Nostalgia is to anticipation as ________ is to ________.

Which one of the following options maintains a similar logical relation in the above sentence?

Consider the following sentences:

(i) I woke up from sleep.

(ii) I woked up from sleep.

(iii) I was woken up from sleep.

(iv) I was wokened up from sleep.

Which of the above sentences are grammatically CORRECT?

Given below are two statements and two conclusions.

Statement 1 : All purple are green.

Statement 1 : All black are green.

Conclusion I: Some black are purple.

Conclusion II : No black is purple.

Based on the above statements and conclusions, which one of the following options is logically CORRECT?        

Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic. AI enables computers to learn, given enough training data. For humans, sitting in front of a computer for long hours can lead to health issues.

Which of the following can be deduced from the above passage?

(i) Nowadays, computers are present in almost all places.

(ii) Computers cannot be used for solving problems in engineering.

(iii) For humans, there are both positive and negative effects of using computers.

(iv) Artificial intelligence can be done without data.

The current population of a city is . If it has been increasing at the rate of  per annum, what was its population 2 years ago?

p and q are positive integers and , then,

The least number of squares that must be added so that the line  becomes the line of symmetry is ________.

Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is __________.

The number of minutes spent by two students,  and , exercising every day in a given week are shown in the bar chart below.

The number of days in the given week in which one of the students spent a minimum of  more than the other student, on a given day, is

Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure below.

The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is