GATE 2026 DA question paper PDF and answer key

Since $\angle PQR = 45^\circ$, the subtended central angle is

With radius 10, triangle $POR$ is right isosceles with legs 10 and 10, and the geometry of the symmetric outer triangle formed with apex $Q$ gives the shaded area as

Therefore, the correct answer is Option C.

Let us denote the students as:

• Rishi (R): Class 5, boy
• Swathi (S): Class 5, girl
• Pavan (P): Class 4, boy
• Tanvi (T): Class 4, girl

A player who loses a game is eliminated permanently, so after 3 games there is exactly one student who never loses.

We use the conditions one by one.

Step 1: The first game must be the only same-class game

If the first game were between the Class 4 students (P vs T), then after one of them loses, the remaining three students would be:

• one Class 4 student
• both Class 5 students

Now the last two games must both be cross-class. But after one cross-class game among these three, the loser is eliminated, leaving either:

• two Class 5 students, or
• two Class 4 students

That would force the third game to be a same-class game, violating condition (i).

So the first game cannot be P vs T.

Hence the first game must be between the Class 5 students:

Step 2: Who wins the first game?

Suppose Swathi wins the first game. Then the winners so far are:

• one Class 5 win
• one girl win

The remaining players are S, P, T, and the next two games must both be cross-class.

To satisfy condition (ii), Class 5 must win more games than Class 4, so Swathi would need to win at least one more game.

But then girls would have at least two wins, contradicting condition (iii), which says:

• boys won exactly 2 games
• girls won exactly 1 game

Therefore, Swathi cannot win the first game.

So the first game must be won by Rishi.

Step 3: Determine the next two games

After Rishi beats Swathi, the active players are:

The second game must be cross-class.

• If Rishi loses the second game, then the remaining two players would be P and T, both from Class 4, so the third game would again be a same-class game. Not allowed.
• Therefore, Rishi must also win the second game.

So the second game must be:

because if R beat T instead, the remaining players would be R and P, and Rishi would then also win the third game, giving boys all 3 wins, which violates condition (iii).

Now only Rishi and Tanvi remain for the third game, and Tanvi must win it.

So the unique valid sequence is:

1. Rishi beats Swathi
2. Rishi beats Pavan
3. Tanvi beats Rishi

The student who never lost any game is therefore Tanvi.

Therefore, the correct answer is Option D.

The first node in pre-order is the root, so $P$ is the root.

Split the in-order traversal around $P$:

• Left subtree in-order: S Q E
• Right subtree in-order: F R G

Using pre-order, the left subtree is rooted at $Q$ with children $S$ and $E$, and the right subtree is rooted at $R$ with children $F$ and $G$.

Hence the post-order traversal is

So (A) and (B) are true, while (C) and (D) are false.

Therefore, the correct answers are A and B.

For

the gradient with respect to $w$ is

Using SGD with learning rate $\eta=0.10$:

Substitute

Therefore, the answer is 9.00.

For each strategy chosen by MAX at the root, MIN will then choose the minimum utility among its three children.

• If MAX chooses strategy 1, MIN chooses $$\min(8,6,-1)=-1$$
• If MAX chooses strategy 2, MIN chooses $$\min(1,5,7)=1$$
• If MAX chooses strategy 3, MIN chooses $$\min(-4,-3,-12)=-12$$

Then MAX chooses the maximum among these resulting values:

This value is achieved by choosing strategy 2 at the root.

Therefore, the answer is 2.