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3
The aromatic region of the 13C{1H} spectrum of N-methylaniline contains six lines at low temperature. How many lines might be expected at high temperature??
[ "2", "4", "6", "8" ]
1
What is the NMR frequency of 1H in the Earth's magnetic field (50 micro Tesla)?
[ "1.065 kHz", "2.129 kHz", "3.194 kHz", "4.258 kHz" ]
1
How many distinct chemical shifts would you expect to find in the 13C spectrum of 2-methylbutane?
[ "1", "2", "3", "4" ]
3
In order to obtain a signal in MRI experiment, what is the first step?
[ "Apply an RF pulse along \\(\\vec B_0\\)", "Change the amplitude of \\(\\vec B_0\\)", "Apply an RF pulse in a different direction from \\(\\vec B_0\\)", "Apply a magnetic field gradient" ]
2
Which of the following decreases the noise of the CT image?
[ "Decrease in dose", "Decrease in slice thickness", "Increase in matrix size", "Decrease in matrix size" ]
3
The 1H spectrum of CH2D2 contains five lines. What are their relative intensities?
[ "1:2:2:2:1", "1:1:1:1:1", "1:2:3:2:1", "1:1:2:1:1" ]
2
A characteristic feature of a projection radiograph is:
[ "Poor spatial resolution", "Lengthy data acquisition", "Tissue superimposition" ]
2
What is \(K_\alpha\) transition?
[ "The ionization of a K shell electron.", "It leads to the emission of Bremsstrahlung.", "It leads to the emission of characteristic radiation." ]
2
Predict the total number of lines in the 1H spectrum of 1,2-dichloro-3,4-dibromobenzene
[ "1", "2", "3", "4" ]
3
When X-rays interact with materials, they are able to:
[ "Cause substances to fluoresce.", "Remove an electron from an atom.", "Cause chemical changes that may lead to cells disfunctions." ]
0
Let's consider two systems of particles (with different gyromagnetic ratio) of spin ½ in a magnetic field \(\vec B_0\). The total population as well as temperature in each system are the same. According to Boltzmann distribution :
[ "The system with highest \\( \\gamma \\) has more down spins than the system with lowest \\( \\gamma \\).", "The system with highest \\( \\gamma \\) has less down spins than the system with lowest \\( \\gamma \\).", "The distribution is exactly the same : it does not depend on \\(\\gamma\\)." ]
1
NMR stands for
[ "Nuclear Moment of Resonance", "Non Magnetic Radiation", "Nuclear Magnetic Radiation", "Nuclear Magnetic Resonance" ]
3
>>In spin echo sequences, what do TR and TE refer to?
[ "TR: the spacing between successive 90-degree pulses; TE: time between the 90-degree pulse and the spin echo", "TR: the spacing between successive 90-degree pulses; TE: the spacing between the 90-degree pulse and the 180-degree pulse", "TR: time before the 90-degree pulse and the spin echo; TE: the spacing betw...
0
What can improve SNR in MRI if it is increased?
[ "Bandwidth", "Gradient strength", "Acquisition time" ]
2
In FDG PET, how is called the factor that takes into account that what one is measuring with deoxyglucose is not the real glucose molecule but an analog of glucose?
[ "The Lumped constant", "The Fick constant" ]
0
What is the duration of a 1H 90° pulse when B1 = 1.00 mT?
[ "4.12 microseconds", "5.87 microseconds", "9.82 microseconds", "12.45 microseconds" ]
1
In diagnostic X-ray systems, filters are used to "harden" the beam. This process is mainly due to:
[ "Coherent scattering.", "Photoelectric effect.", "Compton effect.", "Pair production." ]
1
What is the form of the majority of energy produced by electrons in X-rays tubes?
[ "Light", "Sound", "X-ray energy", "Heat" ]
3
Let's consider two media: the speed of sound in the two media is different and impedances of these two media are identical. A sound pulse reaches the boundary between these two media with normal incidence. Does the reflection occur?
