# GATE CS practice set · 26 October 2026

10 original GATE CS & IT questions from GATE Daily, 15 marks, about 19 minutes. Solve them on the page: https://gatedaily.in/daily/2026-10-26/

Scoring follows GATE: a wrong 1-mark MCQ costs 1/3 mark and a wrong 2-mark MCQ costs 2/3. MSQ and NAT have no negative marking and no partial credit (an MSQ is right only with exactly the right options). Skipped scores zero.

Solutions: each question's answer and worked solution is at the link under it.

### Q.1 · General Aptitude · Probability and counting · MCQ, 1 mark (choose one option)

Five different books $P$, $Q$, $R$, $S$ and $T$ are to be placed in a single row on a shelf. In how many of the arrangements is book $P$ **not** in the leftmost position and book $Q$ **not** in the rightmost position?

(A) 72
(B) 78
(C) 96
(D) 120

Solution: https://gatedaily.in/q/2026-10-26-books-on-shelf-two-forbidden-positions.md

### Q.2 · Engineering Mathematics · Limits, continuity and differentiability · MCQ, 1 mark (choose one option)

The value of

$$\lim_{x\to 1}\frac{x^3-3x+2}{x^4-2x^2+1}$$

is

(A) $0$
(B) $\dfrac{3}{4}$
(C) $\dfrac{3}{2}$
(D) The limit does not exist

Solution: https://gatedaily.in/q/2026-10-26-limit-double-root-rational-function.md

### Q.3 · Discrete Mathematics · Matching, colouring and planarity · NAT, 2 marks (answer with a number)

A *matching* in an undirected graph is a set of edges in which no two edges share an endpoint; the empty set of edges is also a matching.

Let $C_9$ be the cycle on the 9 vertices $v_1, v_2, \dots, v_9$, with the 9 edges $v_1v_2, v_2v_3, \dots, v_8v_9$ and $v_9v_1$.

The number of matchings in $C_9$ is ______.

(Answer in integer)

Solution: https://gatedaily.in/q/2026-10-26-matchings-in-cycle-on-nine-vertices.md

### Q.4 · Digital Logic · Minimization and K-maps · MCQ, 2 marks (choose one option)

Consider the 4-variable Boolean function

$$F(w,x,y,z)=\Sigma m(0,2,5,7,8,10,13,15)$$

where $w$ is the most significant bit and $z$ the least significant bit, and there are no don't-care terms. Which one of the following is the **minimal** sum-of-products form of $F$?

(Here $'$ denotes complement.)

(A) $x'z' + xz$
(B) $x'z + xz'$
(C) $w'x'z' + wx'z' + xz$
(D) $x'z' + xyz$

Solution: https://gatedaily.in/q/2026-10-26-kmap-corners-and-centre-minimal-sop.md

### Q.5 · Computer Organization & Architecture · Pipelining: timing and speedup · NAT, 2 marks (answer with a number)

A processor's instruction execution is divided into five stages with these delays:

| Stage | IF | ID | EX | MEM | WB |
|---|---|---|---|---|---|
| Delay (ps) | 200 | 150 | 380 | 290 | 120 |

In the pipelined implementation each stage is followed by a pipeline register whose delay of 20 ps adds to the clock period. A designer splits EX into two consecutive stages EX1 and EX2 with delays 200 ps and 180 ps, giving a six-stage pipeline with the same 20 ps register delay per stage.

One instruction is issued per clock cycle and there are no stalls or hazards. The speedup of the six-stage pipeline over the five-stage pipeline when executing 500 independent instructions is ______ (rounded to two decimal places).

Solution: https://gatedaily.in/q/2026-10-26-split-ex-stage-new-bottleneck-speedup.md

### Q.6 · Programming & Data Structures · Binary heaps · MCQ, 2 marks (choose one option)

The array $A[1..10]$ below is turned into a **min-heap** in place by the standard bottom-up build-heap procedure: for $i = \lfloor n/2 \rfloor$ down to $1$, sift $A[i]$ down, at each step swapping it with its smaller child as long as that child is smaller than it. The children of $A[i]$ are $A[2i]$ and $A[2i+1]$.

| Index | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| Value | 45 | 12 | 78 | 33 | 9 | 60 | 21 | 5 | 40 | 18 |

Which one of the following is the array $A[1..10]$ after build-heap finishes?

