List of top Questions asked in GATE Engineering Sciences

The second smallest eigenvalue of the eigenvalue problem \[ \frac{d^2 y}{dx^2} + (\lambda - 3)\,y = 0,\qquad y(0)=y(\pi)=0, \] is

Disagree : Protest :: Agree : ____________ (By word meaning)

A ‘frabjous’ number is defined as a 3-digit number with all digits odd, and no two adjacent digits being the same. For example, 137 is a frabjous number, while 133 is not. How many such frabjous numbers exist?

Which one among the following statements must be TRUE about the mean and the median of the scores of all candidates appearing for GATE 2023?

In the given diagram, ovals are marked at different heights ($h$) of a hill. Which one of the following options P, Q, R, and S depicts the {top view} of the hill?

Residency is a famous housing complex with many well-established individuals among its residents.
A survey revealed:
1. All residents who are well established in their respective fields are academicians.
2. Most of these academicians are authors of some best-selling books.
Based only on this information, which one of the following statements can be logically inferred with {certainty}?

Ankita has to climb 5 stairs starting at the ground, while respecting the following rules:

At any stage, Ankita can move either one or two stairs up.
At any stage, Ankita cannot move to a lower step.
Let $F(N)$ denote the number of possible ways in which Ankita can reach the $N^{\text{th}}$ stair. For example, $F(1)=1$, $F(2)=2$, $F(3)=3$. The value of $F(5)$ is ____________.

The village was nestled in a green spot, __________ the ocean and the hills.