GATE CS question library

Consider the following C function. int fun(int n) { int x=1, k; if (n==1) return x; for (k=1; k<n; ++k) x = x + fun(k) * fun (n-k); return x; } The return value of $fun(5)$ is ______.

The number of divisors of $2100$ is ____.

A binary tree T has $20$ leaves. The number of nodes in T having two children is ______.

The minimum number of $\text{JK}$ flip-flops required to construct a synchronous counter with the count sequence $(0, 0, 1, 1, 2, 2, 3, 3, 0, 0, \ldots)$ is _______.

With reference to the $B^+$ tree index of order $1$ shown below, the minimum number of nodes (including the Root node) that must be fetched in order to satisfy the following query. "Get all records with a search key greater than or equal to $7$ and less than $15$ " is ______.

The larger of the two eigenvalues of the matrix $\begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix}$ is _______.

A software requirements specification (SRS) document should avoid discussing which one of the following?

Consider the following two statements. $S_1$: If a candidate is known to be corrupt, then he will not be elected $S_2$: If a candidate is kind, he will be elected Which one of the following statements follows from $S_1$ and $S_2$ as per sound inference rules of logic?

Consider two decision problems $Q_1, Q_2$ such that $Q_1$ reduces in polynomial time to 3-SAT and 3-SAT reduces in polynomial time to $Q_2$. Then which one of the following is consistent with the above statement?

Consider the following transaction involving two bank accounts $x$ and $y$. read(x); x:=x-50; write (x); read(y); y:=y+50; write(y) The constraint that the sum of the accounts $x$ and $y$ should remain constant is that of

Out of the following $4$ sentences, select the most suitable sentence with respect to grammar and usage:

If $p, q, r, s$ are distinct integers such that: $f (p, q, r, s) = \text{ max } (p, q, r, s)$ $g (p, q, r, s) = \text{ min } (p, q, r, s)$ $h (p, q, r, s) = \text{remainder of } \frac{(p \times q)} {(r \times s)} \text{ if } (p \times q) > (r \times s)$ …

In a triangle $PQR, PS$ is the angle bisector of $\angle QPR \text{ and } \angle QPS =60^\circ$. What is the length of $PS$ ?

Four branches of a company are located at $\text{M, N, O}$ and $\text{P. M}$ is north of $\text{N}$ at a distance of $4\;\text{km; P}$ is south of $\text{O}$ at a distance of $2\;\text{km; N}$ is southeast of $\text{O}$ by $1\;\text{km}$. What is the distance between $\text{M}$ and $\text{P}$ in $\text{km}$?

If the list of letters $P$, $R$, $S$, $T$, $U$ is an arithmetic sequence, which of the following are also in arithmetic sequence? $2P, 2R, 2S, 2T, 2U$ $P-3, R-3, S-3, T-3, U-3$ $P^2, R^2, S^2, T^2, U^2$

Based on the given statements, select the most appropriate option to solve the given question. What will be the total weight of $10$ poles each of same weight? Statements: One fourth of the weight of the pole is $5\;\text{Kg}$. The total weight of these poles is $160\;\text{Kg}$ more than the total weight of two poles.

A generic term that includes various items of clothing such as a skirt, a pair of trousers and a shirt is

Consider a function $f(x) = 1- |x| \text{ on } -1 \leq x \leq 1$. The value of $x$ at which the function attains a maximum, and the maximum value of the function are:

Choose the statement where underlined word is used correctly.

We __________ our friends's birthday and we _________ how to make it up to him.