JEE Main JEE Main 2023 Mixed — practice questions
120 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Main JEE Main 2023 Mixed in the app →Rutherford's alpha-particle scattering experiment led to the conclusion that the atom:According to Bohr's postulate, the angular momentum of an electron in the $n$-th allowed orbit of a hydrogen-lThe radius of the $n$-th Bohr orbit of a hydrogen-like atom of atomic number $Z$ varies as:The total energy of an electron in the $n$-th orbit of a hydrogen atom is given by $E_n = -13.6/n^2\,\text{eV}The minimum energy required to remove an electron from the ground state of a hydrogen atom is:The kinetic energy of an electron in the $n$-th Bohr orbit of a hydrogen atom is related to its total energy $The Rydberg formula for the wavelength of radiation emitted when an electron in a hydrogen atom jumps from levWhich spectral series of hydrogen lies entirely in the ultraviolet region?The hydrogen spectral lines that lie in the visible region of the electromagnetic spectrum belong to the:The major shortcoming of the Rutherford atomic model was that it could not explain:For a hydrogen-like ion of atomic number $Z$, the ground-state energy is:An electron in a hydrogen atom undergoes a transition from $n = 3$ to $n = 2$. The energy of the emitted photoA particle moves in a straight line with velocity v = 4t - t² m/s. The displacement of the particle in the timA block of mass 2 kg slides down a rough incline of 30°. Coefficient of kinetic friction is 0.2. Acceleration Two particles of mass m and 4m have same kinetic energy. Ratio of their de Broglie wavelengths:In Young's double slit experiment, if slit separation is halved and wavelength doubled, fringe width becomes:Charge Q is placed at center of a cube. Electric flux through one face:In LCR series circuit, at resonance, impedance equals:A capacitor of capacitance C is charged to voltage V then connected through a resistor R to an uncharged capacA wire of resistance R is bent into a circle. Resistance between two diametrically opposite points:A particle of mass m moves in circle of radius r with constant speed v. Magnitude of momentum change in half rTwo satellites of same mass orbit Earth at radii r and 2r. Ratio of their kinetic energies:Heat capacity of a body is 200 J/K. Heat required to raise its temperature from 20°C to 50°C:For a body in SHM with amplitude A, at displacement x, ratio of KE to total energy:Two coherent sources of intensity I and 4I interfere. Maximum intensity in resulting pattern:Bohr radius for hydrogen is 0.53 Å. Radius of 3rd orbit:Magnetic flux through a coil changes from 5 mWb to 1 mWb in 0.1 s. Induced EMF:Work done in stretching wire by 1 mm is W. Work to stretch it by 2 mm (same wire, within elastic limit):Photon of wavelength 200 nm strikes metal with work function 2 eV. KE of fastest photoelectron (hc = 1240 eV nA car travels 100 km at 50 km/h, then 100 km at 100 km/h. Average speed:At what temperature does kT equal 1 eV?Two resistors 3 Ω and 6 Ω in parallel. Equivalent resistance:Specific heat capacity of monatomic ideal gas at constant V:Pressure increases linearly with depth in incompressible fluid. Pressure at 10 m below water surface (ρ = 1000Electric field due to infinite plane sheet with surface charge density σ:Sound wave intensity I dB scale. 60 dB to 80 dB ratio of intensity:Number of moles of KMnO₄ required to oxidize 1 mole of Fe²⁺ in acidic solution:Electronic configuration of Cr³⁺ (Z = 24):Among Cu, Zn, Pt, Au, which is the noble metal MOST resistant to corrosion?pH of 10⁻⁸ M HCl solution (in water):In octahedral complex with d⁵ metal and strong field ligand, magnetic moment:Number of stereoisomers of 2-bromobutane:Which is the strongest oxidizer in halogens?Order of basicity: NH₃, PH₃, AsH₃, SbH₃:Number of σ and π bonds in CO₂:For first-order reaction with t₁/₂ = 10 min, k =Among NH₃, PH₃, H₂O, H₂S — most acidic:Color of [Cu(NH₃)₄]²⁺:Which gives positive iodoform test?For coordination compound [Co(NH₃)₅Cl]Br₂, total ions in solution:Number of moles of O₂ needed to completely oxidize 1 mole of C₂H₅OH to CO₂ and H₂O:Crystal field stabilization energy (CFSE) for [Co(NH₃)₆]³⁺ (Co³⁺ d⁶ low-spin):Standard enthalpy of formation of an element in its standard state:Bond order of N₂:Hybridization of P in PCl₅:What does Fehling's solution test