GATE CS 2026 1 Question Paper with Solutions: 65 Questions, Answer Key & Section-wise Analysis

The figure shows two 4-tile patterns.

Either one or both of the patterns can be used any number of times and in any
orientation to construct a new pattern. Which one of the options below cannot be
constructed by using only these two 4-tile patterns assuming there are no overlaps
among them?

Consider a knock-out women’s badminton singles tournament where there are no
ties. The loser in each game is eliminated from the tournament. Every player
plays until she is defeated or remains the last undefeated player. The last
undefeated player is declared the winner of the tournament. If there are 64 players
in the beginning of the tournament, how many games should be played in total to
declare the winner of the tournament?

A student needs to enroll for a minimum of 60 credits. A student cannot enroll for
more than 70 credits. The credits are divided amongst project and three distinct
sets of courses namely, core courses, specialization courses, and elective courses.
It is compulsory for a student to enroll for exactly 15 credits of core courses and
exactly 20 credits of project. In addition, a student has to enroll for a minimum of
10 credits of specialization courses. The maximum credits of elective courses that
a student can enroll for is ______

‘When the teacher is in the room, all students stand silently.’

If the above statement is true, which one of the following statements is not
necessarily true?

Combinatorics deals with problems involving counting. For example, “How many
distinct arrangements of N distinct objects in M spaces on a circle are possible?”
is a typical problem in combinatorics. This kind of counting is sometimes used in
the modeling of several physical phenomena. Often, in such models, the different
combinatorial possibilities are assigned probability values. Assigning probabilities
enables the computation of the average values of physical quantities.

Consider the following statements:

P: Combinatorics is always invoked in the modeling of physical phenomena.

Q: Modeling some physical phenomena involves assigning probabilities to
combinatorial possibilities in order to compute average values of physical
quantities.

Based on the passage above, what can be inferred about statements P and Q?

In Panel I of the figure below, the front view and top view of a structure are
shown. Which one of the 3D structures shown in Panel II possesses the views
shown in Panel I?

For positive real numbers 𝑆 and 𝐾, the function 𝐻𝐾(𝑆) is defined as:
𝐻𝐾(𝑆) = max(𝑆 − 𝐾, 0). The max function is defined as:

max(𝑎, 𝑏) = {
𝑎, when 𝑎 > 𝑏
𝑏, when 𝑎 ≤ 𝑏

The graph below shows the plot of a function 𝑁(𝑆) versus 𝑆.


𝑁(𝑆) can be expressed as _____.

In the 2020 summer Olympics’ Javelin throw finals, Neeraj Chopra exhibited a
spectacular performance to win the gold medal. The silver medal was won by
Jakub Vadlejch and the bronze medal was won by Vitezlav Vesely. There were
six rounds of throws with each athlete having one throw per round. The best of
all the throws of each athlete is considered for the medal. Following were the
observations about the throws:

i. The first and second rounds were dominated by Neeraj Chopra with a gold
medal performance in his second throw, while the other two athletes did
not have any medal winning throws in these rounds.

ii. The throws in the last round by both Jakub Vadlejch and Vitezlav Vesely
were fouls and were not considered for scoring.

iii. After four rounds, Vitezlav Vesely was in the second position and could
not improve upon his best throw in the succeeding rounds.

iv. In the fourth round, the throw by Jakub Vadlejch was the best in that
round.

In which round did Vitezlav Vesely have his best throw?

An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5,
and 6 is rolled twice in succession and the number on the top face is recorded
each time. The probability that the number appearing in the second roll is an
integer multiple of the number appearing in the first roll is __________