List of practice Questions

The value of the expression: \[ \displaystyle \sum_{i=2}^{100} \frac{1}{\log_i(100!)} \] is:

Circle C₁ has a radius of 3 units. The line segment PQ is the only diameter of the circle which is parallel to the X-axis. P and Q are points on curves given by the equations y = a^x and y = 2a^x respectively, where a < 1. The value of a is:

The sum of the possible values of \(x\) in the equation \(|x+7| + |x-8| = 16\) is:

There are two windows on the wall of a building that need repairs. A ladder 30 m long is placed against a wall such that it just reaches the first window which is 26 m high. The foot of the ladder is at point A. After the first window is fixed, the foot of the ladder is pushed backwards to point B so that the ladder can reach the second window. The angle made by the ladder with the ground is reduced by half, as a result of pushing the ladder. The distance between points A and B is:

Amitabh picks a random integer between 1 and 999, doubles it and gives the result to Sashi. Each time Sashi gets a number from Amitabh, he adds 50 and gives it back; Amitabh again doubles the received number. The first person whose result exceeds 1000 loses. Let $x$ be the smallest initial number that results in a win for Amitabh. The sum of the digits of $x$ is:

Consider four natural numbers: $x$, $y$, $x+y$, and $x-y$. Two statements are given:
I. All four numbers are prime numbers.
II. The arithmetic mean of the numbers is greater than 4.
Which of the following statements would be sufficient to determine the sum of the four numbers?

Triangle $ABC$ is a right-angled triangle. $D$ and $E$ are the midpoints of $AB$ and $BC$ respectively. Read the following statements.
I. $AE = 19$ II. $CD = 22$ III. $\angle B$ is a right angle.
Which of the following statements would be sufficient to determine the length of $AC$?

$x, 17, 3x - y^2 - 2, and 3x + y^2 - 30$ are four consecutive terms of an increasing arithmetic sequence. The sum of the four numbers is divisible by:

In quadrilateral $PQRS$, $PQ = 5$ units, $QR = 17$ units, $RS = 5$ units, and $PS = 9$ units. The length of the diagonal $QS$ can be:

Consider the statement given below as true: “Men use the plasticity of consumer identity construction to forge atavistic masculine identities based upon an imagined life of self-reliant, pre-modern men who lived outside the confines of cities, families, and work bureaucracies.” Which of the following statements would concur with the above idea and the theme of the main paragraph?

Consider the statement given below as true: “By appropriating fashion discourse, consumers generate personalized fashion narratives and metaphoric and metonymic references that negotiate key existential tensions and that often express resistance to dominant fashion norms in their social milieu or consumer culture at large.” Which of the following statements would concur with the above idea and the theme of the main paragraph?

The main issues of interpretation arising from the work of professionally trained anthropologists are that they are late in colonial/post-colonial trajectories, because professional training shapes their interpretations. However, within field of interest and training, their works are most thorough and systematic. The best conclusion drawn from the above paragraph is analogous to:

Consider merit pay for teachers. Schools face constant pressure to change their management approaches to improve performance, which is usually assessed by standardized reading, math, and science scores. In most schools teacher’s pay is determined by seniority, years of total teaching experience, and credentials. Pay is rarely based on performance, which is contrary to the belief among parents and private sector. Parents and business leaders lament that there are no carrots/sticks used to motivate teachers. Consequently, there has been greater push to implement some form of merit pay to improve the motivation. Which of the following statements will disapprove the claim of the parents and business leaders?

Read the following newspaper report: In a new study by Harvard School of Public Health (HSPH), researchers explored how caffeine can serve as a “mild anti-depressant”. They concluded that “drinking several cups of coffee daily appears to reduce the risk of suicide”. Data pulled in from three large studies in the US showed that the suicide risk of those who drank two to four cups of caffeinated coffee a day was about half of those who drank decaffeinated coffee or very little or no coffee. In the studies, a respondent’s caffeine consumption was assessed every four years through a questionnaire. The respondents were all adults, and the study was published online. The authors, however, cautioned the public from increasing coffee intake as it could result in “unpleasant side effects”. “Overall, our results suggest that there is little further benefit for consumption above two to three cups/day or 400 mg of caffeine/day,” wrote the researchers. The authors observed that there was no major difference in suicide risk for adults who drank two to three cups a day from those who drank four cups or more. Which of the following shaped graph would best capture the above paragraph (x-axis represents “coffee intake” and y-axis represents “suicidal tendency”)?

A group of nine runners will finish the 400 meters race in a certain order. The runners are: Ashok, Benjamin, Chetan, Divya, Eshant, Girish, Himani, Irravaty, and Faneesh. They all finish at different times, and their finishing order is as follows:
1. Faneesh finishes before Ashok
2. Divya finishes before Benjamin and Eshant
3. Irravaty finishes after Chetan
4. Girish finishes after Ashok
Which is the best position Girish can finish?

Consider the statement given below as true: “The failure of men to transition from being shoppers and consumers to producers and creators has implications about their manliness.” Which of the following statements would concur with the above idea and the theme of the main paragraph?