Based on the relationship between each polygon and the number inside it, the value of '  ' is

Given a fair six-faced dice where the faces are labelled '1', '2', '3', '4', '5' and '6', what is the probability of getting a '1' on the first roll of the dice and a '4' on the second roll?

The figure below shows the front and rear view of a disc, which is shaded with identical patterns. The disc is flipped once with respect to any one of the fixed axes 1-1, 2-2 or 3-3 chosen uniformly at random.

What is the probability that the disc DOES NOT retain the same front and rear views after the flipping operation?

There are two identical dice with a single letter on each of the faces. The following six letters: Q, R, S, T, U and V, one on each of the faces. Any of the six outcomes are equally likely. The two dice are thrown once independently at random. What is the probability that the outcomes on the dice were composed only of any combination of the following possible outcomes:

Q, U and V?

Let  be a continuous random variable denoting the temperature measured. The range of temperature is (0,100) degree Celsius and let the probability density function of X be  for . The mean of X is

A class of twelve children has two more boys than girls. A group of three children are randomly picked from this class to accompany the teacher on a field trip. What is the probability that the group accompanying the teacher contains more girls than boys?

An e-mail password must contain three characters. The password has to contain one numeral from 0 to 9. one upper case and one lower case character from the English alphabet. How many distinct passwords are possible?

In a certain code. AMCF is written as EQGJ and NKUF is written as ROYJ. How will DHLP be written in that code?

Rahul, Murali, Srinivas and Arul are seated around a square table. Rahul is sitting to the left of Murali. Srinivas is sitting to the right of Arul. Which of the following pairs are seated opposite each other?

The probability that a k-digit number does NOT contain the digits 0, 5, or 9 is

Six people are seated around a circular table. There are at least two men and two women. There are at least three right-handed persons. Every woman has a left-handed person to her immediate right.

None of the women are right-handed. The number of women at the table is

Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four shirts colored red, pink, blue and white respectively. Arun dislikes the color red and Shweta dislikes the colour white. Gulab and Neel like all the colors. In how many different ways can they choose the shirts so that no one has a shirt with a color he or she dislikes?

There are five buildings called V, W, X, Y and Z in a row (not necessarily in that order). V is to the West of W. Z is to the East of X and the West of V. W is to the West of Y. Which is the building in the middle?

There are 3 red socks, 4 green socks and 3 blue socks. You choose 2 socks. The probability that they are of the same color is

There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labelled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box would you open to determine the contents of all three boxes?

Among 150 faculty members in an institute, 55 are connected with each other through Facebook and 85 are connected through whatsapp. 30 faculty members do not have Facebook or whatsapp accounts. The number of faculty members connected only through facebook accounts is __________.

Shaquille O’ Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free throws out of 100 attempts on average. What is the probability that he will successfully makes exactly 6 free throws in 10 attempts?

Given Set A = {2, 3, 4, 5} and Set B = {11, 12, 13, 14, 15}, two numbers are randomly selected, one from each set. What is the probability that the sum of the two numbers equals 16?

The probabilities that a student passes in Mathematics, physics and Chemistry are m, p, and c respectively of these subject, the student has 75% chance of passing in a least one, a 50 % chance of passing at least two a 40% chance of passing exactly two, following relations are drawn in m, p, c:

(I) p + m + c = 27/20

(II) p + m + c  = 13/20

(III) (p)x(m)x(c) = 1/20

If p, q, r, s are distinct integers such that:

f (p, q, r, s)=max(p, q, r, s)

g (p, q, r, s)=min(p, q, r, s)

h (p, q, r, s)=remainder of  if  or remainder of  if

Also a function fgh (p, q, r, s) = f (p, q, r, s)  g (p, q, r, s) h (p, q, r, s)

Also the same operations are valid with two variable functions of the form f(p, q).

What is the value of fg ( h(2, 5, 7, 3), 4, 6, 8)?

What is the chance that a leap year, selected at random, will contain 53 Saturdays?

A and B are friends. They decide to meet between 1PM and 2PM on a given day. There is a condition that whoever arrives first will not wait for the other for more than 15 minutes. The probability that they will meet on that day is

There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing balanced is of unlimited capacity. Using this balance, the minimum number of weighing required to identify the heavier bag is

25 persons are in a room, 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is: