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Joint Entrance Exam Advanced (JEE Advanced)
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Fani Warraich
CHEMISTRY

Biochemistry
DNA model was presented by Watson and Crick in
A. 1951.
B. 1952.
C. 1953.
D. 1954.
Fani Warraich
CHEMISTRY

Biochemistry
The "energy carrier" ATP is an example of a(n)
A. deoxyribonucleoside triphosphate.
B. dinucleotide.
C. ribonucleotide.
D. ribonucleoside triphosphate.
Fani Warraich
CHEMISTRY

Biochemistry
Sadenosyl methionine is a group donor of
A. Phosphate.
B. Methyl.
C. Adenosine.
D. Sulfate.
Fani Warraich
CHEMISTRY

Biochemistry
When DNA is heated, the temperature at which ________ of the helical structure is lost is defined as the melting temperature.
A. One half.
B. Two half.
C. Three half.
D. Complete.
Fani Warraich
CHEMISTRY

Biochemistry
Nucleotides also serve as carriers of activated intermediates in the synthesis of
A. Carbohydrates.
B. Lipids.
C. Proteins.
D. All of these.
Fani Warraich
MATHEMATICS

Calculus
The solution set of the inequality x + 4 ≥ 2 is
A. ( , 6] [2, ).
B. ( ,6] [ 2, ) .
C. ( , 6] [ 2, ) .
D. None of these.
Fani Warraich
MATHEMATICS

Algebra
Solve the equation 2/6 (3a + 2b) – 1/2 (2a + 4b) 2(12a – 6b)?
A. 6a – 7b.
B. 2a + 4b.
C. 5a + 6b.
D. 7a – 8b.
Shalisha Ladawn
PHYSICS

Classical Mechanics
Electric displacement current through a surface S is by definition proportional to the
A. rate of change of the electric flux through S.
B. magnetic flux through S.
C. rate of change of the magnetic flux through S.
D. time integral of the magnetic flux through S.
Shalisha Ladawn
PHYSICS

Classical Mechanics
Classical mechanics explains how _______ moves.
A. Macroscopic object.
B. Microscopic object.
C. All of above.
D. None of these.
Fani Warraich
PHYSICS

Electromagnetism
The Net Magnetic flux from any closed surface is
A. Infinity.
B. Zero.
C. Negative.
D. Positive.
Gitofa Shah
PHYSICS

Quantum Mechanics
Which of the following statements about the Heisenberg Uncertainty Principle is correct?
A. It states that the position and momentum of a particle cannot be measured at the same time..
B. It implies that the product of the uncertainties in position and momentum measurements is always greater than or equal to ℏ / 2..
C. It suggests that particles do not have definite positions and momenta..
D. It is a consequence of the waveparticle duality of light..
Gitofa Shah
PHYSICS

Quantum Mechanics
In the context of quantum mechanics, what does the term "wavefunction collapse" refer to?
A. The phenomenon where a wavefunction spreads out over time..
B. The process of normalizing a wavefunction..
C. The sudden transition of a wavefunction into one of the eigenstates upon measurement..
D. The interference pattern created by a superposition of wavefunctions..
Gitofa Shah
PHYSICS

Quantum Mechanics
What is the physical significance of the commutator of the position and momentum operators in Quantum Mechanics?
A. It represents the uncertainty principle.
B. It determines the energy eigenvalues.
C. It is a measure of the particle's spin.
D. It is a constant of motion.
Gitofa Shah
PHYSICS

Quantum Mechanics
A particle is in a superposition of two energy eigenstates, ψ= aE1+ bE2. What is the probability of finding the particle in the energy eigenstate E1?
A. a^2 / (a^2 + b^2).
B. a / ( a + b ).
C. b / ( a + b ).
D. None of these.
Gitofa Shah
PHYSICS

Quantum Mechanics
What is the purpose of the wave function renormalization in Quantum Field Theory?
A. To remove the infinite selfenergy of particles.
B. To introduce the concept of antiparticles.
C. To ensure the Lorentz invariance of the theory.
D. To account for the spinstatistics theorem.
Gitofa Shah
PHYSICS

Quantum Mechanics
A beam of particles passes through a SternGerlach apparatus with a magnetic field gradient oriented in the zdirection. What is the effect on the beam?
A. The beam is split into two beams with opposite spin components in the xdirection.
B. The beam is split into two beams with opposite spin components in the ydirection.
C. The beam is split into two beams with opposite spin components in the zdirection.
D. The beam remains unchanged.
Gitofa Shah
PHYSICS

Quantum Mechanics
What is the name of the process by which a particle and its antiparticle annihilate into photons?
A. Pair production.
B. Pair annihilation.
C. Compton scattering.
D. Bremsstrahlung.
Gitofa Shah
PHYSICS

Statistical Mechanics
What is the name of the statistical ensemble that describes a system with a fixed number of particles, volume, and energy?
A. Microcanonical ensemble.
B. Canonical ensemble.
C. Grand canonical ensemble.
D. Isothermalisobaric ensemble.
Gitofa Shah
PHYSICS

Statistical Mechanics
A system is in thermal equilibrium with a reservoir at temperature T. What is the probability of finding the system in a microstate with energy E?
A. 1 / Ω(T).
B. e^(−E/kT) / Z(T).
C. E / kT.
D. Ω(T) / E.
Gitofa Shah
PHYSICS

Statistical Mechanics
What is the name of the theorem that relates the entropy of a system to the number of possible microstates?
A. Boltzmann's theorem.
B. Gibbs' theorem.
C. Shannon's theorem.
D. Onsager's theorem.
Gitofa Shah
PHYSICS

Statistical Mechanics
A system undergoes a reversible adiabatic process. What is the change in entropy of the system?
A. ΔS = 0.
B. ΔS > 0.
C. ΔS.
D. ΔS = k * ln(V2 / V1).
Gitofa Shah
PHYSICS

Statistical Mechanics
What is the name of the statistical mechanical potential that describes a system at constant temperature and pressure?
A. Helmholtz free energy.
B. Gibbs free energy.
C. Landau free energy.
D. Grand potential.
Gitofa Shah
PHYSICS

Thermodynamics
A heat engine operates between two reservoirs at temperatures T1 and T2, with T1 > T2. What is the maximum efficiency of the engine?
A. 1  (T2 / T1).
B. 1  (T1 / T2).
C. T1 / T2.
D. T2 / T1.
Gitofa Shah
PHYSICS

Thermodynamics
A system undergoes a reversible isothermal expansion from volume V1 to V2. What is the change in internal energy of the system?
A. ΔU = 0.
B. ΔU = Q.
C. ΔU = W.
D. ΔU = W.
Gitofa Shah
PHYSICS

Thermodynamics
What is the name of the process by which a system transitions from a metastable state to a stable state with a decrease in free energy?
A. Melting.
B. Boiling.
C. Condensation.
D. Nucleation.
Gitofa Shah
PHYSICS

Thermodynamics
A gas is compressed adiabatically from pressure P1 to P2. What is the change in temperature of the gas?
A. T2 = T1 * (P2 / P1)^(γ  1).
B. T2 = T1 * (P2 / P1)^(1 / γ).
C. T2 = T1 * (P1 / P2)^(γ  1).
D. T2 = T1 * (P1 / P2)^(1 / γ).
Gitofa Shah
PHYSICS

Thermodynamics
What is the name of the thermodynamic potential that describes a system at constant pressure and temperature?
A. Helmholtz free energy.
B. Gibbs free energy.
C. Landau free energy.
D. Enthalpy.
Gitofa Shah
PHYSICS

Electromagnetism
A charged particle moves with a velocity v = 0.6c in a region with a uniform magnetic field B = 2T. What is the magnitude of the force experienced by the particle if its charge is q = 3 × 10^(6) C?
A. 3.6 × 10^(3) N.
B. 3.6 × 10^(2) N.
C. 3.6 × 10^(1) N.
D. 3.6 N.
Gitofa Shah
PHYSICS

