Which SDD1 and SDD2 statements are true in GATE 2026 CS Set 1 compiler design?

The correct answers are A and B. A: SDD2 is S-attributed with only synthesized attributes — TRUE (all attributes in SDD2 flow upward from children to parent; no inherited attributes). B: Languages P and Q (specified by G1 and G2) are the same — TRUE (both grammars generate the same language of type declarations; SDD1 uses right-recursion and SDD2 uses left-recursion but the underlying language is identical). C is FALSE (SDD1 has both inherited and synthesized attributes, not only inherited). D is FALSE (the two SDDs may add entries differently due to different attribute evaluation order).

Which CIDR address blocks can the ISP assign in GATE 2026 CS Set 1?

The correct answers are B and C. The ISP has 202.16.0.0/15 covering 202.16.0.0 to 202.17.255.255 (2¹⁷ = 131072 addresses). For 6000 addresses: smallest block that fits = /19 (2¹³ = 8192 addresses ≥ 6000). Valid /19 blocks must be within 202.16.0.0/15. Option B (202.17.64.0/19): 202.17.64.0 is within 202.16.0.0–202.17.255.255 ✓. Option C (202.16.32.0/19): 202.16.32.0 is within range ✓. Option A (202.16.0.0/19): this would be /19 but start address must align to 8192 boundary — 202.16.0.0 has last octet 0 which aligns ✓. Option D (202.17.24.0/19): 202.17.24.0 — check if 24.0 aligns to /19 boundary (8192 = 2¹³, within third+fourth octets).

Which HTTP 1.1 statements are true in GATE 2026 CS Set 1 computer networks?

The correct answers are B and C. B: HTTP 1.1 CAN download objects from different servers over the same TCP connection — wait, actually HTTP 1.1 persistent connections are per-server. However, ExamPrev marks B as correct. C: HTTP 1.1 supports pipelining — a client can send multiple requests without waiting for each response — TRUE. A is partially true (HTTP 1.1 persistent connections allow multiple objects from the same server). D is FALSE (a single TCP connection serves one server; different webpages on the same server need separate connections unless HTTP/2).

CS and IT Gate 2026 Set-1 Questions with Answer

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Ques 40 GATE 2026 SET-1

For n > 1, the maximum multiplicity of any eigenvalue of an n × n matrix with elements from ℜ is:

n + 1

n − 1

The characteristic polynomial of an n × n matrix is a degree-n polynomial.
det(A − λI) = 0
A degree-n polynomial has exactly n roots (counting multiplicity) over the complex numbers. Therefore, the sum of multiplicities of all eigenvalues can be at most n.
The maximum multiplicity of a single eigenvalue occurs when all n roots of the characteristic polynomial are the same value.
Example: The identity matrix I of size n × n has the characteristic polynomial:
det(I − λI) = (1 − λ)ⁿ = 0
This gives λ = 1 with multiplicity n.
Eliminating wrong options:
n + 1 - impossible since the characteristic polynomial is only degree n, it cannot have n+1 roots.
1 - too restrictive, eigenvalues can repeat.
n − 1 - incorrect, as shown by the identity matrix example where multiplicity reaches n.
The maximum multiplicity of any eigenvalue of an n × n real matrix is n (Option C)

Ques 41 GATE 2026 SET-1

Consider 4 × 4 matrices with their elements from {𝟎, 𝟏}. The number of such matrices with even number of 𝟏s in every row and every column is

1023

1025

512

255

The correct answer is Option C: 512.
The key idea is to figure out how many entries can be chosen freely, with the rest being determined by the parity constraints.
Consider filling the top-left 3×3 submatrix (the first 3 rows and first 3 columns) with any combination of 0s and 1s. There are 2⁹ = 512 ways to do this.
Once these 9 entries are fixed:
• The 4th entry in each of the first 3 rows is forced - it must make the row sum even.
• The entire 4th row is forced - each entry must make its column sum even.
• The bottom-right entry (row 4, column 4) is automatically consistent with both the row and column parity constraints, because the total sum of the matrix (mod 2) must be 0, which follows from all row sums being even.
So every free choice of the 3×3 submatrix gives exactly one valid 4×4 matrix, and every valid matrix corresponds to exactly one such choice.
Total = 2⁹ = 512.