[ "Yes", "No" ]
1
What is true concerning scatter radiation?
[ "They reduce contrast resolution", "They contribute to the image formation." ]
0
Where does the annihilation of positron and electron take place?
[ "In the radionuclide emitting the positron", "At a short distance from the radionuclide" ]
1
How does the particular dendritic conductance of CA1 pyramidal neurons influence the integration of the signals from two synapses, one close to the soma and one close to the distal dendrite, activated with a time delay?
[ "Both signals are integrated to generate an AP in the soma if the delay is short (up to 20 ms) and the distal synapse is activated first or very shortly after the proximal one", "Both signals are integrated to generate an AP in the soma even when the delay is long (up to 50 ms)", "Each of the two signals genera...
0
A neuron can be considered as a dipole. Why does the amplitude of the extracellular potential fall proportionally to the square of the distance from the dipole it originates in?
[ "Because the current is divided by the square of the distance to obtain the extracellular potential in the formula", "Because as one moves further away from the dipole, current and return current cancel each other out more and more in addition to the decrease in amplitude that is proportional to the distance", ...
1
Which method can be used to link a broad range of different time and spatial scales when studying the brain?
[ "Patch clamp", "PET imaging", "Modeling and simulation", "Long-term clinical studies" ]
2
How are different regions of the hippocampus connected to each other?
[ "The connections are largely reciprocal; if region A projects to region B, region B also projects to region A", "The connections are mainly unidirectional along a stream", "The connections allow signals to spread along the longitudinal axis of the hippocampus", "The connections keep the signals mainly in one ...
1
What are fixed point attractors in nonlinear recurrent networks?
[ "Specific neurons that are always activated", "Stable patterns of activity towards which other patterns converge", "Memory traces, if the can be learned by the network", "Connections between neurons that get consolidated upon recall" ]
1
What are the two main ions contributing to the generation of an action potential?
[ "Na+ and Cl-", "Ca2+ and Cl-", "H+ and K+", "Na+ and K+" ]
3
Which important point must be considered when populating the region to model?
[ "The types of cells present in the region", "The shape of the volume to populate", "The density of each cell type", "The location and orientation of the cells in the volume" ]
0
What determines the firing pattern of a neuron in response to step current injections?
[ "The length of its axon", "Its expression of different voltage-gated ion channels", "Which neurotransmitter it expresses", "The post-synaptic domain of the cells that it targets" ]
1
What does simulating a neuron help to understand?
[ "Dendritic integration", "The neural code", "The role of the biophysical make-up of a neuron", "Potentially all of the above, depending on the type of model used" ]
3
Which statement about CA1 pyramidal neurons are true?
[ "The KA density increases with the distance to the soma, the Ih density stays constant", "The density of both K and non-specific ion channels increases when the distance to the soma increases", "They receive two main independent inputs, one from the entorhinal cortex and one from the olfactory bulb that arrive ...
1
Which property of the hippocampus makes it a good model to study the nervous system?
[ "The connections on the hippocampus are almost unidirectional", "The synapses are highly plastic", "Hippocampal neurons can be grown in culture", "All of the above" ]
3
How are somatic and dendritic conductances related to the firing pattern of a cell?
[ "Each cell type has a fixed firing pattern that results from all individual cells of the same type having the same somatic and dendritic conductances", "Each combination of conductances generate a different firing behavior", "Specific conductances must be at certain levels in order to generating a defined firin...
2
How does the calculation of extracellular potentials help with experimental design?
[ "Mismatches between simulations and experimental data highlight mistakes in experimental data and show how experiments need to be modified in order to match the model", "It doesn’t help experimental design, but generates data so that experiments are not necessary anymore in order to answer biological questions", ...
2
What do the simple networks explaining gamma oscillations and ripples not have in common?
