List of top Questions asked in CAT

If $a + b + c = 0$, where $a \neq b \neq c$, then \[ \frac{a}{2a^2 + bc} + \frac{b}{2b^2 + ac} + \frac{c}{2c^2 + ab} \] is equal to:

A right circular cone, a right circular cylinder and a hemisphere, all have the same radius, and the heights of the cone and cylinder are equal to their diameters. Then their volumes are proportional, respectively, to:

A right circular cone of height $h$ is cut by a plane parallel to the base and at a distance $h/3$ from the base. Then the volumes of the resulting cone and the frustum are in the ratio:

If $\log_{9} \log_{5} \left( \sqrt{x+5} + \sqrt{x} \right) = 0$, find the value of $x$.

Two towns A and B are 100 km apart. A school is to be built for 100 students of town B and 30 students of Town A. Expenditure on transport is Rs. 1.20 per km per student. If the total expenditure on transport by all 130 students is to be as small as possible, then the school should be built at:

One man can do as much work in one day as a woman can do in 2 days. A child does one-third the work in a day as a woman. If an estate-owner hires 39 pairs of hands — men, women, and children — in the ratio 6 : 5 : 2 and pays them in all Rs. 1113 at the end of the day's work, what must the daily wages of a child be, if the wages are proportional to the amount of work done?

The number of votes not cast for the Praja Party increased by 25% in the National General Election over those not cast for it in the previous Assembly Polls, and the Praja Party lost by a majority twice as large as that by which it had won the Assembly Polls. If a total 2,60,000 people voted each time, how many voted for the Praja Party in the Assembly Elections?

Identify the set of three statements that are logically related.
A. No wires are hooks.
B. Some springs are hooks.
C. All springs are wires.
D. Some hooks are not wires.
E. No hook is a spring.
F. All wires are springs.

Identify the set of three statements that are logically related.
A. Some abra are dabra.
B. All abra are cabra.
C. All dabra are abra.
D. All dabra are not abra.
E. Some cabra are abra.
F. Some cabra are dabra.

Identify the set of three statements that are logically related.
A. No plane is a chain.
B. All manes are chains.
C. No mane is a plane.
D. Some manes are not planes.
E. Some planes are manes.
F. Some chains are not planes.

Identify the set of three statements that are logically related.
A. All dolls are nice.
B. All toys are nice.
C. All toys are dolls.
D. Some toys are nice.
E. Some nice things are dolls.
F. No doll is nice.

Identify the set of three statements that are logically related.
A. Some buildings are not sky-scrappers.
B. Some sky-scrappers are not buildings.
C. No structure is a sky-scrapper.
D. All sky-scrappers are structures.
E. Some sky-scrappers are buildings.
F. Some structures are not buildings.

Identify the set of three statements that are logically related.
A. All bins are buckets.
B. No bucket is a basket.
C. No bin is a basket.
D. Some baskets are buckets.
E. Some bins are baskets.
F. No basket is a bin.

Identify the set of three statements that are logically related.
A. All vegetarians eat meat.
B. All those who eat meat are not vegetarians.
C. All those who eat meat are herbivorous.
D. All vegetarians are carnivorous.
E. All those who eat meat are carnivorous.
F. Vegetarians are herbivorous.

Identify the set of three statements that are logically related.
A. All roses have thorns.
B. All roses have nectar.
C. All plants with nectar have thorns.
D. All shrubs have roses.
E. All shrubs have nectar.
F. Some roses have thorns.

Identify the set of three statements that are logically related.
A. No spring is a season.
B. Some seasons are springs.
C. Some seasons are autumns.
D. No seasons are autumns.
E. Some springs are not autumns.
F. All springs are autumns.

Identify the set of three statements that are logically related.
A. All falcons fly high.
B. All falcons are blind.
C. All falcons are birds.
D. All birds are yellow.
E. All birds are thirsty.
F. All falcons are yellow.

Classify each sentence as: J: Judgement — opinion, recommendation, or evaluation.
F: Fact — a verifiable statement or observable truth.
I: Inference — a logical conclusion drawn from facts.
A. The prices of electronic goods are falling.
B. Since we have substantial reductions in import duties, this is obvious.
C. The trend is bound to continue in the near future.
D. But the turnover of the electronic industry is still rising, because the consumers are increasing at a rapid rate.

Classify each sentence as: J: Judgement — opinion, recommendation, or evaluation.
F: Fact — a verifiable statement or observable truth.
I: Inference — a logical conclusion drawn from facts.
A. In the past, it appears, wealth distribution, and not wealth creation has dominated the economic policy.
B. Clearly, the government has not bothered to eradicate poverty.
C. Today’s liberalization is far from the hitherto Nehruvian socialism.
D. Results are evident in the form of a boom in the manufacturing sector output and turnover of all industries.

Classify each sentence as: J: Judgement — opinion, recommendation, or evaluation.
F: Fact — a verifiable statement or observable truth.
I: Inference — a logical conclusion drawn from facts.
A. The ideal solution will be to advertise aggressively.
B. One brand is already popular amongst the youth.
C. Reducing prices will mean trouble as our revenues are already dwindling.
D. The correct solution will be to consolidate by aggressive marketing.

Classify each sentence as: J: Judgement — opinion, recommendation, or evaluation.
F: Fact — a verifiable statement or observable truth.
I: Inference — a logical conclusion drawn from facts.
A. If democracy is to survive the people must develop a sense of consumerism.
B. Consumerism has helped improve the quality of goods in certain countries.
C. The protected environment in our country is helping the local manufacturers.
D. The quality of goods suffers if the manufacturers take undue advantage of this.

Classify each sentence as: J: Judgement — opinion, recommendation, or evaluation.
F: Fact — a verifiable statement or observable truth.
I: Inference — a logical conclusion drawn from facts.
A. Unless the banks agree to a deferment of the interest, we cannot show profits this year.
B. This would not have happened had we adopted a stricter credit scheme.
C. The revenues so far cover only the cost and salaries.
D. Let us learn a lesson: we cannot make profits without complete control over credit.

Classify each sentence as: J: Judgement — opinion, recommendation, or evaluation.
F: Fact — a verifiable statement or observable truth.
I: Inference — a logical conclusion drawn from facts.
A. Qualities cannot be injected into one’s personality.
B. They are completely dependent on the genetic configuration that one inherits.
C. Hence changing our inherent traits is impossible as the genes are unalterable.
D. The least one can do is to try and subdue the “bad qualities”.

Classify each sentence as: J: Judgement — opinion, recommendation, or evaluation.
F: Fact — a verifiable statement or observable truth.
I: Inference — a logical conclusion drawn from facts.
A. Everything is purposeless.
B. Nothing before and after the existence of the universe is known with certainty.
C. Man is a part of the purposeless universe; hence man is also purposeless.
D. There is only one way of adding purpose to this universe: Union with Him.

Classify each sentence as: J: Judgement — opinion, recommendation, or evaluation.
F: Fact — a verifiable statement or observable truth.
I: Inference — a logical conclusion drawn from facts.
A. Everyday social life is impossible without interpersonal relationships.
B. The root of many misunderstandings has been cited in poor relations among individuals.
C. Assuming the above to be true, social life will be much better if people understand the importance of good interpersonal relations.
D. A study reveals that interpersonal relations and hence life in general can be improved with a little effort on the part of individuals.