Consider the polynomial p(x)=c₀ + c₁x + c₂x^2 + c_3x^3, where no coefficient is 0. The minimum number of multiplications required to evaluate p on an input x is

If S={x|0 < x < 12}, M={x|1 < x < 9} and N={x|0 < x< 5}, find M' ∩ N'

Let E, F and G be finite sets and let A = (E∩ F) - (F ∩ G) and B = (E - (E ∩ G)) - (E - F). Which one of the following is true?

If the word FORGET is encoded as DPPHCU, then THINK is encoded as

Seven (distinct) road accidents occurred in a week. What is the probability that they all occurred on the same day?

What is the maximum number of different Boolean functions involving n Boolean variables?

Given below is a chart of rainfall amounts in Quinquinox city on a distant planet Quinox revolving around an equally distant Star. It has its own months and years. Year is, of course, the time takenin their own units of measurement to revolve once around their Star.

Examine the chart carefully and answer Question



How many months are there in a year on Quinox?

Given below is a chart of rainfall amounts in Quinquinox city on a distant planet Quinox revolving around an equally distant Star. It has its own months and years. Year is, of course, the time taken in their own units of measurement to revolve once around their Star.

Examine the chart carefully and answer Question



If climate is classified into the following three categories,

QNd Seasonal rainfall with wet season being short

QNe Uniform rainfall throughout the year

QNm Seasonal rainfall with wet season being long

Which category describes the climate of Quinquinox?

If the year on Quinox starts with Mon-Ol (which is also the first data point), which month in a year is the wettest?

Let S be a set of n elements. The number of ordered pairs in the largest and the smallest equivalence relations on S are

Here is a puzzle: find a number x such that x leaves a remainder of 9 when divided by 10, a remainder of 8 when divided by 9, a remainder of 7 when divided by 8, ... , a remainder of 2 when divided by 3 and a remainder of 1 when divided by 2.

How many such numbers are there?

Car A goes 200 Kms at an average speed of 40 Kmph in one direction and returns to the starting point covering the distance of 200 Kms at an average speed of 50 Kmph. Another Car B goes 200 Kms at an average speed of 45 Kmph and does the return journey of 200 Kms also at an average speed of 45 Kmph. Which statement is TRUE about the two cars A and B?

Which of the following is correctly represented by the Venn diagram above?

Questions 14 - 16 are based on the Venn diagram below. S represents all integers between 1 and 30, P represents prime numbers between 1 and 30, M represents multiples of 3 between 1 and 30, and F represents all factors of 30.



If G = P ∩ M ∩ F, then

Questions 14 - 16 are based on the Venn diagram below. S represents all integers between 1 and 30, P represents prime numbers between 1 and 30, M represents multiples of 3 between 1 and 30, and F represents all factors of 30.



What are the numbers in F but not in P or M?

Questions 14 - 16 are based on the Venn diagram below. S represents all integers between 1 and 30, P represents prime numbers between 1 and 30, M represents multiples of 3 between 1 and 30, and F represents all factors of 30.



What is the cardinality of P ∩ F?

Read the paragraphs below and answer Question.

When looking back on any kind of movement or revolution, one always likes to point to a beginning: "It began right there - it all started with so-and-so's famous speech ... " If structured

programming can be thought of as a revolution, then surely Dijkstra's land-mark paper, "Programming Considered as a Human Activity," published in 1965, marks its beginning. Virtually

the entire gospel of structured programming is contained in a few short pages: the arguments

against goto statements, the notion of top-down design, the emphasis on program correctness

and quality (or "elegance," as Dijkstra prefers to call it), and the strong argument against programs that modify themselves.

In addition to these fundamental concepts, there are some rather classic phrases that first appeared in this paper, and that have popped-up in dozens of subsequent articles and books. For

example, when discussing the "divide and conquer" approach characterizing top-down design,

Dijkstra admits, "I have only a very small head, ,and must live with it." What seems obvious to us today was a rather novel idea in 1965: the idea that while computers were - and still are

- getting faster and more powerful, human beings weren't.

This theme is repeated again and again, and is essentially the entire subject matter of Dijkstra's

1972 speech, "The Humble Programmer." ... Once you do read it, you can see why Dijkstra has

the reputation he does. His writing is succinct and yet convincing. Reading Dijkstra, someone

said, has been compared to eating marzipan - it's best to take very small bites, chew slowly,

and digest the mouthful before moving on to the next bite.

What is said to have begun with Dijkstra's landmark paper, "Programming Considered as a Human Activity" in 1965?