[ "The same connectivity pattern", "A high number of basket cells", "Direct auto-inhibitory feedback loops acting on single basket cells", "All of the above" ]
3
Which statement concerning the firing pattern of neurons is true?
[ "There is a correlation between the firing pattern and the calcium binding protein content.", "There is an absolute correlation between the firing pattern and the calcium binding protein content of all interneurons.", "All fast-spiking cells express the potassium channel Kv3.1", "Basket cells are the only fas...
0
What is the effect of the particular dendritic conductance of CA1 pyramidal neurons on back-propagating APs?
[ "AP amplitude along the dendrites increases as the distance to the soma increases", "AP amplitude along the dendrites decreases as the distance to the soma increases", "AP amplitude stays constant along the dendrites over the distance to the soma", "AP amplitude along the axon decreases as the distance to the...
1
How can modeling help with sparse data?
[ "By identifying principles allowing to predict missing data", "By guiding experimental design in highlighting missing data", "By finding connections between data types and data points allowing interpolation of missing data", "All of the above" ]
3
When do the synapses in CA3 need to be plastic?
[ "For pattern separation", "For memory retrieval", "For learning", "All of the above" ]
2
Which statement about hippocampal synaptic plasticity, network oscillations and neuromodulation is true?
[ "Network oscillations in the hippocampus endow it with cognitive functions like learning and memory", "Neuromodulation in the hippocampus gate synaptic plasticity and enhance network oscillations", "The oscillations observed in the hippocampus are similar to those observed in other parts of the cortex", "All ...
3
Which statements about cable theory are true?
[ "The conductance for each ion stays the same all along the axon and dendrites", "It quantifies the propagation of a signal along the axon and dendrites", "The change in voltage over the distance is related to the change in voltage over time", "The neuron is discretized to form several coupled compartments cor...
1
Why is a massive increase in model complexity a challenge?
[ "Because computational capacity has not increased enough during the last century", "Because existing scientific codes like NEURON are not adapted to use massively parallel systems", "Because neuron networks cannot be simulated using parallel systems", "It is not a challenge; very large models can be simulated...
1
Which of the following statements about theta activity are true?
[ "Theta activity can be measured using EEG", "Theta activity are observed in the hippocampus during deep sleep", "Theta activity is the only oscillatory activity observed in the hippocampus", "Theta activity could be correlated to behavior" ]
0
Which statement about genetic metaheuristic optimization algorithms is not true?
[ "They generate sets of parameter values that are used to generate and evaluate the resulting neuronal behaviour", "The algorithms are based on biological evolution; they test the fitness of arbitrary individuals and allow the fittest to create mutated offspring", "The algorithms find the optimal parameter value...
2
Which statement concerning electrical types is true?
[ "Each morphological type can have only one electrical type", "Each electrical type corresponds to only one morphological type", "A specific morphological type can have different electrical types, and vice-versa", "None of the above" ]
2
Which statement about hippocampal synaptic plasticity, network oscillations and neuromodulation is not true?
[ "Network oscillations in the hippocampus endow it with cognitive functions like learning and memory", "Only one form of synaptic potentiation and depression can be studied in the hippocampus", "Neuromodulation in the hippocampus gate synaptic plasticity and enhance network oscillations", "The oscillations obs...
1
What is the purpose of the Productivity Libraries?
[ "Create a bibliography of all the references used for building the model", "Allow simple use of specialized functionalities for complex workflows", "Optimize the execution of the program for the platform used", "Visualize the results of the simulations" ]
1
Why is the current used to calculate the extracellular potential?
[ "It is not, membrane potential is used to calculate the extracellular potential", "Because the current generates a uniform global increase in the whole extracellular fluid, like a strong water current in a lake raise the whole surface of the water", "Because the extracellular fluid cannot conduct electrical cur...
3
How does damage to the hippocampus influence the ability to perceive time?
