Paper Generator

Two moles of an ideal gas undergo free expansion from 10 L to 100 L at 300 K. The values of $\Delta S_{system}$ and $\Delta S_{surroundings}$ are (R is universal gas constant)

Given below are two statements: Statement-I: Oxidation of p-nitrotoluene with acidic $KMnO_{4}$ gives an acid that is stronger than benzoic acid. Statement-II: Reduction of p-nitrotoluene with $Sn/HCl$ followed by neutralization gives an amine that is more basic than aniline. In light of the above statements, choose the most appropriate answer from the options given below.

Given below are two statements: Statement-I: $[Fe(ox)_{3}]^{3-}$ is chiral. Statement-II: trans-$[Cr(H_{2}O)_{2}(ox)_{2}]^{-}$ is chiral. (Given: $oxH_{2}=HOOC-COOH$) In light of the above statements, choose the most appropriate answer from the options given below:

Among the following options, the correct trend in the electron gain enthalpy is

Given below are two statements: Statement-I: Heating NaCl with concentrated $H_{2}SO_{4}$ and $MnO_{2}$ results in oxidation of Mn. Statement-II: Heating NaI with concentrated $H_{2}SO_{4}$ and $MnO_{2}$ results in reduction of Mn. In light of the above statements, choose the most appropriate answer from the options given below.

The lanthanide ion having four unpaired electrons is (Given: Atomic numbers of $Ce=58$, $Nd=60$, $Tb=65$ and $Ho=67$)

The formula of tetraammineaquachloridocobalt(III) chloride is

Consider a spring-mass simple harmonic oscillator in one dimension. The mass of the particle is $m$ kg and the spring constant is $k~Nm^{-1}$. At a given instant, the extension of the spring is $x$-meter and the speed of the particle is $v~ms^{-1}$. On the $x-v$ plane, if the graph of $v$ as a function of $x$ is a circle, then the correct option is:

Two infinitely long parallel conducting wires A and B carry currents $I$ and $2I$, respectively, in the same direction. The wire A has uniform mass per unit length $\lambda$ and lies on an insulated floor. The wire B is kept fixed at a height $h$ above the floor. The minimum magnitude of $h$ so that the wire A does not rise from the floor is: [$g$ is the acceleration due to gravity and $\mu_{0}$ is the permeability of free space.]

One main scale division of a Vernier calliper is equal to 1 mm and the number of divisions on the Vernier scale is 10. When both the jaws touch each other, the Vernier scale shifts to the left of zero of the main scale in such a way that 4th Vernier division coincides with a division of the main scale. If this Vernier calliper measures the length of the wire to be 1 cm, the actual length of the wire is:

A ray of light with wavelength $\lambda$ is incident on three different photoelectric cells namely 1, 2 and 3. The threshold wavelength of these photoelectric cells are $\lambda_{1}$, $\lambda_{2},$ and $\lambda_{3,}$ respectively and the magnitude of stopping potentials of these cells are $V_{1}$, $V_{2}$ and $V_{3},$ respectively. The relation between $\lambda$ and threshold wavelengths are $\lambda_{1}<\lambda$, $\lambda_{2}>\lambda$ and $\lambda_{3}>>\lambda$. The correct option is:

Consider that $\sigma_{S}$, $k_{B}$, b represents Stefan-Boltzmann constant, Boltzmann constant and Wien's displacement law constant, respectively. The dimension of $\sigma_{s}k_{B}^{-1}b$ is

In a solar system, the time-period of revolution of a planet tracing a circular orbit of radius R is proportional to:

Which of the following measurements require 'index correction'?

Consider the following nuclear reaction ${}^{238}U\longrightarrow{}^{234}Th+{}^{4}He$. Take masses of ${}^{238}U$, ${}^{234}Th$ and ${}^{4}He$ as 238.050 u, 234.043 u and 4.003 u, respectively. The Q value for the reaction, in keV, is: [Given: $1~u=931.5~MeV~c^{-2}$]

For sound waves, if the number of nodes for the $5^{th}$ harmonic of an open-ended pipe is n and that for the $9^{th}$ harmonic of the same pipe with one of its ends closed is m, the ratio $\frac{n}{m}$ is

A cylindrical cork of uniform density floats in a liquid of density $\rho_{1}$. If the cork is depressed slightly and released, it oscillates harmonically with time period T. If the same cork floats in another liquid of density $\rho_{2}$, then the similar oscillation has time period 2T. The value of $\rho_{2}/\rho_{1}$ is:

The mean free path of molecules in an ideal gas A is half that of another ideal gas B. The diameter of the spherical molecules of gas A is twice the diameter of the molecules of B. If number densities of the gases A and B are $n_{A}$ and $n_{B}$ respectively, the correct option is:

Consider that an electron is revolving in an excited state of Hydrogen atom with velocity $\sqrt{25.6}\times10^{5}ms^{-1}$. The radius of the orbit is $x\times10^{-9}$ m. The value of x is: [Take the mass of electron to the $9\times10^{-31}$ kg, charge of electron $=-1.6\times10^{-19}C$ and $\frac{1}{4\pi\epsilon_{0}}=9\times10^{9}Nm^{2}C^{-2}$]

A car travels on a circular racetrack of radius 50 m, which is banked at an angle $\theta$. If the car travels at a speed $10~ms^{-1}$, then the wear and tear on its tyres is minimum. Taking the acceleration due to gravity to be $10~ms^{-2}$, the value of $\theta$ is: