > 1}\\ \end{array} \right. $

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Discuss the continuity of the function $f$, where $f$ is defined by $ f(x) = \left\{ \begin{array} {1 1} 2x ,& \quad\text{ if $ x $ < 0}\\ 0,& \quad\text{if $ 0 $ $\leq x$ $\leq1$}\\ 4x ,& \quad\text{ if $ x $ > 1}\\ \end{array} \right. $

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Discuss the continuity of the function $f$, where $f$ is defined by \[ f(x) = \left\{ \begin{array} {1 1} 3 ,& \quad\text{ if $ 0 $ $\leq x$ $\leq1$}\\ 4,& \quad\text{if $ 1 $ < $x$ < 3 }\\ 5 ,& \quad\text{ if $ 3 $ $\leq x$ $\leq10$}\\ \end{array} \right. \]

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Is the function defined by $ f(x) = \left\{ \begin{array} {1 1} x + 5 ,& \quad\text{ if $ x $ $\leq 1$}\\ x - 5,& \quad \text{if $x$ > 1}\\ \end{array} \right. $ a continuous function?

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Find all points of discontinuity of $f$, where $f$fined by $ f(x) = \left\{ \begin{array} {1 1} x^{10} -1 ,& \quad\text{ if $ x $ $\leq 1$}\\ x^2,& \quad \text{if $x$ > 1}\\ \end{array} \right. $

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Find all points of discontinuity of $f$, where $f$ is defined by $ f(x) = \left\{ \begin{array} {1 1} x^3-3 ,& \quad\text{ if $ x $ $\leq 2$}\\ x^2+1,& \quad \text{if $x$ > 2}\\ \end{array} \right. $

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Find all points of discontinuity of $f$, where $f$ is defined by $f(x) = \left\{ \begin{array} {1 1} x + 1,& \quad\text{ if $ x $ $\geq 1$}\\ x^2+1,& \quad \text{if $x$ < 1}\\ \end{array} \right. $

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Find all points of discontinuity of $f$, where $f$ is defined by $f(x) = \left\{ \begin{array} {1 1} \large \frac x { |\;x\;| },& \quad\text{ if $x$ < 0 }\\ -1 ,& \quad \text{if $x$ $ \geq 0$}\\ \end{array} \right. $

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Find all points of discontinuity of $f$, where $f$ is defined by $ f(x) = \left\{ \begin{array} {1 1} \large \frac{ |\;x\;| }x,& \quad\text{ if x $\neq$ 0 }\\ 0 ,& \quad \text{if $x$ =0}\\ \end{array} \right. $

asked Nov 9, 2012 by thanvigandhi_1

1 answer

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