List of practice Questions

Consider a square $ABCD$ of side $60$ cm. It contains arcs $BD$ and $AC$ drawn with centres at $A$ and $D$ respectively. A circle is drawn such that it is tangent to side $AB$, and the arcs $BD$ and $AC$. What is the radius of the circle?

In a plane rectangular coordinate system, points $L, M, N,$ and $O$ are represented by the coordinates $(-5,0), (1,-1), (0,5),$ and $(-1,5)$ respectively. Consider a variable point $P$ in the same plane. The minimum value of $PL + PM + PN + PO$ is:

Let $PQRS$ be a quadrilateral. Two circles $O_1$ and $O_2$ are inscribed in triangles $PQR$ and $PSR$ respectively. Circle $O_1$ touches $PR$ at $M$ and circle $O_2$ touches $PR$ at $N$. Find the length of $MN$. % Statement I A circle is inscribed in the quadrilateral $PQRS$. % Statement II The radii of the circles $O_1$ and $O_2$ are 5 and 6 units respectively.

The scheduling officer for a local police department is trying to schedule additional patrol units in each of two neighbourhoods – southern and northern. She knows that on any given day, the probabilities of major crimes and minor crimes being committed in the northern neighbourhood were 0.418 and 0.612, respectively, and that the corresponding probabilities in the southern neighbourhood were 0.355 and 0.520. Assuming that all crime occur independent of each other and likewise that crime in the two neighbourhoods are independent of each other, what is the probability that no crime of either type is committed in either neighbourhood on any given day?

There are four machines in a factory. At exactly 8 pm, when the mechanic is about to leave the factory, he is informed that two of the four machines are not working properly. The mechanic is in a hurry, and decides that he will identify the two faulty machines before going home, and repair them next morning. It takes him twenty minutes to walk to the bus stop. The last bus leaves at 8:32 pm. If it takes six minutes to identify whether a machine is defective or not, and if he decides to check the machines at random, what is the probability that the mechanic will be able to catch the last bus?

Indian government may hold top executives responsible if state-run power companies fail to meet performance targets and punish them with fines and transfers. Performance parameters are aimed at ensuring that at least the reduced target of 62,000 MW of generation capacity addition is achieved before the end of the 11th Plan.
While the target for the 11th five-year plan has already been scaled down by the government from 78,500 MW, in the first three years of the plan only 22,302 MW of fresh capacity was achieved.
If you were the chairman of one of these power PSUs, which of the following statements (all of which are assumed to be true) could best be used in order to strengthen your case against the government holding top executives responsible?
i. The labour unions, owing allegiance to ruling party at the Center, are not allowing work to progress with their demands for wage hikes that are untenable.
ii. The actions of the mid-level management are not in line with the objectives laid down by the top management.
iii. The delays have been due to difficulties in obtaining funds at reasonable interest rates on account of the recessionary conditions.
iv. We are not to blame. The government is not doing enough to ensure availability of sufficient fuel to power the existing plants, let alone the new plants.
v. The government had ignored the infrastructure availability like roads etc., and environmental clearances required for such projects and therefore set an unrealistic target to begin with, and the revised target is also unrealistic as well.

On 1st March, Timon arrived in a new city and was looking for a place to stay. He met a landlady who offered to rent her apartment at a reasonable price but wanted him to pay the rent on a daily basis. Timon had a silver bar of 31 inches, and an inch of the silver bar was exactly equal to a day’s rent. He agreed to pay an inch of the silver bar towards the daily rent. Timon wanted to make the minimum number of pieces of the silver bar but did not want to pay any advance rent. How many pieces did he make?

Statement: No cats are dogs.
Conclusion: No dogs are cats.
Is the conclusion valid?

Statement: Some birds can fly.
Conclusion: Some birds cannot fly.
Is the conclusion valid?