[ "It does not influence the perception of time", "It changes the perception of time in humans, but not animals", "It is not known, as we have no way to study the encoding of time in the nervous system", "It impairs the ability to recall the temporal order of events" ]
3
How does pruning happen when reconstructing the connectome?
[ "Too strong connections between cells are removed", "Synapses are removed randomly until the model matches experimental data", "Too weak connections between cells are removed", "All of the above" ]
3
What is cable theory about?
[ "It states that the conductance for each ion stays the same all along the axon and dendrites", "It quantifies the propagation of a signal along the axon and dendrites", "It states that the change in voltage over the distance is related to the change in voltage over time", "It highlights the differences betwee...
1
What are reasons to use a model?
[ "Replace experiments in a more time-efficient manner", "Integrate data, space and time scales", "Study a system in a data-independent way", "Simulate complex interactions and predict a system’s behavior" ]
1
According to the theory of complementary learning systems, which statements are true?
[ "The hippocampus is responsible for the learning process in memory, and the neocortex for memory recall", "The neocortex is specialized in slow statistical learning of general information and the hippocampus for rapid learning of arbitrary stimuli combinations", "The neocortex is responsible for the learning pr...
1
What are the two possible types of models explaining the formation of spatial representations in the hippocampus?
[ "Feedforward models explain the properties of place cells relying on the activity of the cells to project to", "Feedback or recurrent models rely on negative feedback of place cells to themselves to form a representation of the environment", "Feedforward models combine the inputs of several other cells to expla...
2
Which of the following statements apply to data-driven models?
[ "They are built based on a specific hypothesis, to answer a specific biological question", "They might exclude important elements due to their minimalistic nature", "They can be used to test multiple hypotheses", "They can not identify new relationships between model variables" ]
2
What are the synaptic integration properties of a CA1 pyramidal neuron?
[ "It receives two main inputs at the same location on its dendrites", "It receives two main inputs, which are synchronized before following different pathways", "The inputs reach the pyramidal neuron with a delay between them", "Both inputs reach the dendrites of the pyramidal neuron at the same time" ]
1
What determines the firing pattern of a neuron?
[ "The length of its axon", "Its neurotransmitter expression", "Its expression of different sodium, potassium and calcium channels", "The morphology of its soma" ]
2
Which of the following statement concerning release probability isnottrue?
[ "The depletion and replenishment rates of the vesicle pools affect the release probability", "A high release probability always leads to a pronounced depression of the consequent EPSPs", "A low release probability leads to a pronounced facilitation of the consequent EPSPs", "When several release sites exist b...
1
Which statement about network oscillations is false?
[ "They are associated with LTP in the hippocampus", "They are only present in the hippocampus, not in other cortical regions", "They are critical for cognitive functions like learning and memory", "Hippocampal slices are a good basic experimental model to study network oscillations" ]
1
How are different hippocampal cell types involved in modulating network oscillations?
[ "All cell types contribute to all types of oscillations to the same extent", "All cell types fire in a synchronous manner during ripple oscillations", "Some cell types contribute more that other to specific network oscillations", "Pyramidal cells are the only cell type which membrane potential does not go up ...
2
Which statement about genetic metaheuristic optimization algorithms is true?
[ "The algorithms find the optimal parameter values over the whole possible parameter space", "It generates sets of parameter values (genotypes) that are used to generate and evaluate the resulting neuronal phenotype", "It generates a large number of random sets of parameter values that are ranked according to go...
1
What are neuromodulators?
[ "Cell populations that initiate or block network oscillations", "Network oscillations that regulate synaptic plasticity", "Specific stimuli used to experimentally study network oscillations", "Chemical brain messengers like hormones or neuropeptides that modulate network activity" ]
3
How is space encoded in the hippocampus?
[ "Grid cells represent space in a coordinate system", "Head direction cells encode in which cardinal direction the animal is facing", "The activity of space cells correlates with the position and direction of the animal", "The activity of some hippocampal cells correlate with the color of the environment of th...
