List of practice Questions

The $ \Delta^+ $ baryon with spin $ \frac{3}{2} $, at rest, decays to a proton and a pion ($ \Delta^+ \to p + \pi^0 $). The $ \Delta^+ $ has positive intrinsic parity and $ \pi^0 $ has negative intrinsic parity. The orbital angular momentum of the proton-pion system (in integer) is:

A particle is scattered from a potential $ V_{\vec{r}} = g \delta^3(\vec{r}) $, where $ g $ is a positive constant. Using the first Born approximation, the angular $(\theta, \phi)$ dependence of the differential scattering cross section $ \frac{d\sigma}{d\Omega} $ is:

A circle with center at $ (x, y) = (0.5, 0) $ and radius = 0.5 intersects with another circle with center at $ (x, y) = (1, 1) $ and radius = 1 at two points. One of the points of intersection $ (x, y) $ is:

The sum of the following infinite series is: \[ 1 + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \frac{1}{5!} + \dots \]

Two plane polarized light waves combine at a certain point, whose "E" components are: \[ E_1 = E_0 \sin \omega t, \quad E_2 = E_0 \sin \left( \omega t + \frac{\pi}{3} \right) \] Find the amplitude of the resultant wave.

The remainder when $ 64^{64} $ is divided by 7 is equal to:

In a resonance tube closed at one end. Resonance is obtained at lengths $ l_1 = 120 \, \text{cm} $ and $ l_2 = 200 \, \text{cm} $. If $ v_s = 340 \, \text{m/s} $, find the frequency of sound.

The dimensions of a physical quantity $ \epsilon_0 \frac{d\Phi_E}{dt} $ are similar to [Symbols have their usual meanings]

The unit interval $(0, 1)$ is divided at a point chosen uniformly distributed over $(0, 1)$ in $\mathbb{R}$ into two disjoint subintervals. The expected length of the subinterval that contains 0.4 is ___________. (rounded off to two decimal places)

A quadratic polynomial $ (x - \alpha)(x - \beta) $ over complex numbers is said to be square invariant if \[ (x - \alpha)(x - \beta) = (x - \alpha^2)(x - \beta^2). \] Suppose from the set of all square invariant quadratic polynomials we choose one at random. The probability that the roots of the chosen polynomial are equal is ___________. (rounded off to one decimal place)

Consider the following C program:

The output of the above program is __________ . (Answer in integer)

An application executes $ 6.4 \times 10^8 $ number of instructions in 6.3 seconds. There are four types of instructions, the details of which are given in the table. The duration of a clock cycle in nanoseconds is ____________. (rounded off to one decimal place)

Let $ \Sigma = \{1,2,3,4\} $. For $ x \in \Sigma^* $, let $ {prod}(x) $ be the product of symbols in $ x $ modulo 7. We take $ {prod}(\epsilon) = 1 $, where $ \epsilon $ is the null string. For example, \[ {prod}(124) = (1 \times 2 \times 4) \mod 7 = 1. \] Define \[ L = \{ x \in \Sigma^* \mid {prod}(x) = 2 \}. \] The number of states in a minimum state DFA for $ L $ is ___________. (Answer in integer)

Consider the following algorithm someAlgo that takes an undirected graph $ G $ as input.
someAlgo(G) Let $ v $ be any vertex in $ G $.
1. Run BFS on $ G $ starting at $ v $. Let $ u $ be a vertex in $ G $ at maximum distance from $ v $ as given by the BFS.
2. Run BFS on $ G $ again with $ u $ as the starting vertex. Let $ z $ be the vertex at maximum distance from $ u $ as given by the BFS. 3. Output the distance between $ u $ and $ z $ in $ G $.
The output of tt{someAlgo(T)} for the tree shown in the given figure is ____________ . (Answer in integer)

A computer system supports a logical address space of $ 2^{32} $ bytes. It uses two-level hierarchical paging with a page size of 4096 bytes. A logical address is divided into a $ b $-bit index to the outer page table, an offset within the page of the inner page table, and an offset within the desired page. Each entry of the inner page table uses eight bytes. All the pages in the system have the same size. The value of $ b $ is ___________ . (Answer in integer)

In a B+- tree where each node can hold at most four key values, a root to leaf path consists of the following nodes:
$ A = (49, 77, 83, -) $
$ B = (7, 19, 33, 44) $
$ C = (20^*, 22^*, 25^*, 26^*) $
The *-marked keys signify that these are data entries in a leaf. Assume that a pointer between keys $ k_1 $ and $ k_2 $ points to a subtree containing keys in $[ k_1, k_2 )$, and that when a leaf is created, the smallest key in it is copied up into its parent. A record with key value 23 is inserted into the B+- tree. The smallest key value in the parent of the leaf that contains 25* is __________ . (Answer in integer)

A 5-stage instruction pipeline has stage delays of 180, 250, 150, 170, and 250, respectively, in nanoseconds. The delay of an inter-stage latch is 10 nanoseconds. Assume that there are no pipeline stalls due to branches and other hazards. The time taken to process 1000 instructions in microseconds is ___________ . (rounded off to two decimal places)

Given a computing system with two levels of cache (L1 and L2) and a main memory. The first level (L1) cache access time is 1 nanosecond (ns) and the “hit rate” for L1 cache is 90% while the processor is accessing the data from L1 cache. Whereas, for the second level (L2) cache, the “hit rate” is 80% and the “miss penalty” for transferring data from L2 cache to L1 cache is 10 ns. The “miss penalty” for the data to be transferred from main memory to L2 cache is 100 ns. Then the average memory access time in this system in nanoseconds is ___________ . (rounded off to one decimal place)

Consider the following relational schema:

Which of the following options is/are correct SQL query/queries to retrieve the names of the students enrolled in course number (i.e., courseno) 1470?

Consider the database transactions $ T1 $ and $ T2 $, and data items $ X $ and $ Y $. Which of the schedule(s) is/are conflict serializable?

Let $\Sigma = \{a, b, c\}$. For $x \in \Sigma^*$, and $\alpha \in \Sigma$, let $\#\alpha(x)$ denote the number of occurrences of $\alpha$ in $x$. Which one or more of the following option(s) define(s) regular language(s)?

$ x $ is a peptide which is hydrolyzed to 2 amino acids $ y $ and $ z $. $ y $ when reacted with HNO$_2$ gives lactic acid. $ z $ when heated gives a cyclic structure as below:

Statement-1: $ \text{ClF}_3 $ has 3 possible structures.
Statement-2: $ \text{III} $ is the most stable structure due to least lone pair-bond pair (lp-bp) repulsion.

Which of the following options is correct?

Consider the following graph between Rate Constant (K) and $ \frac{1}{T} $: Based on the graph, determine the correct order of activation energies $ E_{a1}, E_{a2}, $ and $ E_{a3} $.