(A) 5, 9, 21, 12, 18, 60, 78, 33, 40, 45
(B) 5, 9, 21, 12, 18, 78, 60, 45, 40, 33
(C) 5, 9, 21, 12, 45, 60, 78, 33, 40, 18
(D) 5, 9, 12, 18, 21, 33, 40, 45, 60, 78

Solution: https://gatedaily.in/q/2026-10-26-build-min-heap-bottom-up-final-array.md

### Q.7 · Algorithms · Divide and conquer · MCQ, 1 mark (choose one option)

Match each algorithm in List-I with the design paradigm in List-II that it follows.

| List-I | List-II |
|---|---|
| (P) Bellman-Ford algorithm for single-source shortest paths | (i) Divide and conquer |
| (Q) Kruskal's algorithm for a minimum spanning tree | (ii) Dynamic programming |
| (R) Strassen's matrix multiplication | (iii) Greedy method |
| (S) Solving the N-Queens problem by placing queens one column at a time and undoing a placement when no safe square remains | (iv) Backtracking |

(A) P-iii, Q-ii, R-i, S-iv
(B) P-ii, Q-iii, R-i, S-iv
(C) P-ii, Q-iii, R-iv, S-i
(D) P-ii, Q-ii, R-i, S-iv

Solution: https://gatedaily.in/q/2026-10-26-match-algorithms-to-design-paradigms.md

### Q.8 · Theory of Computation · Regular expressions and regular languages · MCQ, 1 mark (choose one option)

Let $L$ be the set of all strings over the alphabet $\{a, b\}$, including the empty string $\varepsilon$, that do **not** contain $bb$ as a substring. Which one of the following regular expressions denotes exactly $L$?

(A) $(a + ba)^*(\varepsilon + b)$
(B) $(a + ba)^*$
(C) $(a + ab)^*(\varepsilon + b)$
(D) $(\varepsilon + b)(a + ba)^*$

Solution: https://gatedaily.in/q/2026-10-26-regex-strings-without-bb.md

### Q.9 · Operating Systems · Paging and virtual memory · NAT, 2 marks (answer with a number)

A system uses 39-bit virtual addresses, a page size of 4 KB and a three-level page table ($1\text{ KB} = 2^{10}$ bytes, $1\text{ MB} = 2^{20}$ bytes). A page-table entry is 8 bytes at every level, and every page table at every level occupies exactly one page.

The outermost (first-level) table is allocated when a process is created. A second-level or third-level table is allocated only if it contains at least one valid entry.

A process has exactly two regions of its virtual address space mapped, and every page in both regions is valid:

- a code-and-data region from virtual address 1 MB up to, but not including, 7 MB;
- a stack occupying the highest 1 MB of the virtual address space.

The total memory occupied by this process's page tables, over all three levels, is ______ KB.

(Answer in integer)

Solution: https://gatedaily.in/q/2026-10-26-three-level-page-table-two-regions-memory.md

### Q.10 · Databases · Transactions and serializability · MSQ, 1 mark (choose every correct option)

Consider the following schedule $S$ of two transactions $T_1$ and $T_2$. Here $r_i(Z)$ and $w_i(Z)$ denote a read and a write of data item $Z$ by $T_i$, and $c_i$ denotes the commit of $T_i$. Assume a single-version database in which each read returns the value of the latest preceding write to that item, or its initial value if no write precedes it.

$$S:\ r_1(X);\ w_1(X);\ r_2(X);\ r_1(Y);\ w_1(Y);\ c_1;\ r_2(Y);\ w_2(X);\ c_2$$

Which of the following statements about $S$ is/are TRUE?

(A) $S$ is conflict serializable.
(B) $S$ is recoverable.
(C) $S$ is cascadeless (it avoids cascading aborts).
(D) $S$ is strict.

Solution: https://gatedaily.in/q/2026-10-26-schedule-recoverable-but-not-cascadeless.md