0
What do the simple network explaining gamma oscillations and ripples have in common?
[ "The same connectivity pattern", "A high number of basket cells", "Direct auto-inhibitory feedback loops acting on single basket cells", "Feedback loops between pyramidal cells and inhibitory basket cells" ]
3
In 1957, the amnesia of patient H.M. after surgery highlighted the importance of the hippocampus in memory encoding. Which type of memory is encoded in the hippocampus according to actual knowledge?
[ "Episodic memory", "Semantic memory", "Procedural memory", "All of the above" ]
0
Which integration method should be used to solve ODEs with a large time step and why?
[ "Crank-Nicolson, because there the error is proportional to dt2", "Crank-Nicolson, because there is no net error proportional to dt", "Backward Euler, because there the error is proportional to dt2", "Backward Euler, because there is no net error proportional to dt" ]
3
What are the main characteristics of the two possible types of models explaining the formation of cognitive maps by place cells in the hippocampus?
[ "Feedforward models explain the properties of place cells relying on the activity of the cells they project to", "Feedback or recurrent models explain the properties of place cells using external inputs and the internal dynamics of the hippocampal network", "Feedforward models combine the inputs of several othe...
1
How do neuromodulators work?
[ "They originate in a hippocampal region that they then regulate", "They organize changes in the excitability and synaptic properties of cell populations", "They originate in subcortical regions below the hippocampus and target specific cell population and synapses", "They change the connectivity patterns of t...
1
Which statements about the hippocampus are true?
[ "Its structure is well conserved among mammalian species", "It has the same number of layers than the rest of the neocortex", "There is one hippocampus in each temporal lobe", "Its spherical structure makes the use of polar coordinates easy" ]
0
What three types of neurotransmitter-containing vesicles can be found in a single neuron?
[ "Excitatory, inhibitory and mixed vesicles", "Fast-acting, long-acting and recycled vesicles", "Immediately releasable, readily releasable and reserve vesicles", "Lysosomes, peroxisomes and endosomes" ]
2
CA1 pyramidal cells have intrinsic dendritic nonlinearities. When modeled with detailed morphology and many ion channels, single cells were able to…
[ "Function as a recurrent network", "Function equivalently to a two-layer artificial neural network", "Learn by evolving towards fixed activity patterns", "Represent simple functions, as long as they were linear" ]
1
Which statements about the type of network implemented in the hippocampus are true?
[ "They often have fixed point attractors, stable patterns of activity towards which other patterns converge", "They have all-to-all and symmetrical connections", "The connections of the CA3 area form a nonlinear recurrent network that may implement auto-associative memory", "They do not receive external inputs...
0
Which statements about the action of neuromodulators are true?
[ "A specific cell can only be modulated by several different neuromodulators", "A specific neuromodulator always has the same effect on all its target cells", "Neuromodulators can influence a broad range of mechanisms on different time scales such as synaptic plasticity, network oscillations and neurogenesis", ...
0
What effect did a brief train of stimuli have on the efficacy of synaptic transmission of excitatory synapses in CA1?
[ "An increase in transmission efficacy that lasted hours", "A decrease in transmission efficacy that lasted hours", "A long-term loss of synaptic connections in the perforant path to granule cell synapses", "An increase in transmission efficacy that a few milliseconds" ]
0
What is the meaning of synaptic plasticity?
[ "The ability of synapses to change their morphology in response to changes in their activity", "The ability of synapses to change the type of neurotransmitter used by the postsynaptic cell in response to signals from the presynaptic cell", "The ability of synapses to adapt to physical pressure and stress in ord...
3
Why was the hippocampus important in the study of plasticity?
[ "Long-term potentiation was first described in the hippocampus", "The first theories about synaptic plasticity are based on studies of the hippocampus", "Durable long-term depression achieved through prolonged low frequency stimulation was observed in the hippocampus", "Long-term depression requires direct fe...
