List of practice Questions

The angles of elevation of an electric pole from two points A and B lying on the level ground on either side of the pole are 30° and 60° respectively. If the two points A and B are 500 m apart, then at what distance from point A is the electric pole?

In an election in which there were only two candidates A and B, B got 50% of the votes that A got. Had A got 200 votes less, there would have been a tie. How many people cast their votes in all?

If the numerator and the denominator of a fraction are each decreased by 3, the fraction becomes 2/3. If both the numerator and the denominator are increased by 7, the fraction becomes 3/4. Find the fraction.

Ten years from now, the age of Raja’s father will be twice Raja’s age. Ten years ago, the age of Raja’s father was thrice Raja’s age. Find the present age of Raja and his father.

Read the following poem and answer the question that follows: I sought a soul in the sea
And found a coral there
Beneath the foam for me
An ocean was all laid bare.
Into my heart’s night
Along a narrow way
I groped; and lo! The light,
An infinite land of day.
Which of the following would best capture the ESSENCE of the poem above?

Choose the best pronunciation of the word, Sobriquet, from the following options:

The subject of this book is knavery, skullduggery, cheating, betrayal, unfairness, crime, sneakiness, malingering, cutting corner, immorality, dishonesty, betrayal, graft, wickedness, and sin.
Which of the following options best captures ALL the italicized words above?

The FIRST and the LAST sentences of the paragraph are numbered 1 & 6. The others, labelled as P, Q, R and S are given below. Arrange them to form the MOST LOGICALLY ORDERED paragraph.
1. Suppose I know someone, Smith.
P. One day you come to me and say: “Smith is in Cambridge.”
Q. I inquire, and find you stood at Guildhall and saw at the other end a man and said: “That was Smith.”
R. I’d say: “Listen. This isn’t sufficient evidence.”
S. I’ve heard that he has been killed in a battle in this war.
6. If we had a fair amount of evidence he was killed I would try to make you say that you’re being credulous.
Which of the following combinations is the MOST LOGICALLY ORDERED?

The FIRST and the LAST sentences of the paragraph are numbered 1 & 6. The others, labelled as P, Q, R and S, are given below. Arrange them to form the MOST LOGICALLY ORDERED paragraph.
1. The word “symmetry” is used here with a special meaning, and therefore needs to be defined.
P. For instance, if we look at a vase that is left-and-right symmetrical, then turn it $180^\circ$ around the vertical axis, it looks the same.
Q. When we have a picture symmetrical, one side is somehow the same as the other side.
R. When is a thing symmetrical — how can we define it?
S. Professor Hermann Weyl has given this definition of symmetry: a thing is symmetrical if one can subject it to a certain operation and it appears exactly the same after operation.
6. We shall adopt the definition of symmetry in Weyl’s more general form, and in that form we shall discuss symmetry of physical laws.
Which of the following combinations is the MOST LOGICALLY ORDERED?

In recent past, Indian football team has lost most of the matches in international football tournaments. The most successful coaches in Indian club football tournaments are from Latin American countries. In most of the Latin American countries, football is more popular sport than cricket.
From the passage above, choose the correct option:

Consider the two related statements below:
Statement I: Offices and positions for the marginalized sections should be open to those with greater savings among them.
Statement II: Offices and positions must be open to everyone based on the principle of fair opportunity.

This season will pass. The Prime Minister may not win Lok Sabha elections, or she may; she may not continue as Prime Minister, or she may. The country will survive whatever the texture of politics in this decade or the next.
Which of the following, IF TRUE, will BEST reinforce the author's view?

Read the following conversation:
OINOS: I can comprehend you thus far—that certain operations of what we term Nature, or the natural laws, will, under certain conditions, give rise to that which has all the appearance of creation. Shortly before the final overthrow of the earth, there were, I well remember, many very successful experiments in what some philosophers were weak enough to denominate the creation of animalculae.
AGATHOS: The cases of which you speak were, in fact, instances of the secondary creation—and of the only species of creation which has ever been, since the first word spoke into existence the first law.
Which of the following options CANNOT be DEFINITELY inferred based on the above conversation?

... there is a degree of convergence in the definition of trust which can be summarized as follows: Trust is a particular level of the subjective probability with which an agent assesses that another agent or group of agents will perform a particular action. When we say we trust someone or that someone is trustworthy, we implicitly mean that the probability that he will perform an action that is beneficial to us….
Which of the following statement BEST COMPLETES the passage above?

If ‘A + B’ means A is the brother of B, ‘A – B’ means A is the sister of B, and ‘A × B’ means A is the father of B, then which of the following means that M is the daughter of N?

The integral $\displaystyle\int \frac{dx}{(1+ \sqrt{x}) \sqrt{x - x^2}}$ is equal to (where $C$ is a constant of integration)

One mole of an ideal monatomic gas undergoes a process described by the equation $PV^{3}=$ constant. The heat capacity of the gas during this process is -