Electromagnetism
A parallelplate capacitor has a capacitance C = 5 μF and is charged to a voltage V = 12 V. If the plates are separated by a distance d = 2 mm, what is the energy density of the electric field between the plates?
A. 1.8 × 10^5 J/m^3.
B. 1.8 × 10^4 J/m^3.
C. 1.8 × 10^3 J/m^3.
D. 1.8 × 10^2 J/m^3.
Gitofa Shah
PHYSICS

Electromagnetism
A coil of 500 turns and crosssectional area A = 0.02 m^2 is placed in a region with a uniform magnetic field B = 0.1 T. If the coil is rotated at a constant angular velocity ω = 20 rad/s, what is the maximum emf induced in the coil?
A. 1.57 V.
B. 3.14 V.
C. 6.28 V.
D. 12.56 V.
Gitofa Shah
PHYSICS

Electromagnetism
A beam of light with a wavelength λ = 500 nm is incident on a diffraction grating with 5000 lines per meter. What is the angular separation between the firstorder maxima?
A. 0.01 rad.
B. 0.1 rad.
C. 1 rad.
D. 10 rad.
Malen Bara
CHEMISTRY

Organic Chemistry
Which of the following statements about the bonding in ethyne (acetylene, C2H2) is correct?
A. Ethyne has two sp3 hybridized carbons with a triple bond between them..
B. Ethyne has two sp2 hybridized carbons with a double bond between them..
C. Ethyne has two sp hybridized carbons with a triple bond between them..
D. Ethyne has two sp2 hybridized carbons with a single bond between them..
Malen Bara
CHEMISTRY

Organic Chemistry
Which of the following functional groups can act as both an acid and a base?
A. Alcohol.
B. Amine.
C. Carboxylic acid.
D. Amide.
Malen Bara
CHEMISTRY

Organic Chemistry
Which of the following compounds is chiral?
A. 2Butanol.
B. 1Butanol.
C. 2Methylpropane.
D. Ethanol.
Malen Bara
CHEMISTRY

Organic Chemistry
In which of the following reactions does the formation of a carbocation intermediate occur?
A. SN2 reaction.
B. E2 reaction.
C. SN1 reaction.
D. DielsAlder reaction.
Malen Bara
CHEMISTRY

Organic Chemistry
What is the first step in the retrosynthetic analysis of 1bromo2phenylethane?
A. Remove the bromine atom..
B. Identify the phenyl group attachment..
C. Identify a precursor for the ethane chain..
D. Consider a FriedelCrafts alkylation..
Malen Bara
CHEMISTRY

Organic Chemistry
In proton NMR spectroscopy, what splitting pattern would you expect for the protons on the methylene group in ethyl acetate (CH3COOCH2CH3)?
A. Singlet.
B. Doublet.
C. Triplet.
D. Quartet.
Malen Bara
CHEMISTRY

Organic Chemistry
Which of the following compounds is not aromatic?
A. Benzene.
B. Pyridine.
C. Cyclooctatetraene.
D. Naphthalene.
Malen Bara
CHEMISTRY

Organic Chemistry
In an electrophilic aromatic substitution reaction, which intermediate is formed?
A. Carbocation.
B. Free radical.
C. Anion.
D. Sigma complex.
Malen Bara
CHEMISTRY

Organic Chemistry
Which of the following statements about the polymerization of ethylene to form polyethylene is correct?
A. It is a condensation polymerization..
B. It involves the elimination of water..
C. It is a free radical polymerization..
D. It forms a crosslinked polymer..
Malen Bara
CHEMISTRY

Organic Chemistry
Which of the following heterocycles contains nitrogen and is aromatic?
A. Furan.
B. Thiophene.
C. Pyrrole.
D. Oxazole.
Malen Bara
CHEMISTRY

Organic Chemistry
Which type of enzyme catalysis involves the formation of a covalent bond between the enzyme and the substrate?
A. Acidbase catalysis.
B. Covalent catalysis.
C. Metal ion catalysis.
D. Proximity and orientation effects.
Malen Bara
CHEMISTRY

Organic Chemistry
Which of the following principles is not one of the Twelve Principles of Green Chemistry?
A. Designing safer chemicals..
B. Using renewable feedstocks..
C. Maximizing atom economy..
D. Increasing chemical yields..
Malen Bara
CHEMISTRY