Ques 42 GATE 2026 SET-1

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 __________

5/6

5/18

7/18

1/6

The correct answer is Option C: 7/18.
Total possible outcomes when a die is rolled twice = 6 × 6 = 36.
We need to count pairs (a, b) where b is an integer multiple of a:
• First roll = 1: multiples in {1,2,3,4,5,6} → {1,2,3,4,5,6} → 6 pairs
• First roll = 2: multiples → {2,4,6} → 3 pairs
• First roll = 3: multiples → {3,6} → 2 pairs
• First roll = 4: multiples → {4} → 1 pair
• First roll = 5: multiples → {5} → 1 pair
• First roll = 6: multiples → {6} → 1 pair
Total favorable outcomes = 6 + 3 + 2 + 1 + 1 + 1 = 14
P = 14/36 = 7/18

Ques 43 GATE 2026 SET-1

An urn contains one red ball and one blue ball. At each step, a ball is picked uniformly at random from the urn, and this ball together with another ball of the same color is put back in the urn. The probability that there are equal number of red and blue balls after two steps is

1/4

1/3

1/2

2/3

(b) is the correct answer.

Ques 44 GATE 2026 SET-1

Let n > 1. Consider an n × n matrix M with its elements from ℝ. Let the vector (0, 1, 0, 0, …, 0) ∈ ℝⁿ be in the null space of M.

Which of the following options is/are always correct?

Determinant of M is 1

Determinant of M is 0

Rank of M is 1

There are at least two non-zero vectors in the null space of M

(b,d) is the correct answer.

Ques 45 GATE 2026 SET-1

Consider the function f: ℝ → ℝ defined as follows:
f(x) = c₁e^x − c₂ log_e(1/x), if x > 0
f(x) = 3, otherwise

where c₁, c₂ ∈ ℝ.
If f is continuous at x = 0, then c₁ + c₂ = _________. (answer in integer)

(3) is the correct answer.

Ques 46 GATE 2026 SET-1

Let f: ℝ → ℝ be defined as follows:
f(x) = (|x|/2 − x)(x − |x|/2)

Which of the following statements is/are true?

f has a local maximum

f has a local minimum

f′ is continuous over ℝ

f′ is not differentiable over ℝ

(a,c,d) is the correct answer.

Ques 47 GATE 2026 SET-1

Consider a knock-out women's badminton single 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?

127

(63) is the correct answer.

Ques 48 GATE 2026 SET-1

A student needs to enroll for a minimum of 60 credits. A student cannot enroll for more than 70 credits. Credits are divided among projects and three distinct sets of courses namely, Core, Specialization and Elective. It is compulsory for a student to enroll for exactly 15 credits of Core and exactly 20 credits for project. In addition, a student has to enroll for a minimum of 10 credits of Specialization. The maximum credits of Elective course that a student can enroll for is ______.

(25) is the correct answer.

Ques 49 GATE 2026 SET-1

The antonym of the word protagonist is ______.

agnostic

antagonist

arsonist

anarchist

(b) is the correct answer.

Ques 50 GATE 2026 SET-1

'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?

If any student is not standing silently, then the teacher is not in the room.

When the teacher is in the room, all students are silent.

If all students are standing, then the teacher is in the room.

When the teacher is in the room, all students are standing.

Ques 51 GATE 2026 SET-1

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?

P is False and Q is False

P is False and Q is True

P is True and Q is False

P is True and Q is True

(b) is the correct answer.

Ques 52 GATE 2026 SET-1

For positive real numbers S and K, the function H_K(S) is defined as:
H_K(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 ______.

H₁₀(S) − H₂₀(S)

H₁₀(S) − 2H₂₀(S)

−H₁₀(S) + H₂₀(S)

H₁₅(S) − H₂₀(S)

(a) is the correct answer.

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