IIM Bangalore UG and BBA DBE · Paper 5

If $2^{x+y} = 4^{x-y} = \sqrt{32}$, then $xy = $ ___.

A bank offers $5\%$ compound interest per annum, calculated on half-yearly basis. A customer deposits ₹3200 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:

For two events $A$ and $B$, $P(A) = 0.6$, $P(B) = 0.4$ and $P(A \cup B) = 0.8$. What is $P(A \mid B)$?

In a flight of 1400 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 450 km/h and the time of flight increased by 60 minutes. The speed of the aircraft due to bad weather is what percent (rounded off to 2 decimal places) of the original speed of the aircraft?

A boy agrees to work at the rate of one rupee on the first day, two rupees on the second day, four rupees on third day and so on, thus getting on any day twice the amount he received just the day before. How many rupees will the boy earn in all, if he started working on the $5^{th}$ of March and completed the work on the $28^{th}$ of March?

In an election between two candidates, A and B, 18% of total voters did not cast their votes. 15% of the votes polled were declared invalid. B received 56% of the total valid votes and won by a majority of 6273 votes. The number of valid votes received by A was:

A person hosts a party of 13 guests and places 5 of them on one table and the remaining on the other table, the tables being round. In how many ways can he arrange the guests?

What is the acute angle between the lines $\frac{x - 3}{1} = \frac{2 - y}{2} = \frac{z + 1}{2}$ and $\frac{x + 1}{2} = \frac{y - 4}{1} = \frac{z}{2}$?

Let $A = \{1, 2, 3, 4\}$. How many equivalence relations on $A$ contain the ordered pair $(1, 2)$?

If all the letters of the word MANAGER are arranged to form 7-letter words (with or without meaning), and all such words are arranged lexicographically (as in a dictionary), how many of these words will precede the word MANAGER?

A group of students are sitting in a line facing north. Arpit is 36th from the left end and 30th from the right end. How many students are sitting in the line?

Statement: An advertisement says, "Our new water purifier removes 99% of germs. Buy it and keep your family healthy."

Assumptions:

I. Germs in drinking water can harm health.

II. No other purifier on the market removes as many germs.

Which of the assumptions is implicit in the statement?

If 26th December 1999 is Sunday, then what will be the day of the week on 21st April 2005?

K is the sister of L. L is the father of M. M is the son of N. N is the mother of O. O is the wife of P. P is the father of Q. How is L related to Q?

$n$ is a positive integer such that $n^2$ is divisible by 8 and $n^3$ is divisible by 16. Which of the following must be true?

Fill in the blank with the correct adjective:

The _______ old man gave his warm coat to the beggar.

Which of the following analogies best represents the relationship between "Ocean" and "Water"?

Identify the sentence that best completes the paragraph, ensuring logical flow and coherence.

The rapid growth of social media has transformed the way individuals communicate and share information. While it has made connectivity easier, it has also contributed to shorter attention spans and superficial interactions. Many users now prefer quick updates over meaningful discussions. ______.

The following sentences should form a coherent paragraph.

Select the option which has the odd sentence that does not belong to the thematic unity of the paragraph.

Read the sentence and choose the word that is most similar in meaning to the underlined word ("lauded").

The athlete was lauded for her outstanding performance at the championship, earning praise from fans and critics alike.