IIM Bangalore UG and BBA DBE · Paper 10

An educational council has six affiliated institutes, U to Z, with 5500 students (male and female) in all. Institute V has 8% of all the students, of whom 200 are male. Institute Z has 20% of all the students, of whom 700 are male.

The ratio of the number of female students in institute Z to the number of female students in institute V is:

The 5th term of an arithmetic progression is 17 and its 12th term is 45. What is the sum of its first 20 terms?

A solid metal sphere of radius 6 cm is melted and recast into small solid cones, each with base radius 2 cm and height 3 cm. How many cones are made, assuming no metal is lost?

A bar graph shows a factory's yearly output and sales, in thousand units.

Every unsold unit is added to stock, and nothing leaves the stock except through sales. The stock at the start of 2021 was 30 thousand units. What was the stock at the end of 2025, in thousand units?

The function $f : \mathbb{R} - \{3\} \to \mathbb{R} - \{3\}$ is given by $f(x) = \frac{3x + 2}{x - 3}$. What is $f^{-1}(x)$?

What is the value of $\int_{-2}^{2} \left(x^3\cos x + |x|\right)dx$?

In the financial year 2022-23, Country 2's fiscal deficit was 5.04% of its GDP and its debt to GDP ratio was 101.91%, while Country 3's fiscal deficit was 6.06% of its GDP. The debt to GDP ratio measures the government's total debt relative to GDP; the fiscal deficit is total expenditure minus total revenue.

If the fiscal deficit of Country 3 amounted to ₹$x$, surpassing that of Country 2 by 50%, what would be the debt (in ₹) of Country 2 during the financial year 2022-23?

Two circles of radii 21 cm each intersect in such a way that one of them passes through the centre of the other. What is the approximate value of the perimeter (in cm) of the region covered by the two circles together?

How many integers $x$ satisfy both $x^2 - 9x + 14 < 0$ and $x^2 > 20$?

The sum of the cost prices of three items was ₹24,150. The person sold the first item at a profit of 72%, the second item at a profit of 40% and the third item at a profit of 126%. The total profit earned from the sale of these three items was ₹19,432. If the cost price of the second item was ₹175 more than what it actually was, then the ratio of the cost prices of the second and the third items, respectively, would have been $4 : 5$. What was the difference (in ₹) between the profits earned from the sale of the first and the second items?

Select the set in which the numbers are related in the same way as are the numbers of the following sets.

(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. For example, with 13, operations such as adding, subtracting or multiplying 13 can be performed; breaking 13 down into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)

(15, 105, 7)

(12, 60, 5)

What should come in place of ? in the given series based on the English alphabetical order?

EGB, IKF, MOJ, QSN, ?

Statements: Some doctors are singers. All singers are dancers.

Conclusions: (I) Some doctors are dancers. (II) Some dancers are singers.

Taking the statements to be true, decide which conclusions must hold.

L, M, N, O, P and Q each scored different marks. Only two people scored more marks than O. M scored more than L but less than Q. Q scored less than O. N did not score the maximum marks.

Who amongst them scored the second highest marks?

What comes next in the series?

2, 12, 36, 80, 150, ?

Select the CORRECT preposition.

In a fit of rage, Angel threw the letter ______ the fire.

In the sentence below, some words are missing. Select the CORRECT option to fill in each blank.

Companies talk of investing in factories and governments in infrastructure, but there is a softer, less ______ focus of investment that can be more important: knowledge and skills.

Select the word closest in meaning to the bold word ("exacerbated") in the sentence below.

The long drought exacerbated the debts of farmers who had already borrowed to buy seed.

Choose the pair that shows the same relationship as the pair given below.

Thermometer : Temperature

Read the passage and answer the question that follows.

In speaking of social reform… we have in mind not only leaders and professional workers but also the supporters of social movements, whether these be of a practical nature for the attainment of an easily defined end or aiming at the fulfilment of a deeper longing for social justice and betterment. They comprise, therefore, not only radicals or theorists but the large number of people who earnestly wish to live decent lives and leave the world a little better than they found it. Among them we find, in the main, persons and groups of a conservative temperament, indeed, for the most part men and women who are by no means certain of the ultimate consequences of the measures they advocate or support, or conscious even of the exact motives that impel them to do so. Before their social creeds, vague and unexpressed as they mostly are, can be correlated, it is necessary that conscientious men and women of this practical type should search their own souls, should systematize their own ideas and, by discussion in small groups, try to arrive at a separation of those convictions which with them are fundamental and those that are tentative and subject to modification by further study. What follows, therefore, is no more than a preliminary effort. It would be impossible with any certainty to present the dominant note in the social reform movement of America, much less of the Western world as a whole; but we may try to look below the obvious differences of faith and opinion among our socially minded contemporaries so as to ascertain whether the social reform movement in its larger phases has any unity at all: whether, in fact, it is a movement or merely a medley.

Identify the statement that most exactly presents the ideas developed in the passage.