GATE 2026 DA Q.37: solution and answer

GATE 2026 · DAQ.37 · 2 marks · MCQ

Which of the following statements is true for Ridge Regression?

(A)
The regularizer in the objective function of Ridge Regression is used to guard against scenarios where the model works well for the test data, but poorly for the training data.
(B)
The regularizer of Ridge Regression uses L_1 norm.
(C)
Ridge Regression aims to reduce the number of parameters that have negative values.
(D)
The regularizer of Ridge Regression may increase the bias of the model, but it helps in reducing the variance in predictions.

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Answer and solution

ANSWER

The answer is (D). The Ridge regulariser may add some bias but it reduces the variance of the predictions.

Official answer: DSource: Official answer key, GATE 2026 DA (IIT Guwahati)

Ridge regression minimises $∥ y - X w ∥^{2} + λ ∥ w ∥_{2}^{2}$ , so its penalty is the squared $L_{2}$ norm of the weights. This rules out (B), which names the $L_{1}$ norm (that is Lasso).
The penalty shrinks every weight towards zero, whatever its sign. It does not count weights or single out negative ones, so (C) is false.
Overfitting is a model that does well on training data but poorly on test data, and regularisation guards against that case. (A) states the reverse (good on test data, poor on training data), so it is false.
Setting the gradient to zero gives the closed form $\hat{w} = (X^{⊤} X + λ I)^{- 1} X^{⊤} y$ . For $λ > 0$ this differs from the unbiased least-squares solution $(X^{⊤} X)^{- 1} X^{⊤} y$ , and the gap grows with $λ$ . So the penalty can increase the bias.
Adding $λ I$ also makes $X^{⊤} X + λ I$ better conditioned, so the estimate changes less from one training set to another. Variance falls. This is the bias-variance trade-off, so (D) is true.

KEY IDEA

Ridge adds a squared $L_{2}$ penalty $λ ∥ w ∥_{2}^{2}$ . It shrinks the weights, which adds a little bias and lowers variance (the bias-variance trade-off). It is a guard against overfitting.

WATCH OUT FOR

Reading (A) carelessly. Overfitting means good on training data and poor on test data, and (A) says the opposite. Another slip is mixing up Ridge ( $L_{2}$ ) with Lasso ( $L_{1}$ ).

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GATE 2026 DA Q.37: solution and answer

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