Inorganic Chemistry
Which of the following elements has the highest second ionization energy?
A. Sodium (Na).
B. Magnesium (Mg).
C. Aluminum (Al).
D. Silicon (Si).
Malen Bara
CHEMISTRY

Inorganic Chemistry
Which of the following molecules has the most polar bond?
A. HCl.
B. CO.
C. HF.
D. H2O.
Malen Bara
CHEMISTRY

Inorganic Chemistry
In a facecentered cubic (fcc) lattice, what is the coordination number of each atom?
A. 4.
B. 6.
C. 8.
D. 12.
Malen Bara
CHEMISTRY

Inorganic Chemistry
Which of the following ligands will cause the greatest splitting in the dorbital energies of a central metal ion according to the spectrochemical series?
A. H2O.
B. NH3.
C. CN⁻.
D. Cl⁻.
Malen Bara
CHEMISTRY

Inorganic Chemistry
In the compound ferrocene (Fe(C5H5)2), what is the oxidation state of the iron center?
A. 0.
B. +1.
C. +2.
D. +3.
Malen Bara
CHEMISTRY

Inorganic Chemistry
Which metal ion is at the active site of the enzyme carbonic anhydrase?
A. Fe.
B. Zn.
C. Cu.
D. Mg.
Malen Bara
CHEMISTRY

Inorganic Chemistry
Which of the following elements forms a stable diatomic molecule in the gas phase?
A. Phosphorus (P).
B. Sulfur (S).
C. Nitrogen (N).
D. Silicon (Si).
Malen Bara
CHEMISTRY

Inorganic Chemistry
Which of the following transition metals exhibits the highest number of oxidation states?
A. Iron (Fe).
B. Manganese (Mn).
C. Chromium (Cr).
D. Copper (Cu).
Malen Bara
CHEMISTRY

Inorganic Chemistry
Which of the following actinides is commonly used as a fuel in nuclear reactors?
A. Thorium (Th).
B. Uranium (U).
C. Neptunium (Np).
D. Curium (Cm).
Malen Bara
CHEMISTRY

Inorganic Chemistry
Which of the following compounds acts as both a Lewis acid and a Lewis base?
A. H₂O.
B. NH₃.
C. BF₃.
D. AlCl₃.
Malen Bara
CHEMISTRY

Inorganic Chemistry
Which of the following is a typical example of an innersphere electron transfer reaction?
A. Oxidation of Fe²⁺ by Ce⁴⁺.
B. Reduction of MnO₄⁻ by Fe²⁺.
C. Reduction of Cr₂O₇²⁻ by Zn.
D. Oxidation of Cl⁻ by MnO₄⁻.
Malen Bara
CHEMISTRY

Inorganic Chemistry
Which of the following methods is commonly used to synthesize graphene?
A. Solgel process.
B. Chemical vapor deposition.
C. Hydrothermal synthesis.
D. Coprecipitation.
lorrin mike
PHYSICS

Biophysics
What is the primary reason for the asymmetry of the protein structure?
A. Hydrogen bonding.
B. Hydrophobic interactions.
C. Electrostatic interactions.
D. van der Waals forces.
lorrin mike
PHYSICS

Biophysics
Which technique would you use to study the dynamics of a proteinligand interaction?
A. Xray crystallography.
B. NMR spectroscopy.
C. Molecular dynamics simulations.
D. Fluorescence spectroscopy.
lorrin mike
PHYSICS

Biophysics
What is the name of the process by which cells generate force to move or change shape?
A. Mechanotransduction.
B. Chemotaxis.
C. Osmosis.
D. Cytoskeleton dynamics.
lorrin mike
PHYSICS

Biophysics
Which biophysical technique measures the rotation of a molecule around its axis?
A. Circular dichroism.
B. Fluorescence anisotropy.
C. Nuclear magnetic resonance.
D. Infrared spectroscopy.
lorrin mike
PHYSICS

Biophysics
What is the term for the minimum energy required for a protein to fold into its native structure?
A. Activation energy.
B. Binding energy.
C. Folding energy.
D. Conformational energy.
lorrin mike
PHYSICS

