List of practice Questions

Arun’s present age in years is 40% of Barun’s. In another few years, Arun’s age will be half of Barun’s. By what percentage will Barun’s age increase during this period?

If $ x = -0.5 $, then which of the following has the smallest value?

The ratio of two numbers is 3 : 5. If 39 is added to the first, and 14 is added to the second, then the ratio becomes 6 : 7. What will be the ratio if 11 is added to the first number and 6 is added to the second number?

Consider two distinct positive numbers $ m, n $ with $ m > n $. Let \[ x = n^{\log_n m}, \quad y = m^{\log_m n}. \] The relation between $ x $ and $ y $ is -

Consider the supervised learning task. The objective function being minimized is $ f(w) = w \cdot x $, where $ w \in \mathbb{R} $ is the parameter. Stochastic Gradient Descent with learning rate of 0.10. Let $ w = 10.00 $ be the $ i^{\text{th}} $ iteration ($ w_i $). The value of $ w $ at the end of iteration $ (i+1) $ is if $ x = 10 $ ________. Round off 2 decimal.

The value of \[ \sum_{j=0}^{\infty} \sum_{i=1}^{\infty} 2^{-j} 3^{-i} \] is ________.

Consider the Ridge LRR is being used to learn prediction function $ y_{\text{pred}} = w^T x $ where $ w, x \in \mathbb{R}^2 $ & mean absolute error (MAE) is used to measure the prediction error. A weight of 0.20 is associated with the regularizer. At an intermediate step of training process assume that the parameter $ w = [-3.00, 4.00]^T $. In the next step for the I/P $ x = [1.00, 2.00]^T $, the predicted value of $ y $ is noted. Let the relation b/w $ x = [x_1, x_2]^T $ & the true value of $ y $ be $ y_{\text{true}} = x_1 + x_2 $. The value of the overall regularized loss for instance is __________ (upto 2 decimal).

S$_1$ = \{x = (x$_1$, x$_2$, x$_3$)$^T$ $\in$ R$^3$ $|$ x$^T$x $\le$ 16\}. Let S$_2$ be subspace of R$^3$ with dimension 2 then Area of S$_1$ $\cap$ S$_2$ ?

Let $ M = \left(I_n - \frac{1}{n} 11^T \right) $ be a matrix where $ 1 = (1,1,\dots,1)^T \in \mathbb{R}^n $ and $ I_n $ is the identity matrix of order $ n $. The value of \[ \max_{x \in S} x^T M x \] where \[ S = \{ x \in \mathbb{R}^n \mid x^T x = 1 \} \] is ________.

I was just enjoying a daydream _________ winning the Nobel Prize for literature.

The children sat silent _________ the carpet, entranced _________ the puppet show.

The actor's entry _________ the world _________ politics surprised most people.

Let L = lim$_{n \to \infty \sum_{k=0}^{n} \frac{e^{-n} }n^k}{k!}$ value of L

R(A B C D E)
F = A$\rightarrow$ BC, CD$\rightarrow$ E, E$\rightarrow$A
Which of the following is correct?

For a given data set ${X$_1$, X$_2$, ..., X$_n$}$ where n = 100
$\frac{1}{2000} \sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - x_j)^2 = 99$
Let us denote $\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i$
The value of $\frac{1}{99} \sum_{i=1}^{n} (x_i - \bar{x})^2$ is __________.

You are given the following preorder and In-order traversal of binary Tree T with nodes E, F, G, P, Q, R, S-
Preorder : P, Q, S, E, R, F, G
Inorder: S, Q, E, P, F, R, G
Which of the following statements is/are true about the binary True T?

Let X be a random variable that follows uniform (-1, 1) dist. The conditional dist. of the random variable Y given X = x is the Uniform (x$^2$ - 0.1, x$^2$ + 0.1) dist. The value of correlation (X, Y) is _______.

A recursive function is given:
def mystery(n):
if n $<=$ 0:
return 1
else:
return mystery(n-1) + mystery(n-2)
Find the value of mystery(4).

Assume a typical runtime stack is used for the recursive function mystery(n) as defined earlier. How many total function calls (stack activations), including the initial call, are made to compute mystery(4)?