GATE CS Engineering Mathematics questions

Suppose that the expectation of a random variable $X$ is $5$. Which of the following statements is true?

Two friends agree to meet at a park with the following conditions. Each will reach the park between 4:00 pm and 5:00 pm and will see if the other has already arrived. If not, they will wait for 10 minutes or the end of the hour whichever is earlier and leave. What is the probability that the two will not meet?

In a room containing $28$ people, there are $18$ people who speak English, $15$ people who speak Hindi and $22$ people who speak Kannada. $9$ persons speak both English and Hindi, $11$ persons speak both Hindi and Kannada whereas $13$ persons speak both Kannada and English. How many speak all three languages?

The binary relation $R = \{(1, 1), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4)\}$ on the set $A=\{1, 2, 3, 4\}$ is

Consider the following determinant $\Delta = \begin{vmatrix} 1 & a & bc \\ 1 & b & ca \\ 1 & c & ab \end{vmatrix}$ Which of the following is a factor of $\Delta$?

The rank of the matrix given below is: $$\begin{bmatrix} 1 &4 &8 &7\\ 0 &0& 3 &0\\ 4 &2& 3 &1\\ 3 &12 &24 &21 \end{bmatrix}$$

How many sub strings of different lengths (non-zero) can be formed from a character string of length $n$?

The number of functions from an $m$ element set to an $n$ element set is

Let $R_1$ and $R_2$ be two equivalence relations on a set. Consider the following assertions: $R_1 \cup R_2$ is an equivalence relation $R_1 \cap R_2$ is an equivalence relation Which of the following is correct?

Suppose $A$ is a finite set with $n$ elements. The number of elements in the largest equivalence relation of A is

What is the converse of the following assertion? I stay only if you go

Consider the function $y=|x|$ in the interval $[-1, 1]$. In this interval, the function is

Consider the following set of equations $x+2y=5$ $4x+8y=12$ $3x+6y+3z=15$ This set

A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is

The number of equivalence relations of the set $\{1,2,3,4\}$ is

A partial order $≤$ is defined on the set $S=\left \{ x, a_1, a_2, \ldots, a_n, y \right \}$ as $x$ $\leq _{i}$ $a_{i}$ for all $i$ and $a_{i}\leq y$ for all $i$, where $n ≥ 1$. The number of total orders on the set S which contain the partial order $≤$ is

A polynomial $p(x)$ is such that $p(0) = 5, p(1) = 4, p(2) = 9$ and $p(3) = 20$. The minimum degree it should have is

Let $A=(a_{ij})$ be an $n$-rowed square matrix and $I_{12}$ be the matrix obtained by interchanging the first and second rows of the $n$-rowed Identity matrix. Then $AI_{12}$ is such that its first

What is the maximum value of the function $f(x) = 2x^2 - 2x + 6$ in the interval $\left[0,2 \right]$?

In the lattice defined by the Hasse diagram given in following figure, how many complements does the element ‘$e$’ have?