IIM Bangalore UG and BBA DBE · Paper 3

A pair of consecutive odd positive integers, both of which are smaller than 19, have a sum that is more than 22. How many such pairs will be there, if we allow a number to be in more than one pair?

The simple interest on a certain sum of money invested at $7.5\%$ per annum for 4 years is ₹243. What was the sum (in ₹) invested?

The function $f(x) = \frac{1 - \cos 2x}{x^2}$ for $x \neq 0$, with $f(0) = k$, is continuous at $x = 0$. What is the value of $k$?

The roots of the equation $x^2 + 18x - 703 = 0$ are given as $a$ and $b$, with $a > b$. The roots of the equation $x^2 - 10x - 336 = 0$ are given as $c$ and $d$, with $c > d$. Which of the options below gives the correct relation between $a$, $b$, $c$, and $d$?

81 equally efficient people could complete a piece of work in 15 days. Initially 45 such people started working together. But after they worked together for 6 days their employer wanted that the work should be completed in a total of 21 days. However any new worker who joins is only $60\%$ as efficient as any of the 45 people already working. How many new workers did the employer hire to work alongside the initial 45 people to meet the deadline?

Out of 7 different consonants and 4 different vowels, how many words (not necessarily meaningful) of 4 consonants and 2 vowels can be formed?

A train running between two towns arrives at its destination 10 minutes late when it goes at 60 km per hour and 16 minutes late when it goes at 40 km per hour. Determine the speed at which the train reaches on time.

In $\triangle ABC$, $AD$ is the bisector of $\angle A$ meeting $BC$ at $D$. If $AB = 30$ cm, $BC = 20$ cm and the length of $BD$ is 4 cm less than $DC$, then the length (in cm) of $AC$ is

How many 4-digit even numbers greater than 4000 can be formed using the digits 0, 1, 2, 3, 4, 5 and 6, if no digit is repeated?

What is the area of the region enclosed by the parabola $y^2 = 4x$ and the line $y = 2x - 4$?

Rahul ranked 16th from the top and 27th from the bottom in his class. How many students are there in the class?

Complete the series.

ZA144, YB121, XC100, WD81, ?

Ravi starts from his house facing north and walks 7 km. He turns right and walks 5 km, turns right again and walks 12 km, and then turns left and walks 7 km. How far is he now from his house, and which direction is he facing?

If 4 March 1993 is a Thursday, what will be the day of the week on 12 November 2004?

Five colleagues, Arun, Bela, Chetan, Diya and Eshan, joined a company in five different years from 2019 to 2023, one in each year. Each works in a different department: HR, Finance, Sales, IT and Legal.

The Sales employee joined exactly two years after the IT employee.

Eshan joined the year after Arun.

Bela joined after Arun, and Chetan joined after Bela.

Diya joined before the HR employee.

Arun works in either IT or Legal.

The Legal employee joined in an odd-numbered year.

The Finance employee joined after the HR employee.

Who joined in 2022, and in which department?

Select the most appropriate option that corrects the underlined error ("immediately") in the given sentence.

They have immediately shifted to a new house.

Choose the most appropriate option that best completes the analogy.

Scalpel is to surgeon as gavel is to ________.

Match the words in Column I with their correct antonyms in Column II and select the correct option.

Column I: A. Ephemeral, B. Benevolent, C. Obscure, D. Meticulous

Column II: 1. Careless, 2. Permanent, 3. Clear, 4. Malevolent

Replace the bold words ("aroused curiosity") in the sentence below with the CORRECT synonym.

"The Professor's erudite lectures on astrophysics aroused curiosity in the mind of his students, inspiring them to delve deeper into the mysteries of the cosmos."

Select the most appropriate option that corrects the underlined error ("has operated") in the given sentence.

By 2028, the company has operated in this market for fifteen years.