Biophysics
Which type of spectroscopy measures the vibrational modes of molecules?
A. Infrared spectroscopy.
B. Nuclear magnetic resonance spectroscopy.
C. Ultravioletvisible spectroscopy.
D. Fluorescence spectroscopy.
lorrin mike
PHYSICS

Biophysics
What is the name of the process by which cells sense and respond to mechanical forces?
A. Mechanotransduction.
B. Chemotaxis.
C. Osmosis.
D. Pinocytosis.
lorrin mike
PHYSICS

Biophysics
Which biophysical technique measures the distance between two points in a biomolecule?
A. FRET (Fluorescence Resonance Energy Transfer).
B. EPR (Electron Paramagnetic Resonance).
C. NMR (Nuclear Magnetic Resonance).
D. AFM (Atomic Force Microscopy).
lorrin mike
PHYSICS

Biophysics
What is the term for the study of the physical principles underlying biological systems?
A. Biophysics.
B. Biochemistry.
C. Molecular biology.
D. Systems biology.
lorrin mike
PHYSICS

Biophysics
Which type of microscopy uses a focused laser beam to image biological samples?
A. Confocal microscopy.
B. Fluorescence microscopy.
C. Electron microscopy.
D. Atomic force microscopy.
lorrin mike
PHYSICS

Atomic Physics
Which quantum number specifies the shape of an atomic orbital?
A. Principal quantum number (n).
B. Orbital quantum number (l).
C. Magnetic quantum number (m_l).
D. Spin quantum number (m_s).
lorrin mike
PHYSICS

Atomic Physics
Which phenomenon occurs when an electron moves from a higher to a lower energy level within an atom, emitting a photon?
A. Ionization.
B. Fluorescence.
C. Absorption.
D. Emission.
lorrin mike
PHYSICS

Atomic Physics
Which element has the electron configuration 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 5s² 5p⁶?
A. Xenon (Xe).
B. Argon (Ar).
C. Krypton (Kr).
D. Radon (Rn).
lorrin mike
PHYSICS

Atomic Physics
Which of the following transitions in the hydrogen atom results in the emission of the highest energy photon?
A. n = 1 to n = 2.
B. n = 2 to n = 3.
C. n = 3 to n = 4.
D. n = 4 to n = 5.
lorrin mike
PHYSICS

Atomic Physics
What is the term for the minimum amount of energy required to remove an electron from the outermost shell of an atom in its ground state?
A. Electron affinity.
B. Ionization energy.
C. Binding energy.
D. Excitation energy.
lorrin mike
PHYSICS

Nuclear Physics
Which of the following particles is emitted during betaminus decay?
A. Proton.
B. Neutron.
C. Electron.
D. Alpha particle.
lorrin mike
PHYSICS

Nuclear Physics
Which nuclear reaction is responsible for the energy production in the Sun and other stars?
A. Nuclear fission.
B. Nuclear fusion.
C. Alpha decay.
D. Beta decay.
lorrin mike
PHYSICS

Nuclear Physics
What is the fundamental force responsible for binding protons and neutrons together in the nucleus?
A. Electromagnetic force.
B. Gravitational force.
C. Weak nuclear force.
D. Strong nuclear force.
lorrin mike
PHYSICS

Nuclear Physics
Which of the following particles has the same charge as an electron but approximately 1836 times greater mass?
A. Proton.
B. Neutrino.
C. Alpha particle.
D. Positron.
lorrin mike
PHYSICS

Nuclear Physics
What is the approximate binding energy per nucleon in a typical stable nucleus?
A. 1 MeV.
B. 5 MeV.
C. 8 MeV.
D. 10 MeV.
Togus Bash
STATISTICS

Probability Distributions
What is the primary purpose of probability distributions?
A. To describe the likelihood of events.
B. To make predictions about populations.
C. To analyze data from samples.
D. To summarize data.
Togus Bash
STATISTICS

Probability Distributions
What is the primary purpose of probability distributions?
A. To describe the likelihood of events.
B. To make predictions about populations.
C. To analyze data from samples.
D. To summarize data.
Togus Bash
STATISTICS

