GUJCET 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 GUJCET JEE Main 2023 Mixed in the app →A 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?How many *angular* nodes does a $3d$ orbital have?The number of *radial* nodes in a $4s$ orbital isThe ionisation energy of hydrogen in its ground state isFor $He^+$, the ionisation energy from its ground state isWhich transition in the hydrogen atom emits the largest amount of energy?Which of the following experimental phenomena could **NOT** be explained by classical EM wave theory?The Bohr model failed to explainIn the photoelectric effect, the *stopping potential* $V_0$ varies with the frequency of incident light asWhich of the following is **NOT** a possible set of quantum numbers for a 3d electron?The total number of electrons that can fit in the $M$ shell ($n=3$) isThe Bohr radius for hydrogen ($n=1, Z=1$) is approximatelyThe proton was discovered through experiments involving