List of top Mathematics Questions on Number System asked in NEST

The probability that the sum of two integers $m$ and $n$, where $m, n \in \{1, 2, \dots, 50\}$, chosen randomly and independently, being divisible by 3 is

In a building, an elevator starts from the ground floor (that is, 0th floor) with 10 passengers and stops at every floor until the 15th floor which is the topmost floor. No new passengers enter the elevator on any floor from the 1st through the 15th floor. If all the passengers got off the elevator then the probability that at most one passenger got off at each floor is

Let $S = \{(x, y) \mid x, y \in \mathbb{N}, 1 \le x \le 15, 1 \le y \le 20\}$ be a set. Let $\mathcal{R}$ be the equivalence relation on $S$ defined by $(x, y) \mathcal{R} (x', y')$ if and only if $x + y = x' + y'$. Then the number of equivalence classes of $\mathcal{R}$ on $S$ is

Let $m$ and $p$ be real numbers such that the polynomial $f(x) = x^2 + mx + p$ has two distinct negative rational roots. Then the polynomial $g(x) = x^2 - (m^2 - 2p)x + p^2$ has distinct

Amar, Akbar, and Anthony write a test independently. The probability that Amar passes the test and Akbar fails the test is $\frac{3}{20}$. The probability that Akbar passes the test and Anthony fails the test is $\frac{1}{4}$. The probability that Amar and Anthony both pass the test is $\frac{2}{5}$. Then the probability that at least one of Amar, Akbar and Anthony fails the test is

A possible solution of the system of equations \[ x^2 - 8xy + 16y^2 = 0 \] \[ (\log_{10} x)^2 + 2(\log_{10} x)(\log_{10} y) + (\log_{10} y)^2 = 4 \] is

Let \(S\) be the set of all rational numbers \(r\) such that if \[ r=\frac{p}{q} \] with \(p,q\in\mathbb{Z}\), \(q\neq0\), then the two roots of the quadratic equation \[ x^{2}+2px+q^{2}=0 \] are equal. Then the number of elements in \(S\) is: