List of practice Questions

Consider the language $L$ over the alphabet $\{0,1\}$: \[ L = \{\, w \in \{0,1\}^* \;\mid\; \text{$w$ does not contain three or more consecutive $1$'s}\,\}. \] The minimum number of states in a Deterministic Finite-State Automaton (DFA) for $L$ is ________.

An 8-way set associative cache of size 64 KB (1 KB = 1024 bytes) is used in a system with a 32-bit address. The address is sub-divided into TAG, INDEX, and BLOCK OFFSET. Find the number of bits in the TAG.

The forwarding table of a router is shown below. A packet addressed to a destination address 200.150.68.118 arrives at the router. It will be forwarded to the interface with ID

Let $U = \{1,2,\ldots,n\}$ with $n > 1000$. Let $k < n$ be a positive integer. Let $A,B \subseteq U$ with $|A| = |B| = k$ and $A \cap B = \varnothing$. A permutation of $U$ separates $A$ from $B$ if either all members of $A$ appear before any member of $B$, or all members of $B$ appear before any member of $A$.

How many permutations of $U$ separate $A$ from $B$?

The mass of proton, neutron and helium nucleus are respectively $10073\, u$, $10087\, u$ and $40015\, u$ The binding energy of helium nucleus is:

The ratio of the density of oxygen nucleus $\left({ }_8^{16} O \right)$ and helium nucleus $\left({ }_2^4 He \right)$ is

Consider the following radioactive decay process ${ }_{84}^{218} A \xrightarrow{\alpha} A_1 \xrightarrow{\beta^{-}}A_2 \xrightarrow{\gamma} A_3 \xrightarrow{\alpha} A_4 \xrightarrow{\beta^{+}} A_5 \xrightarrow{\gamma}A_6$ The mass number and the atomic number of $A_6$ are given by:

Nucleus $A$ having $Z=17$ and equal number of protons and neutrons has $12 MeV$ binding energy per nucleonAnother nucleus $B$ of $Z=12$ has total 26 nucleons and $18 MeV$ binding energy per nucleons The difference of binding energy of $B$ and $A$ will be ___$MeV$

A radioactive nucleus decays by two different process The half life of the first process is 5 minutes and that of the second process is $30 s$. The effective half-life of the nucleus is calculated to be $\frac{\alpha}{11}$ s The value of $\alpha$ is _______

A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3: 2$ The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$ The value of ' $x$ ' is:-

Assume that protons and neutrons have equal masses Mass of a mucleon is $16 \times 10^{-27} kg$ and radius of nucleus is $15 \times 10^{-15} A ^{1 / 3} m$ The approximate ratio of the nuclear density and water density is $n \times 10^{13}$ The value of $n$ is ___

The energy released per fission of the nucleus of $^{240}\text{X}$ is $200 \, \text{MeV}$. The energy released if all the atoms in $120 \, \text{g}$ of pure $^{240}\text{X}$ undergo fission is _____ $10^{25} \, \text{MeV}$. (Given $N_A = 6 \times 10^{23}$)

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$
Assertion (A): The nuclear density of nuclides ${ }_5^{10} B ,{ }_3^6 Li ,{ }_{26}^{56} Fe ,{ }_{10}^{20} Ne$ and ${ }_{83}^{209} Bi$ can be arranged as $\rho_{ Bi }^N>\rho_{ Fe }^N>\rho_{ Ne }^N>\rho_{ B }^N>\rho_{ Li }^N$.
Reason R: The radius $R$ of nucleus is related to its mass number $A$ as $R=R_0 A^{1 / 3}$, where $R_0$ is a constant.
In the light of the above statements, choose the correct answer from the options given below

For the given radioactive decay $^{298}_{94}X → ^{294}_{92}X + ^{4}_{2}ɑ + Q$ - value, binding energy per nucleon of X, Y and ɑ are a, b and c. The Q - value is equal to

If half life of a radio-active nuclide A is equal to average life of another radio-active nuclide B. Find the ratio of decay constant of A to that of B.

Which of the following correctly represents the variation of electric potential (V) of a charged spherical conductor of radius (R) with radial distance (r) from the center?

As shown in the figure, a point charge $Q$ is placed at the centre of conducting spherical shell of inner radius $a$ and outer radius $b$. The electric field due to charge $Q$ in three different regions I, II and III is given by: (I: r $<$ a, II: $a $<$ r $<$ b$, III: $r$>$b)$

A capacitor of capacitance $900\, \mu F$ is charged by a $100\, V$ battery The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor The loss of energy in this process is measured as $x \times 10^{-2} J$ The value of $x$ is ______

A capacitor has capacitance $5 \mu F$ when it's parallel plates are separated by air medium of thickness d A slab of material of dielectric constant $15$ having area equal to that of plates but thickness $\frac{d}{2}$ is inserted between the plates Capacitance of the capacitor in the presence of slab will be ___$\mu F$

A parallel plate capacitor with air between the plate has a capacitance of $15\, pF$ The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant $3.5$. Then the capacitance becomes $\frac{x}{4} pF$ The value of $x$ is _______

A point charge of $10\, \mu C$ is placed at the origin At what location on the $X$-axis should a point charge of $40 \, \mu C$ be placed so that the net electric field is zero at $x=2 \, cm$ on the $X$-axis?

A parallel plate capacitor with plate area A and plate separation d is filled with a dielectric material of dielectric constant K = 4. The thickness of the dielectric material is x, where x < d. Let C1 and C2 be the capacitance of the system for $x =$ $\frac{1}{3}d$ and $x=\frac{2}{3}d$, respectively. If C₁ = 2μF, the value of C₂is _______ μF.

Find the energy stored in the capacitor in a given circuit.

Potential at the surface of a uniformly charged non-conducting sphere is V. Then the potential at its centre is

A parallel plate capacitor with plate area A and plate separation d is filed with a dielectric material of dielectric constant K = 4. The thickness of the dielectric material is x, where $x < d$.

Let C₁ and C₂ be the capacitance of the system for $x=\frac{1}{3d}$ and $x=\frac{2d}{3}$, respectively. If $C_1 = 2μF$, the value of C₂ is __________μF.