List of top Questions asked in IIITH UGEE- 2026

What is the maximum number of electrons that can be accommodated in a subshell with orbital angular momentum quantum number \(l = 3\)?

If the \(n^{th}\) term of an A.P. is \(2n + 5\), find the sum of the first 10 terms.

A pair of fair dice is rolled. What is the probability that the second die lands on a higher value than the first?

Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is a prime number?

If \(P_A^{0}\) and \(P_B^{0}\) are the vapour pressures of pure liquids A and B, what is the total pressure of an ideal solution where the mole fraction of A is \(0.4\)?

A block of mass \(m\) is moving on a horizontal frictionless surface with velocity \(v\). It hits a spring of constant \(k\) and compresses it by a distance \(x\). If the initial velocity is doubled, what will be the new compression?

Let \(P\) be any point on the curve \(x^{2/3}+y^{2/3}=a^{2/3}\). Then, what would be the length of the segment of the tangent between the coordinate axes?

Number of ways of distributing \(10\) identical chocolates among \(3\) children such that everyone gets at least one?

If \( \dfrac{d^2y}{dx^2} = \cos \left(\dfrac{dy}{dx}\right) \), find the order and the degree of the resulting differential equation.

If \( f(x) = \displaystyle \int e^x \left(\frac{x^2 + x + 1}{\sqrt{x^2 + 1}}\right) dx \) such that the value of the function is \(1\) when \(x\) vanishes, find the value of \(f(1)\).

Find the value of \( (125)^{\log_{625} 5} \)