ISRO Scientist/Engineer CS Solved Papers

Read the following statements about principal components analysis (PCA):
A: The principal components are eigenvectors of the centred data matrix.
B: The principal components are right singular vectors of the centred data matrix.
C: The principal components are eigenvectors of the sample covariance matrix.
D: The principal components are right singular vectors of the sample covariance matrix.
Which of these statements is/are true?

A decision tree grown to full depth is more likely to
I. Fit the noise in the data.
II. Suffer from over fitting.
III. Generalizes well on unseen data.

Consider the minimizer $\omega^*$ of the $l_2$-regularized least squares objective
$$J(\omega) = \|X\omega - y\|^2 + \lambda\|\omega\|^2$$
with $\lambda > 0$. Which of the following are true?

A multiclass classification problem of $K$ class can be solved either via considering the multiclass case to be a 1-vs.-all scenario with $K$ binary classifiers or via a multiclass classifier such as softmax regression. When would one prefer softmax regression as opposed to $K$ 1-vs.-all logistic regression for multiclass classification?

Sigmoidal activation function in neural networks suffer from which of the following practical problems?

Consider one layer of weights (edges) in a convolutional neural network (CNN) for grayscale images, connecting one layer of units to the next layer of units. Which one of the type of layer has the fewest parameters to be learned during training?

Which of the following statements on regularization are true?
I. Batch normalization can have an implicit regularizing effect, especially with smaller minibatches.
II. Using L-2 regularization enforces a Laplacian prior on your network weights.
III. Using L-2 regularization enforces a Gaussian prior on your network weights.
IV. Choice of regularization factor can cause your model to underfit.

The logit function, $L(x)$ is defined as the log of odds function. What is the range of the logit function in the domain $x = (0, 1)$?

In a Support Vector Machine (SVM) specified with weight $W$ and bias $b$ and the margin value fixed to 1, the distance of the support vectors from the separating hyperplane is:

The technique that combines the predictions from multiple machine learning algorithms together to make more accurate predictions than any individual model is called:

Consider a single unit in a neural network that receives two binary inputs $x_1, x_2 \in \{0, 1\}$ and computes a linear combination followed by a threshold activation function, namely,
$$\sigma(z) = \begin{cases} 1, & z \ge 0 \\ 0, & \text{otherwise} \end{cases}$$
We have chosen a bias term of $b = 5$. The weights $w_1$ and $w_2$ that allow to compute the NAND function are

What is the main purpose of Dropout in a neural network architecture?

Which of the following statements about using convolutional layers instead of fully connected ones for visual tasks are TRUE:
A. They reduce the number of hidden layers
B. They enable spatial context modelling
C. The model becomes translation invariant
D. The number of parameters in the model increases
E. Enables increased parameter sharing

Let,
$p =$ a number from $\{8, 9, 10, 11, 12\}$
$q =$ not a composite number
$r =$ a square number
$s =$ a prime number
Then, what is the value of $\sim((p \rightarrow \sim q) \wedge (\neg r \vee \neg s))$?

Which search uses the problem specific knowledge beyond the definition of the problem?

Which of the following statements are true for benefits of using the backpropagation algorithm to compute gradients?
I. Compared to native gradient computation, it improves the speed of each iteration of gradient descent by eliminating repeated computations of the same subproblem.
II. Its running time is linear in the total number of units (neurons) in the network.
III. Compared to native gradient computation, it reduces the number of iterations required to get close to a local minimum, by protecting against sigmoid unit saturation (vanishing gradients).
IV. Its running time is linear in the total number of edges in the network.

In terms of the bias-variance decomposition, a 1-nearest neighbour classifier has _______ than a 3-nearest classifier. Choose the correct option.
I. Higher variance
II. Higher bias
III. Lower variance
IV. Lower bias

If the posterior distribution has the same distribution family as the prior, the term most aptly describing this condition is called

For a feature map $\Phi$ and a kernel function $k(X_i, X_j) = \langle\Phi(X_i), \Phi(X_j)\rangle$ ($\langle\cdot, \cdot\rangle$ is the inner product), which of the statements are true?
I. The kernel trick implies we do not explicitly compute $\Phi(X_i)$ for any sample point $X_i$.
II. Running times of kernel algorithms do not depend on the dimension $D$ of the feature space $\Phi(\cdot)$.

In the RSA public key cryptosystem, the private and public keys are $(e, n)$ and $(d, n)$ respectively, where $n = p \times q$ and $p$ and $q$ are large primes. Besides, $n$ is public and $p$ and $q$ are private. Let $M$ be an integer such that $0 < M < n$ and $f(n) = (p-1) \times (q-1)$. Now consider the following equations:
I. $M' = M^e \pmod n$, $M = (M')^d \pmod n$
II. $e \times d \equiv 1 \pmod n$
III. $e \times d \equiv 1 \pmod{f(n)}$
IV. $M' = M^e \pmod{f(n)}$, $M = (M')^d \pmod{f(n)}$
Which of the clauses are required for RSA to work:

The remainder when $3^{100,000}$ is divided by $53$ is:

Which of the following is NOT the aim of the Digital Signature scheme?
I. Authenticity
II. Non-Repudiation
III. Confidentiality
IV. Integrity

In security, Sandboxing is a mechanism used for

In a public cloud environment, out of the following, the key cyber-security concerns are
A. Virtualization
B. Data Access
C. Denial of service
D. Misconfiguration
E. Data Leakage

IPSec is designed to provide security at which of these layers of the stack?