IIM Bangalore UG and BBA DBE · Paper 9

A train departs station A at 6:30 a.m. at a speed of 84 km/h. After one hour, another train departs station A in the same direction as that of the first train at a speed of 96 km/h. When and at what distance from station A do the two trains meet?

Five years ago, the ratio of Riya's age to her father's age was $1 : 4$. Five years from now, the ratio will be $2 : 5$. What is the father's present age (in years)?

On which interval is the function $f(x) = 2x^3 - 9x^2 + 12x + 5$ strictly decreasing?

What is the value of $1 \times 2 + 2 \times 3 + 3 \times 4 + \dots + 20 \times 21$?

How many numbers can be made with digits 0, 7, 8 which are greater than 0 and less than a million?

If $\alpha$ and $\beta$ are the roots of $x^2 - 7x + 11 = 0$, what is the value of $\alpha^3 + \beta^3$?

In triangle ABC, D lies on AB and E lies on AC such that DE is parallel to BC. If AD = 4 cm and DB = 6 cm, what is the ratio of the area of triangle ADE to the area of the quadrilateral DBCE?

A random variable $X$ takes the values 0, 1, 2 and 3 with probabilities $k$, $2k$, $3k$ and $4k$ respectively. What is the variance of $X$?

At the recent National Games, the athletes from Kerala took part in five types of events: track 528, field 576, swimming 504, racket sports 144, and boxing and wrestling 408.

67.5% of all participants from Kerala at the Games were female. If we look at the sex ratio of participants from Kerala by type of event, 56.25% of those in track events and $\frac{7}{9}$ of those in field events were female. The ratio of female and male participants from the state in swimming events was given as $9 : 5$. If the number of female participants from Kerala in boxing and wrestling was $y$ times the number of their male counterparts in the same type of events, which of the options below is the closest to the minimum value of $y$?

Regarding the functions $f(x) = x^2 - 5x + 1$ and $g(x) = 1 - x - x^3$ on the set of real numbers, which of the following statements is not true?

Raj starts from point A and walks 7 km towards the West. He then takes a left turn and walks 11 km, turns left and walks 11 km, turns left and walks 7 km. He then takes the final left turn, walks 4 km and stops at point B. How far (shortest distance) and towards which direction should he drive in order to reach point A again? (All turns are 90 degree turns only unless specified.)

A, B, C, D and E have different ages. Only one person is elder than E. B is younger than C but elder than D. A is elder than C. How many people are elder than C?

Seven people, M, N, O, P, Q, R and S, are sitting in a row, facing north. Only one person sits to the left of P. Only two people sit to the right of S. O sits second to the left of S. Only one person sits between O and N. Q is not the immediate neighbor of S. Only two people sit between Q and M. How many people are sitting between P and R?

A wooden cube is painted red on two opposite faces, blue on two other opposite faces and green on the remaining two faces. It is then cut into 64 equal smaller cubes. How many of the small cubes have exactly one red face and one green face painted, and no other face painted?

Eight friends, A, B, C, D, E, F, G and H, sit around a circular table. Four of them face the centre and the other four face away from the centre.

A faces the centre.

C sits second to the right of A.

C sits to the immediate left of H, and C and H face the same direction.

E sits to the immediate left of B.

Both immediate neighbours of B face the centre.

D sits second to the right of E.

G sits to the immediate right of D.

E and G face opposite directions, and so do D and E.

Who sits second to the right of B?

Identify the sentence that contains a future tense verb:

Select the option that is odd one out based on the meaning of the word given below.

Benevolent

Identify the phrasal verb in the following complex sentence:

“Although encountering numerous setbacks, they eventually broke through the barriers and achieved unprecedented success in their fields”

Arrange the sentences in order to make complete paragraph.

Despite its potential, VR faces challenges such as high costs, technological limitations, and the need for improved user comfort and accessibility.

Virtual reality (VR) creates immersive, interactive environments that simulate real or imagined worlds, enhancing experiences in gaming, education, and training.

It is being used in various industries, including healthcare for surgical training, real estate for virtual property tours, and tourism for virtual travel experiences.

By providing a sense of presence, VR allows users to explore and interact with 3D spaces in ways that traditional media cannot.

Complete the following statement using the most appropriate and grammatically CORRECT prepositions from the given choices.

The discovery of a hidden chamber ______ the ancient temple sent archaeologists into a frenzy ______ excitement.