IIM Bangalore UG and BBA DBE · Paper 2

For what value of $\lambda$ are the vectors $\vec{a} = 2\hat{i} + \lambda\hat{j} + \hat{k}$ and $\vec{b} = \hat{i} - 2\hat{j} + 3\hat{k}$ perpendicular?

A cylindrical vessel of base radius 42 cm contains water to a certain level. A solid cylinder of height 18 cm is dropped into it and is completely submerged in water. If the level of the water in the vessel rises by 8 cm, what is the total surface area (in cm²) of the solid cylinder? (Use $\pi = \frac{22}{7}$) (Assuming no overflow.)

While selling $15$ items, a shopkeeper earned a profit equal to the total cost price of $3$ items. If each item is marked $25\%$ above its actual cost and a discount of ₹2 is given while selling it, then what is the difference between the total cost price of $20$ items and the total selling price of $12$ items?

In $\Delta XYZ$, length of $XY = 13$ cm. If the length of the median drawn from vertex $Z$ to base $XY$ is $6.5$ cm, then $\Delta XYZ$ is a/an:

A businessman purchased some notebooks for ₹960. If he had bought 8 more notebooks for the same amount, the cost of each notebook would have decreased by ₹4. What was the original number of notebooks purchased?

Ravish paid ₹640 for a jar of 40 chocolates where the amount paid included the cost of the jar. Harish paid a total of ₹1540 for one jar containing 55 chocolates and a second jar containing 45 chocolates, where the amount paid included the cost of both the jars. If all jars cost the same, and all chocolates cost the same, how much (in ₹) would Satish have to pay for a jar containing 35 chocolates, if the amount he has to pay includes the cost of the jar as well as that of the chocolates he bought?

A merchant made two types of mixed oils P & Q with three different types of oils, X, Y and Z in the ratios 3:2:5 and 4:3:3 respectively with the costs of each litre of X, Y and Z being ₹120, ₹125 and ₹150 respectively. How much profit will the merchant make if he sells 100 litres each of P and Q at the same rate of ₹136 per litre?

The table gives a shop's revenue (in ₹ lakh) from its four product lines.

By how many percentage points did the share of Accessories in the shop's total revenue rise from 2024 to 2025?

The function $y$ satisfies $\frac{dy}{dx} + \frac{y}{x} = x^2$ for $x > 0$, and $y = 1$ when $x = 1$. What is the value of $y$ when $x = 2$?

Two inlet pipes A and B can fill a tank in 18 hours and 24 hours, respectively, while an outlet pipe C can empty the full tank in $X$ hours. Initially, all three pipes are opened together. After 8 hours, pipe B is closed, and another 6 hours later, pipe C is also closed. The remaining portion of the tank is then filled by pipe A alone. If the tank gets completely filled in a total of 16 hours, find the value of $X$.

Based on the English alphabetical order, three of the following four letter-clusters are alike in a certain way and thus form a group. Which is the one that does not belong to that group? (Note: The odd one out is not based on the number of consonants/vowels or their position in the letter-cluster.)

What should come in place of '?' in the given series? 325, 306, 289, 274, 261, ?

If 'P' stands for '$\div$', 'Q' stands for '$\times$', 'R' stands for '$+$' and 'S' stands for '$-$', then the resultant of which of the following would be 14?

What comes in place of the question mark in the series?

2, 5, 14, 41, 122, ?

Eight friends, P, Q, R, S, T, U, V and W, sit around a circular table, all facing the centre.

R sits third to the right of P.

T sits opposite P.

Only one person sits between R and U.

U is not an immediate neighbour of P.

V sits second to the right of T.

W sits second to the left of Q.

Who sits to the immediate left of S?

The sentence below contains an error. Choose the option that best corrects it.

The documentary was so inform that viewers struggled to stay engaged, despite its visually appealing cinematography.

Select the CORRECT option to fill in the blank.

During the international climate summit, young activists from across the globe delivered passionate speeches. They highlighted rising temperatures, melting glaciers, and endangered species. Their urgent appeal __________ global leaders to take immediate and measurable action. The movement was praised for its clarity, determination, and its power to unite voices for environmental change.

Choose the most appropriate sequence of prepositions that appropriately fills the blanks in the sentence below.

_____ rising tensions, the ambassador worked with international observers and entered _____ constructive dialogue to transform regional hostility into a framework _____ peaceful cooperation, and sustainable diplomatic engagement across neighbouring nations.

Select the CORRECT synonym for the bold word ("erudition") in the below sentence.

Despite the professor's erudition, the lecture was easy, accessible and engaging for all students.

Select odd sentence out.

The seed for independence was sown around 1857, and we got our freedom only around 90 years later, i.e. 1947. The freedom we enjoy today is a struggle endured by those who envisioned a free country. Shri Rajendra Prasad became our first president. Celebrating our freedom fighters and honoring them is essential.