List of top Questions asked in GATE CS- 2023

Consider two functions of time $(t)$, \[ f(t) = 0.01t^2, g(t) = 4t \] where $0<t<\infty$.
Now consider the following two statements:
(i) For some $t>0$, $g(t)>f(t)$.
(ii) There exists a $T$, such that $f(t)>g(t)$ for all $t>T$.
Which one of the following options is TRUE?

f(x) and g(y) are functions of x and y, respectively, and \( f(x) = g(y) \) for all real values of x and y. Which one of the following options is necessarily TRUE for all x and y?

A series of natural numbers \(F_1, F_2, F_3, F_4, F_5, F_6, F_7, \ldots\) obeys \[ F_{n+1} = F_n + F_{n-1}, \text{for all integers } n \geq 2. \] If \(F_6 = 37\) and \(F_7 = 60\), then what is \(F_1\)?

A survey for a certain year found that 90% of pregnant women received medical care at least once before giving birth. Of these women, 60% received medical care from doctors, while 40% received medical care from other healthcare providers. Given this information, which one of the following statements can be inferred with certainty?

Looking at the surface of a smooth 3-dimensional object from the outside, which one of the following options is TRUE?

We reached the station late, and ________ missed the train.}

Which of the following sequences when stored in an array at locations A[1],..., A[10] forms a max-heap?

The Lucas sequence L_n is defined by the recurrence relation: L_n = L_n−1 + L_n−2, for n ≥ 3, with L₁ = 1 and L₂ = 3. Which one of the options given is TRUE?