Probability Distributions
Which of the following is a discrete probability distribution?
A. Normal distribution.
B. Exponential distribution.
C. Poisson distribution.
D. Uniform distribution.
Togus Bash
STATISTICS

Probability Distributions
What is the main characteristic of a binomial distribution?
A. Continuous.
B. Discrete.
C. Symmetric.
D. Skewed.
Togus Bash
STATISTICS

Probability Distributions
In a normal distribution, what is the relationship between the mean and median?
A. Mean is always greater than median.
B. Mean is always less than median.
C. Mean and median are always equal.
D. Mean and median are not necessarily equal.
Togus Bash
STATISTICS

Probability Distributions
What is the purpose of the standard normal distribution?
A. To standardize data.
B. To make predictions about populations.
C. To analyze data from samples.
D. To summarize data.
Togus Bash
STATISTICS

Probability Distributions
Which of the following is a property of the Poisson distribution?
A. Mean is always greater than variance.
B. Variance is always greater than mean.
C. Mean and variance are always equal.
D. Mean and variance are not necessarily equal.
Togus Bash
STATISTICS

Probability Distributions
What is the relationship between the mean and standard deviation in a normal distribution?
A. Mean is always greater than standard deviation.
B. Mean is always less than standard deviation.
C. Mean and standard deviation are always equal.
D. Mean and standard deviation are not necessarily equal.
Togus Bash
STATISTICS

Probability Distributions
In a geometric distribution, what does the parameter p represent?
A. Probability of success in a single trial.
B. Probability of success in multiple trials.
C. Number of trials.
D. Number of failures.
Togus Bash
STATISTICS

Probability Distributions
What is the purpose of the Central Limit Theorem?
A. To describe the shape of a distribution.
B. To make inferences about population parameters.
C. To determine the sampling distribution of the mean.
D. To calculate probabilities.
Togus Bash
STATISTICS

Probability Distributions
Which of the following is a continuous probability distribution?
A. Binomial distribution.
B. Poisson distribution.
C. Exponential distribution.
D. Hypergeometric distribution.
Togus Bash
STATISTICS

Probability Distributions
In a normal distribution, what does the 689599
A. 68% of data lies within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.
B. 95% of data lies within 1 standard deviation, 99.7% within 2 standard deviations, and 99.9% within 3 standard deviations.
C. 68% of data lies within 1 standard deviation, 95% within 3 standard deviations, and 99.7% within 5 standard deviations.
D. 95% of data lies within 1 standard deviation, 99.7% within 2 standard deviations, and 99.9% within 4 standard deviations.
Togus Bash
STATISTICS

Probability Distributions
What is the main assumption of the Poisson distribution?
A. Events occur independently.
B. Events occur at a constant rate.
C. Events occur in continuous time.
D. Events occur in discrete time.
Togus Bash
STATISTICS

Probability Distributions
In a geometric distribution, what is the expected number of trials until the first success?
A. 1/p.
B. p.
C. 1p.
D. p/(1p).
Togus Bash
STATISTICS

Probability Distributions
What is the relationship between the normal and binomial distributions?
A. Binomial distribution approaches normal distribution as n increases and p is close to 0.5.
B. Binomial distribution is always normal.
C. Normal distribution is always binomial.
D. There is no relationship between the two distributions.
Togus Bash
STATISTICS

Probability Distributions
In an exponential distribution, what does the parameter ? represent?
A. Mean.
B. Variance.
C. Standard deviation.
D. Rate parameter.
Togus Bash
STATISTICS

Probability Distributions
What is the purpose of the Poisson approximation to the binomial distribution?
A. To simplify calculations.
B. To make the binomial distribution discrete.
C. To make the binomial distribution continuous.
D. To make the binomial distribution normal.
Togus Bash
STATISTICS

Probability Distributions
In a hypergeometric distribution, what is the main assumption?
A. Sampling is done with replacement.
B. Sampling is done without replacement.
C. Population size is infinite.
D. Events occur independently.
Togus Bash
STATISTICS