0
Which gold standard framework is used in this course for modeling and simulating neurons?
[ "The programming language R for statistical computing", "The computing system Wolfram Mathematica", "The numerical simulation environment NEURON", "All of the above" ]
2
How is the model validated during the reconstruction process?
[ "The model is compared to corresponding experimental data at each step of the reconstruction", "The validation takes place when the whole circuit has been reconstructed and can be simulated", "Since the modeling process is data-based, there is no need for further validation with other data", "If a reconstruct...
0
>>The contribution of a neuron to the extracellular potential depends on the sum of all the currents crossing its membrane. If this sum must always be zero according to the principle of conservation of charge, how can the extracellular potential be different than zero?
[ "Because of extracellular currents that are independent from neurons", "Because of the influence of intracellular currents on the extracellular potential", "Because the sum of all currents is weighted, some weights are larger for closer current sources than for sources further away", "All of the above" ]
2
Which coordinate system is used to indicate a point in the hippocampus?
[ "Straight axes perpendicular to each other", "Pole and polar axis", "Longitudinal, transverse and radial axes", "Homogeneous coordinates using a projective plane" ]
2
Why is understanding how the brain work especially difficult?
[ "Because several overlapping timescales must be considered", "Because we do not have adapted experimental tools to study electrophysiology", "Because the brain consists of many different elements with non-linear dynamics that interact in a complex way", "Because the brain does not use task-specific solutions"...
0
What is the spatial distribution of KAand Ihion channels in CA1 pyramidal neurons?
[ "Both ion channels show a constant density in their lateral dendrites", "The KA density increases with the distance to the soma, the Ih density stays constant", "The density of both ion channels decreases when the distance to the soma increases", "The density of both ion channels increases when the distance t...
3
Why are models getting larger and larger with time?
[ "Because the number of neurons in the models has increased", "Because the number of synapses in the models has increased", "Because the models are more detailed", "All of the above" ]
3
What cannot be done in the NEURON GUI?
[ "Import the 3D morphology of neurons", "Define the architecture of the neuron network", "Optimize the execution of the program for the platform used", "Visualize the results of the simulations" ]
2
What formula is the formula used for calculating the extracellular potential based on?
[ "Ohm’s law, V = IR", "Joule heating formula, P = I2R", "The formula for the conductance, C = q/V", "Coulomb’s law, |F| = ke|q1q2|/r2" ]
0
How are the contributions from several compartments and several neurons combined to obtain the extracellular potential at a specific location?
[ "All the contributions from each compartment and each neuron are multiplied", "All the contributions from each compartment and each neuron are added up", "The contributions form all compartments from one neuron are added up to obtain the neuron’s contribution, and the contributions of each neuron are multiplied...
1
Which statements concerning autoassociative networks are true?
[ "All neurons are connected to all other neurons in a symmetric manner", "they receive external inputs and feedback from the output of their neurons", "They can store a limited number of pattern and that number is smaller than the number of neurons in the network", "The number of patterns that can be stored de...
1
What are some properties of long-term potentiation and long-term depression?
[ "They always require protein synthesis", "They can be induced within a very short time period of one second or less", "The changes in synaptic weight typically last for hours", "No further change can take place while a previously induced change in synaptic weight lasts" ]
1
How can extracellular simulations be used for model validation?
[ "Since all parts of a detailed model come together to determine extracellular potentials, they help test the validity of how all pieces of the model are interacting", "Extracellular potentials depend on synaptic physiology and an thus be used to validate the modeling of synaptic activity", "Extracellular potent...
0
What are the levels of analysis for information processing systems?
[ "Molecular, cellular and whole organism", "Computational, algorithmic and implementational", "Top-down and bottom-up", "Milliseconds, seconds to minutes, days to months" ]
1
What roles does the hippocampus play in memory according to standard theory?