detect?Value of ∫₀^(π/2) sin² x dx:Number of arrangements of letters in 'BANANA':For matrix A = [[1, 2], [3, 4]], det(A):lim_(x→0) (e^x - 1)/sin x =Number of ways to choose 4 students from class of 10 if 2 specific students must be included:Solution of differential equation dy/dx = y/x:Two cards drawn from a deck of 52 (without replacement). P(both aces):Number of solutions of sin x = 1/2 in [0, 2π]:For vectors a, b with |a| = |b| = 1 and a · b = 1/2, angle:Equation of circle with center (1, -2) and radius 3:Coefficient of x² in expansion of (1 + 2x)¹⁰:Number of integers between 1 and 100 (inclusive) divisible by 3 or 5:Slope of tangent to y = x² + 3x at point (1, 4):sec²(arctan(2)) =Argument of complex number 1 + i:Sum of first 10 terms of AP with a = 3, d = 2:For GP with first term 2 and common ratio 1/2, sum to infinity:Distance from point (1, 2, 3) to plane x + y + z - 6 = 0:Roots of equation x² - 5x + 6 = 0:sin(75°) =In a triangle ABC, if a = 2, b = 3, C = 60°, find c (using cosine rule):Find eigenvalues of [[3, 1], [1, 3]]:For y = cos x, y'' + y =If f(x) = x³ - 3x² + 2, find x where local maximum occurs:Integration: ∫ tan(x) dx =The wave number $\bar{\nu}$ of electromagnetic radiation is defined asIn vacuum, the velocity of electromagnetic radiation isA photon has wavelength $400\,nm$. Its frequency is approximatelyThe wave number of a photon of frequency $6 \times 10^{14}\,Hz$ (in vacuum) isAccording to Planck's quantum theory, energy is emitted or absorbed in discrete packets calledThe energy of a photon of wavelength $\lambda$ is given byA photon of wavelength $300\,nm$ has approximately what energy in eV? (Use $hc = 1240\,eV\,nm$.)In the photoelectric effect, the kinetic energy of the ejected electron depends onThe threshold frequency $\nu_0$ for a metal is the minimum frequencyLight of frequency $\nu = 2\nu_0$ ejects photoelectrons from a metal with threshold frequency $\nu_0$. The maxIn a photoelectric experiment, doubling the *intensity* of incident light (frequency unchanged) willRutherford's $\alpha$-particle scattering experiment used a thin foil of which metal?In Rutherford's experiment, the observation that a few $\alpha$-particles bounced *back* impliedThe radius of a nucleus of mass number $A$ is approximately $R = R_0 A^{1/3}$ with $R_0 = 1.33 \times 10^{-15}Bohr's postulate quantises the angular momentum of an electron in a stationary orbit asFor a hydrogen-like atom of nuclear charge $Z$, the radius of the $n$th Bohr orbit scales asThe energy of the $n$th Bohr orbit of a hydrogen-like atom isThe ratio of the radii of the third Bohr orbit of $He^+$ and the first Bohr orbit of $H$ isThe velocity of the electron in the $n$th Bohr orbit of a hydrogen-like atom is proportional toThe energy required to remove the electron from the first excited state ($n=2$) of $He^+$ isWhich series of the hydrogen spectrum lies entirely in the *visible* region?Rydberg's formula for the wave number of a hydrogen spectral line isWhen an electron in a hydrogen atom returns to the ground state from $n = 5$, the maximum number of distinct sThe longest wavelength line in the Lyman series of hydrogen corresponds to the transitionA hydrogen atom in its ground state absorbs a photon and is excited to $n = 4$. The number of *possible* spectThe de Broglie wavelength of a particle of mass $m$ and momentum $p$ isThe de Broglie wavelength of an electron in the $n$th Bohr orbit, in terms of the orbit radius $r_n$, isAn electron is accelerated through a potential difference of $100\,V$. Its de Broglie wavelength is approximatHeisenberg's uncertainty principle relates the uncertainties in position and momentum asThe minimum uncertainty in the velocity of an electron whose position is known to within $\Delta x = 0.1\,nm$ The principal quantum number $n$ can take valuesFor principal quantum number $n$, the orbital quantum number $l$ takes valuesFor orbital quantum number $l$, the magnetic quantum number $m_l$ takes valuesHow many orbitals are present in the $n = 3$ shell?The maximum number of electrons in the subshell with $n = 4, l = 2$ isWhich set of quantum numbers $(n, l, m_l, m_s)$ is **NOT** allowed?Hund's rule applies during the filling ofThe Aufbau principle dictates that orbitals fill in order of increasingWhich of the following orbital shapes is dumbbell-shaped along an axis?