Probability Distributions
What is the relationship between the mean and variance in an exponential distribution?
A. Mean is always greater than variance.
B. Variance is always greater than mean.
C. Mean and variance are always equal.
D. Mean and variance are not necessarily equal.
Togus Bash
STATISTICS

Probability Distributions
In a normal distribution, what does the 95% confidence interval represent?
A. 95% of the data lies within the interval.
B. 95% of the population lies within the interval.
C. 95% of the time the sample mean will fall within the interval.
D. 95% of the time the population mean will fall within the interval.
Togus Bash
STATISTICS

Probability Distributions
What is the purpose of the Poisson process?
A. To model the number of events in a fixed interval of time or space.
B. To model the time between events.
C. To model the number of events in a continuous time interval.
D. To model the number of events in a discrete time interval.
Togus Bash
STATISTICS

Probability Distributions
In a binomial distribution, what is the probability mass function?
A. P(X=x) = n!/(x!(nx)!) * p^x * (1p)^(nx).
B. P(X=x) = ?^x * e^(?) / x!.
C. P(X=x) = (Nn)!/(x!(nx)!) * p^x * (1p)^(nx).
D. P(X=x) = (N!/(x!(Nx)!)) * p^x * (1p)^(Nx).
Togus Bash
STATISTICS

Probability Distributions
What is the relationship between the normal and lognormal distributions?
A. Lognormal distribution is the logarithm of a normal distribution.
B. Normal distribution is the logarithm of a lognormal distribution.
C. There is no relationship between the two distributions.
D. Lognormal distribution is always normal.
Togus Bash
STATISTICS

Probability Distributions
In a geometric distribution, what is the probability mass function?
A. P(X=x) = p * (1p)^(x1).
B. P(X=x) = (1p)^(x1) * p.
C. P(X=x) = p^x * (1p)^(nx).
D. P(X=x) = n!/(x!(nx)!) * p^x * (1p)^(nx).
Togus Bash
STATISTICS

Probability Distributions
What is the purpose of the Poisson approximation to the binomial distribution when n is large and p is small?
A. To simplify calculations.
B. To make the binomial distribution discrete.
C. To make the binomial distribution continuous.
D. To make the binomial distribution normal.
Togus Bash
STATISTICS

Probability Distributions
In a hypergeometric distribution, what is the probability mass function?
A. P(X=x) = (C(n,x) * C(Nn,nx)) / C(N,n).
B. P(X=x) = (n!/(x!(nx)!)) * p^x * (1p)^(nx).
C. P(X=x) = ?^x * e^(?) / x!.
D. P(X=x) = p * (1p)^(x1).
Togus Bash
STATISTICS

Probability Distributions
What is the relationship between the mean and variance in a Poisson distribution?
A. Mean is always greater than variance.
B. Variance is always greater than mean.
C. Mean and variance are always equal.
D. Mean and variance are always 1.
Togus Bash
STATISTICS

Probability Distributions
In an exponential distribution, what is the probability density function?
A. f(x) = ? * e^(?x).
B. f(x) = (?^x * e^(?)) / x!.
C. f(x) = (1/sv(2p)) * e^((x?)^2 / (2s^2)).
D. f(x) = p * (1p)^(x1).
Togus Bash
STATISTICS

Probability Distributions
What is the purpose of the normal approximation to the binomial distribution?
A. To simplify calculations.
B. To make the binomial distribution discrete.
C. To make the binomial distribution continuous.
D. To make the binomial distribution skewed.
Togus Bash
STATISTICS

Probability Distributions
In a geometric distribution, what is the expected number of failures before the first success?
A. 1/p.
B. p.
C. 1p.
D. p/(1p).
Togus Bash
STATISTICS

Probability Distributions
What is the relationship between the normal and uniform distributions?
A. Uniform distribution approaches normal distribution as the range increases.
B. Normal distribution is always uniform.
C. Uniform distribution is always normal.
D. There is no relationship between the two distributions.
Togus Bash
STATISTICS

Probability Distributions
In a Poisson distribution, what is the probability mass function?
A. P(X=x) = ?^x * e^(?) / x!.
B. P(X=x) = (n!/(x!(nx)!)) * p^x * (1p)^(nx).
C. P(X=x) = (1/sv(2p)) * e^((x?)^2 / (2s^2)).
D. P(X=x) = p * (1p)^(x1).
Togus Bash
STATISTICS

