IIM Bangalore UG and BBA DBE · Paper 4

Find the sum of the squares of the first twelve positive multiples of 8.

The length of each side of a regular hexagon is 12 cm. The length of one of the diagonals of a rhombus whose area is equal to $\sqrt{3}$ times the area of the hexagon is 72 cm. What is the length (in cm) of the other diagonal of the rhombus?

Nidhi reached her institute in 3 hours while travelling by bus with a wheel radius of 70 cm and making 250 revolutions in one minute. One day, she left for the institute one hour later than usual time. Then to reach her institute on time, she should increase her speed by ____. [Use $\pi = \frac{22}{7}$]

The time taken by a boat to cover a certain distance in still water is 20% less than the time it takes to cover the same distance upstream. The speed of the stream is 4.5 km/h. How much total time (in hours) will the boat take to cover 60 km downstream and 30 km upstream?

Two British and three Indian men and their wives are to be seated around a circular table. If the seating arrangements are defined only by the relative positions of the people, then the total number of ways in which each British man can be seated next to his wife and each Indian man can also be, simultaneously, seated next to his wife is:

What is the variance of the first 10 natural numbers, 1, 2, 3, ..., 10? (Take variance as $\frac{1}{n}\sum (x_i - \bar{x})^2$.)

If $A = \begin{pmatrix} 4 & 2 \\ 1 & 3 \end{pmatrix}$ and $A^2 + pA + qI = O$, where $I$ is the identity matrix and $O$ is the zero matrix of order 2, what is the value of $p + q$?

ABCD is a cyclic quadrilateral. AB and DC are produced to meet at P. AD and BC are produced to meet at Q.

If $\angle AQB=2x^\circ$, $\angle QAB=3x^\circ$ and $\angle BPC=x^\circ$, then what is the value of $x$?

In an election held in a town, there were three candidates Arjun, Bhavesh, and Charan. Out of the total registered voters, 18% did not cast their votes. During counting, it was found that 6% of the votes polled were declared invalid. Among the valid votes, Arjun received 40% of the votes, while Bhavesh and Charan received the remaining valid votes in the ratio of $7 : 5$, respectively. If Arjun won the election by 1,44,525 votes over Charan, then find the total number of registered voters in the town.

A right circular cylinder is inscribed in a sphere of radius $6\sqrt{3}$ cm. What is the greatest possible volume of the cylinder, in cm³?

Based on the English alphabetical order, three of the following four letter cluster pairs are alike in a certain way and thus form a group. Which is the one that does not belong to that group?

Statements:

All pens are books.

Some books are bags.

No bag is a chair.

Conclusions:

I. Some pens are bags.

II. Some books are not chairs.

Assuming the statements are true, which conclusion(s) logically follow?

In this question, a statement is followed by two conclusions numbered I and II. You have to assume everything in the statement to be true and decide which of them logically follows beyond a reasonable doubt from the information given in the statement.

Statement - Due to changes in the application forms, the last date for payment of Income Tax has been extended by a month by the Finance Ministry. It can now be paid up to 30th September 2025 without any penalty for late payment.

Conclusion -

I. No interest will be charged on income tax payments that are made after 30th September 2025

II. No penalty will be charged for income tax payments that are made before 30th September 2025

Each of P, Q, R, S, T, U and V has an exam on a different day of a week starting from Monday and ending on Sunday of the same week. R has an exam on Tuesday. Only four people have exams before U. T has an exam immediately before V but not on Wednesday. S has an exam on some day after Q but not on Thursday. How many people have exams between P and T?

A clock gains 5 minutes every hour. It is set to the correct time at 6 a.m. Later the same day it shows 3 p.m. What is the correct time at that moment?

Select the most appropriate option to fill in the blank.

The miser _______ a cry when he learnt that his money was lost.

Choose the word to replace the word “effects” in the below sentence

Dumping medical waste into the atmosphere effects the environment, badly.

Choose the CORRECT idiom that fits in the blank.

As the summit on global trade policy unfolded, the delegations from developing nations and industrialized countries found themselves ___________ grappling with entrenched positions on tariffs, subsidies, and market access, each side fiercely defending their economic interests and ideological principles amidst mounting diplomatic tension.

Humanity is a social species by nature. When the internet entered daily life around 1983, worldwide connections became an instant possibility. _____________________. The backyard fence was replaced by a computer monitor. Whether for private purposes or business, communication is what humans do - not always gracefully or truthfully, but certainly continuously.

Complete the sentence by choosing the word that best fits the context:

Despite the initial setbacks, the team remained _______ and determined to achieve their goals.