Recent questions tagged easy

In a hostel, 60% of the students read Hindi news paper, 40% read English news paper and 20% read both Hindi and English news papers. A student is selected at random. (a) Find the probability that she reads neither Hindi nor English news papers. (b) If she reads Hindi news paper, find the probability that she reads English news paper. (c) If she reads English news paper, find the probability that she reads Hindi news paper.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

One card is drawn at random from a well shuffled deck of 52 cards. Are E and F independant if: E : the card drawn is a spade F : the card drawn is an ace

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Probability of solving specific problem independently by A and B are $\large \frac{1}{2} $ and $\large \frac{1}{3} $ respectively. If both try to solve the problem independently, find the probability that $ \text {(i) the problem is solved (ii) exactly one of them solves the problem.} $

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top, by cutting off square from each corner and folding up the flaps. What should be the side of the square in cms to be cut off so that the volume of the box is maximum ?

asked Nov 27, 2012 by thanvigandhi_1

1 answer

A square piece of tin of side 18 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible.

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that (i) both balls are red. (ii) first ball is black and second is red. (iii) one of them is black and other is red.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A die is tossed thrice. Find the probability of getting an odd number at least once.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6. Find (i) P(A and B) (ii) P(A and not B) (iii) P(A or B) (iv) P(neither A nor B)

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Events A and B are such that $P (A) = \frac{1}{2} , P(B) = \frac{7}{12}$ and P(not A or not B) = $ \frac{1}{4} $ . State whether A and B are independent?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find two positive numbers whose sum is 16 and the sum of whose cubes is minimum.

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Find two positive numbers $x$ and $y$ such that their sum is 35 and the product $x^2 y^5$ is a maximum.

asked Nov 27, 2012 by thanvigandhi_1

1 answer

If A and B are two events such that $P (A) = \large \frac{1}{4} , P (B) = \large\frac{1}{2} $ and $P(A \cap B) = \large \frac{1}{8} $ , find $P$ (not A and not B).

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Let A and B be independent events with P (A) = 0.3 and P(B) = 0.4. Find (i) P(A $\cap$ B) (ii) P(A $\cup$ B) (iii) P ($\large\frac{A}{B}$) (iv) P ($\large\frac{B}{A}$)

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find two numbers whose sum is 24 and whose product is as large as possible.

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Given that the events A and B are such that $P(A) = \large \frac{1}{2} , P (A \cap B) = \large \frac{3}{5} $ and $P(B) = p$. Find p if they are (i) mutually exclusive (ii) independent.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find the maximum and minimum values of $ x + \sin\: 2x$ on $[0, 2\pi].$

asked Nov 27, 2012 by thanvigandhi_1

1 answer

It is given that at $x = 1$, the function $x^4 – 62x^2 + ax + 9$ attains its maximum value, on the interval $[0, 2].$ Find the value of $a.$

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Let E and F be events with $P (E) = \frac{3}{5} , P (F)= \frac{3}{10} $ and $P (E \cap F) = \frac{1}{5} $ . Are E and F independent?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find the maximum value of $2x^3 – 24x + 107$ in the interval $[1, 3]$.

asked Nov 27, 2012 by thanvigandhi_1

1 answer

A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event of the number being even, and B be the event of the number being red. Are A and B independent?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A fair coin and an unbiased die are tossed. Let A be the event - head appears on the coin and B be the event 3 on the die. Check whether A and B are independent events or not.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

At what points in the interval $[0, 2\pi]$, does the function $\sin\: 2x$ attain its maximum value?

asked Nov 27, 2012 by thanvigandhi_1

1 answer

If $P(A) = \frac{3}{5} $ and $P(B) = \frac{1}{5} $ , find $P (A \cap B) $ if A and B are independent events.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find both the maximum value and the minimum value of $3x^4 - 8x^3 + 12x^2 - 48x + 25$ on the interval $[0, 3].$

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Find the maximum profit that a company can make, if the profit function is given by $ p(x) = 41 - 72x - 18x^2$

asked Nov 27, 2012 by thanvigandhi_1

1 answer

If A and B are events such that P(A|B) = P(B|A), then which of the following is true?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

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

If $ A = \begin{bmatrix} 1 & 2 & -3 \\ 5 & 0 & 2 \\ 1 & -1 & 1 \end{bmatrix} , B = \begin{bmatrix} 3 & -1 & 2 \\ 4 & 2 & 5 \\ 2 & 0 & 3 \end{bmatrix} \text{ and } C = \begin{bmatrix} 4 & 1 & 2 \\ 0 & 3 & 2 \\ 1 & -3 & 2 \end{bmatrix} $, then compute $( A + B )$ and $( B - C )$. Also verify that $A + ( B - C ) = ( A + B ) - C. $

asked Nov 26, 2012 by pady_1

1 answer

Simplify $\cos\theta\begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}$ + $\sin\theta\begin{bmatrix} \sin\theta & -\cos\theta \\ \cos\theta & \sin\theta \end{bmatrix} $

asked Nov 26, 2012 by pady_1

1 answer

Find $X$ , if $Y = \begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix} $ and $ 2X + Y = \begin{bmatrix} 1 & 0 \\ -3 & 2 \end{bmatrix} $

asked Nov 26, 2012 by pady_1

1 answer

Find $x$ and $y$, if $ 2\begin{bmatrix} 1 & 3 \\ 0 & x \end{bmatrix} + \begin{bmatrix} y & 0 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 5 & 6 \\ 1 & 8 \end{bmatrix} $

asked Nov 26, 2012 by pady_1

1 answer

Solve the equation for $x, y, z$ and $t$ if $ 2\begin{bmatrix}x & z \\ y & t \end{bmatrix} + 3\begin{bmatrix} 1 & -1 \\ 0 & 2 \end{bmatrix} = 3\begin{bmatrix} 3 & 5 \\ 4 & 6 \end{bmatrix} $

asked Nov 26, 2012 by pady_1

1 answer

Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals: $\: f (x) = x^3, x \in [– 2, 2] $

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Prove that the following functions do not have maxima or minima: $ (i)\: f (x) = e^x $

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: $ (i)\: f (x) = x^2 $

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Find the maximum and minimum values, if any, of the following functions given by $ f (x) = |x + 2| - 1$

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Find the maximum and minimum values, if any, of the following functions given by?$\;f(x)=(2x-1)^2+3$

asked Nov 26, 2012 by thanvigandhi_1

1 answer

If the radius of a sphere is measured as $9 \: m$ with an error of $0.03 \: m$, then find the approximate error in calculating its surface area.

asked Nov 26, 2012 by thanvigandhi_1

1 answer

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