[ "Supporting late recall using patterns completed by the neocortex", "Supporting early recall by learning in one shot and completing patterns in the neocortex", "Directing consolidation by allowing the neocortex to integrate new memories into existing ones", "Consolidating memories in response to neocortex-ini...
1
According to Hebb’s postulate, where in the synapse can the metabolic change causing plasticity take place?
[ "In the presynaptic bouton", "In the postsynaptic spine", "In both the presynaptic bouton and the postsynaptic spine", "In the presynaptic neuron’s soma" ]
2
Which of the following statement concerning release probability is not true?
[ "The depletion and replenishment rates of the vesicle pools affect the release probability", "A high release probability always leads to a pronounced depression of the consequent EPSPs", "A low release probability leads to a pronounced facilitation of the consequent EPSPs", "When several release sites exist b...
1
What is CoreNEURON?
[ "An optimized version of the compute engine of NEURON that does not include the interactive parts of NEURON", "A function of NEURON that allows you to extract a core sub-network of your model", "A version of neuron for beginners that includes only the core functions", "A massively parallel supercomputer that ...
0
When a back-propagating AP elicited in the soma happens simultaneously with a dendritic AP, the resulting AP has a higher amplitude. Which process is this a basis for?
[ "Spatial localization", "Perception of time", "Associative learning", "Synapse pruning" ]
2
What are the two types of cells in the local CA1 circuitry?
[ "Inhibitory pyramidal cells and excitatory interneurons", "Excitatory motor neurons and inhibitory interneurons", "Excitatory pyramidal cells and inhibitory Purkinje cells", "Excitatory pyramidal cells and inhibitory interneurons" ]
3
(MAN 2021) Soit \(R\) la région du plan bornée, délimitée par les graphes des fonctions \[f(x)=19x^2-9x\,,\qquad g(x)=9x^2+x+20\,.\] Alors l'aire de \(R\) est égale à \begin{multicols}{2}
[ "\\(\\displaystyle \\int_{-2}^1(f(x)-g(x))\\,dx\\)", "\\(\\displaystyle \\int_{-1}^2(f(x)-g(x))\\,dx\\)", "\\(\\displaystyle \\int_{-1}^2(g(x)-f(x))\\,dx\\)", "\\(\\displaystyle \\int_{-2}^1(g(x)-f(x))\\,dx\\)\n\n\\end{multicols}" ]
2
(MAN 2021) Considérons la fonction \(f:[1,4[ \to \bR\) définie par \[f(x)=(2-x)^3\,.\] Parmi les affirmations suivantes, lesquelles sont correctes?
[ "\\(f\\) n'atteint ni son minimum ni son maximum", "\\(f\\) possède un extremum en \\(x_0=2\\)", "\\(f\\) atteint son maximum mais pas son minimum", "\\(f\\) atteint son minimum mais pas son maximum" ]
2
Soit \((a_n)\) une suite qui n'est pas majorée. Parmis les affirmations suivantes, lesquelles sont correctes?
[ "Il existe \\(M\\) tel que \\(a_n\\geq M\\) pour tout \\(n\\).", "Pour tout \\(M>0\\), il existe \\(n\\) tel que \\(a_n\\geq M\\).", "\\(a_n\\to\\infty\\) lorsque \\(n\\to\\infty\\)", "\\(a_n>M\\) pour tout \\(M\\)." ]
1
Donner l'ensemble \(E\subset \bR\) de toutes les valeurs du paramètre \(t\) pour lesquelles la série ci-dessous converge: \[ \sum_{n\geq 1}\Bigl(\frac{1+t}{1-t}\Bigr)^n \]
[ "\\(E=\\bR\\setminus \\{1\\}\\)", "\\(E=]-1,1[\\)", "\\(E=]-\\infty,0[\\)", "\\(E=]-\\infty,0[\\cup ]1,+\\infty[\\)" ]
2