Nature is ____________ and unchangeable, and it is ____________ as to whether its hidden reasons and ____________ are ____________ to man or not. The option that best fills the blanks in the above sentence would be:

In spite of being perceived as ________ by all, the club members decided to ________ Arun, a skinny teenager with prominent ________, as the member of the year, so that the whole affair would be ________ to Arun’s father who was recuperating after a serious illness. The option that best fills the blanks in the above sentence would be:

Perhaps this war will pass like the others which divided us, leaving us dead, killing us along with the killers but the shame of this time puts its burning fingers to our faces. Who will erase the ruthlessness hidden in innocent blood? Which of the following is certainly not implied in the above verse?

The author has ____________ his composition to the best of his ____________; yet listen to it with a sympathetic ____________, O ____________ souls, and judge it. The option that best fills the blanks in the above sentence would be:

There is much difficulty __________ getting __________ this place and it is not possible to reach __________ without the grace of the lord. The option that best fills the blanks in the above sentence would be:

__________ you have a doubt, why not go and verify? I shall be waiting in the shade __________ this banyan tree till you come back __________ me. The option that best fills the blanks in the above sentence would be:

Travelling is my hobby. Today in the Himalayas, as I drag my feet through the __________, I cannot but think of the same time last year when I was negotiating the thick __________ of the Ganges delta or for that matter the time I spent with my children __________ about in the waters of the Arabian Sea. The option that best fills the blanks in the above sentence would be:

Pick the odd one out:

Choose the odd one out:

Choose the odd one out:

Read the following sentences and choose the option that best arranges them in a logical order: 1. In law a fiduciary individual is someone who is entrusted with the power to act on behalf of and for the benefit of another.
2. Following the weight of corporate law and legal precedent, the director primacy model positions directors as autonomous fiduciaries, not agents.
3. The term fiduciary derives from the Latin fiducia, or trust, and the fiduciary is expected to act in good faith and honesty for the beneficiary’s interests.
4. A person who accepts the role of fiduciary in law must single-mindedly pursue the interests of his or her beneficiary, in this case the corporation, even when the latter cannot monitor or control the fiduciary’s behaviour.

Read the sentences and choose the option that best arranges them in a logical order:
a. Generally, it is unusual for a new problem in international relations to be considered without at the same time some international organization being developed to deal with it.
b. International society has, in spite of the diversity of culture and political systems, been progressively drawn closer together and become more unified.
c. Despite the fears and concerns of some governments that international organizations are increasing too fast and that they are a burden on their exchequers, they are still proliferating at a considerable rate.
d. People and their governments now look far beyond national frontiers and feel a common responsibility for the major problems of the world and for lesser problems that may subsist within smaller groups of states.
e. More recently in the 1990s the problems of international trade, which was growing increasingly complex, led to the development of the WTO.
f. For instance, concern with the instability of commodities markets led to the establishment in the 1980s of the Common Fund for Commodities and the competition for the newly discovered wealth of the international seabed area resulted in the creation of the ISA under the Law of the Sea Convention of 1982, based on the concept of the “common heritage of mankind”.

Few sentences are given below continuously. Identify the best sequence of punctuations among the given options. (The rule of capitalization at the beginning of sentences has been ignored in the passage given below). Note: the arrows in the options indicate text that would be within the punctuations. A person’s frames of perception and action are narrow in early stages of development focused on social membership and technical competence the early life of the organizations often is focused on survival and efficiency only later and rarely emphasizing process of learning and development however in later stages both individual and organization become more concerned with the learning process itself the way the perceptions and practices are articulated and revised in interactions and how more people can be engaged in mutual learning and inquiry.

Impressions are direct, vivid, and forceful products of immediate experience; ideas are merely feeble copies of these original impressions.
Assuming the above statement is true, which of the statements logically follow from it?
I. Every impression leads to an idea.
II. Ideas must follow an antecedent impression.
III. The colour of the 2011 XAT test booklet right in front of a candidate is an impression to her, whereas the memory of the colour of her television set is an idea.
IV. If one was interested in origin of the idea of the colour of a television set, then one need to understand the impressions from which this idea was derived.

Media are not just passive channels of information. Not only do they supply the stuff of thought, but they also shape the process of thought. And what the internet seems to be doing is chipping away our capacity for concentration. Which of the following, if true, would most strengthen the argument presented above?

Which of the following, if true, would most weaken the argument presented in the previous question?