Probability Distributions
What is the purpose of the lognormal distribution?
A. To model variables that are the product of many independent random variables.
B. To model variables that are the sum of many independent random variables.
C. To model variables that are always positive.
D. To model variables that are always negative.
Togus Bash
STATISTICS

Probability Distributions
In a hypergeometric distribution, what is the expected number of successes?
A. n * (Nn)/N.
B. n * p.
C. n * (1p).
D. n * (Nn).
Togus Bash
STATISTICS

Probability Distributions
What is the relationship between the normal and exponential distributions?
A. Exponential distribution is the reciprocal of a normal distribution.
B. Normal distribution is the reciprocal of an exponential distribution.
C. There is no relationship between the two distributions.
D. Exponential distribution approaches normal distribution as the rate parameter increases.
Togus Bash
STATISTICS

Probability Distributions
In a binomial distribution, what is the expected number of successes?
A. n * p.
B. n * (1p).
C. n * (n1) * p^2.
D. n * (n1) * p * (1p).
Togus Bash
STATISTICS

Probability Distributions
What is the purpose of the Central Limit Theorem in the context of probability distributions?
A. To show that the sampling distribution of the mean approaches a normal distribution as the sample size increases.
B. To prove that all probability distributions are normal.
C. To simplify calculations involving probability distributions.
D. To make inferences about population parameters.
Togus Bash
STATISTICS

Probability Distributions
In a normal distribution, what is the probability density function?
A. f(x) = (1/sv(2p)) * e^((x?)^2 / (2s^2)).
B. f(x) = ? * e^(?x).
C. f(x) = (?^x * e^(?)) / x!.
D. f(x) = p * (1p)^(x1).
Togus Bash
STATISTICS

Probability Distributions
What is the relationship between the Poisson and exponential distributions?
A. Poisson distribution models the number of events in a fixed interval, while exponential distribution models the time between events.
B. Poisson distribution is always exponential.
C. Exponential distribution is always Poisson.
D. There is no relationship between the two distributions.
Togus Bash
STATISTICS

Probability Distributions
In a geometric distribution, what is the variance?
A. p/(1p).
B. 1/p.
C. (1p)/p^2.
D. p^2/(1p)^2.
Togus Bash
STATISTICS

Probability Distributions
What is the purpose of the Poisson approximation to the binomial distribution when n is large and p is small?
A. To simplify calculations.
B. To make the binomial distribution discrete.
C. To make the binomial distribution continuous.
D. To make the binomial distribution normal.
Togus Bash
STATISTICS

Probability Distributions
In a hypergeometric distribution, what is the variance?
A. n * (Nn) * (Nn1) / (N^2 * (N1)).
B. n * (Nn) / N.
C. n * p * (1p).
D. n * (1p).
Togus Bash
STATISTICS

Probability Distributions
What is the relationship between the normal and lognormal distributions?
A. Lognormal distribution is the logarithm of a normal distribution.
B. Normal distribution is the logarithm of a lognormal distribution.
C. There is no relationship between the two distributions.
D. Lognormal distribution is always normal.
Togus Bash
STATISTICS

Probability Distributions
In a Poisson distribution, what is the variance?
A. ?.
B. 1/?.
C. ?^2.
D. v?.
Togus Bash
STATISTICS

Probability Distributions
What is the purpose of the normal approximation to the binomial distribution when n is large and p is close to 0
A. To simplify calculations.
B. To make the binomial distribution discrete.
C. To make the binomial distribution continuous.
D. To make the binomial distribution skewed.
Togus Bash
STATISTICS

Probability Distributions
In an exponential distribution, what is the cumulative distribution function?
A. F(x) = 1  e^(?x).
B. F(x) = (?^x * e^(?)) / x!.
C. F(x) = (1/sv(2p)) * e^((x?)^2 / (2s^2)).
D. F(x) = p * (1p)^(x1.
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Fani Warraich
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lorrin mike
Togus Bash
? means here λ.