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5557 quizzes
A sample starts as a pure radioactive nuclide A, of half-life 6.0 h. Each nucleus of A decays into a nucleus of B, which is itself radioactive, with a half-life of 2.0 h, and decays into a stable nuclide. After how long is the activity of B in the sample greatest? New
High School (11–12) · Nuclei and Radioactivity
Olympiad, JEE Advanced
StemPy LabStemPy Lab
Advanced
Excess silver powder is shaken at 298 K with a solution of iron(III) perchlorate, [Fe³⁺] = 0.100 mol L⁻¹, in dilute perchloric acid. The acid stops the iron(III) ions from hydrolysing, and perchlorate does not react. The reaction is Ag(s) + Fe³⁺(aq) ⇌ Ag⁺(aq) + Fe²⁺(aq). At the start there are no Ag⁺ or Fe²⁺ ions. Take E°(Fe³⁺/Fe²⁺) = 0.77 V, E°(Ag⁺/Ag) = 0.80 V and 2.303RT/F = 0.059 V. Treat the solution as ideal, and take its volume as fixed. The mixture is left until it reaches equilibrium. What is [Ag⁺] at equilibrium? Give the answer in mmol L⁻¹, to two decimal places. New
High School (11–12) · Galvanic Cells, Electrode Potential and the Nernst Equation
JEE Advanced, Olympiad
StemPy LabStemPy Lab
Advanced
In each statement, a, b, c are the sides of a triangle, Δ is its area and R is its circumradius. A statement that says "every triangle" must hold for all triangles of that kind. Which of the following statements are true? One or more of them are. New
High School (11–12) · Triangles
Olympiad
StemPy LabStemPy Lab
Advanced
Which description of bark is the most complete? New
High School (11–12) · Anatomy of Flowering Plants
A-Level, IB
StemPy LabStemPy Lab
Hard
Five expressions use comprehensions, map and filter. Which of these expressions give the list [1, 4, 9]? Choose every correct option. New
High School (11–12) · Comprehensions, Iterators and Generators
PCAP (Python Institute)
StemPy LabStemPy Lab
Hard
Which sentence is the best limit for a report on 20 winter days in one hill town?
Middle Stage (6–8), High School (9–10), High School (11–12), Undergraduate, General · Averages: Mean, Median and Mode
StemPy LabStemPy Lab
Easy
In a double-slit experiment the slits are 0.40 mm apart and the screen is 1.00 m away. The slits are lit at the same time by light of wavelengths 600 nm and 450 nm. Which of the following statements are correct? New
High School (11–12) · Wave Optics
Olympiad, JEE Advanced
StemPy LabStemPy Lab
Advanced
Benzoic acid is a weak acid used as a food preservative. A 0.00800 mol L⁻¹ solution of it in water at 298 K has a conductivity of 2.63 × 10⁻⁴ S cm⁻¹, after the small conductivity of the water has been taken away. The limiting molar conductivities of three strong electrolytes at 298 K are, in S cm² mol⁻¹: HCl 425.9, NaCl 126.4 and sodium benzoate 82.4. The first two values are NCERT's. Use Kohlrausch's law of independent migration of ions, and take the degree of dissociation as α = Λm/Λm°. Use Ostwald's law in full, Ka = cα²/(1 - α), keeping the 1 - α. The dissociation constant of benzoic acid is Ka = x × 10⁻⁶ mol L⁻¹. What is x, to the nearest integer? New
High School (11–12) · Conductance, Electrolysis and Batteries
JEE Advanced, JEE Main
StemPy LabStemPy Lab
Hard
Each statement below is about points or whole numbers chosen in any way at all, and claims that a certain pair must always exist. One or more of the statements are true. Which are they? In (A) and (B) the points may lie inside the shape or on its boundary. New
High School (11–12) · Permutations and Combinations
Olympiad
StemPy LabStemPy Lab
Advanced
Under a lens, a student sees a ring with wide pale cells on its inner side and narrow dark cells on its outer side. Which part was made first in the year? New
High School (11–12) · Anatomy of Flowering Plants
A-Level, IB
StemPy LabStemPy Lab
Medium
A folder holds a file notes.txt with the text hi. It has no file new.txt. Each line below is run on its own, in a fresh copy of the folder. Which lines run without raising an exception? Choose every correct option. New
High School (11–12) · Files and Data Formats
PCAP (Python Institute)
StemPy LabStemPy Lab
Advanced
A student writes: \"The mean highest temperature in the hill town was 12 °C, so every day was about 12 °C.\" What is wrong?
Middle Stage (6–8), High School (9–10), High School (11–12), Undergraduate, General · Averages: Mean, Median and Mode
StemPy LabStemPy Lab
Medium
Two long, smooth, horizontal metal rails, 0.50 m apart, lie in a uniform vertical magnetic field of 0.80 T. At one end they are joined by an uncharged capacitor of 0.50 F. A metal rod of mass 0.20 kg lies across the rails, as in the figure, and is given a push so that it starts sliding away from the capacitor at 7.0 m/s. No other force acts along the rails. The rod and rails together have a resistance of 2.0 Ω. How much heat is produced in the circuit in all, by the time the current has stopped? New
High School (11–12) · Electromagnetic Induction
Olympiad, JEE Advanced
StemPy LabStemPy Lab
Advanced
A steel rod is given a hard chromium coat by electrolysis. The bath is chromic acid, in which chromium is in the +6 state, and chromium metal deposits on the rod, which is the cathode. Only 20.0 per cent of the current deposits chromium; the rest makes hydrogen. The coat must be 20.0 µm thick over an area of 60.0 cm². The density of chromium is 7.19 g cm⁻³ and its molar mass is 52.0 g mol⁻¹. A steady current of 10.0 A is used, and F = 96487 C mol⁻¹. For how long must the current flow, in min, to the nearest integer? New
High School (11–12) · Conductance, Electrolysis and Batteries
JEE Advanced, JEE Main
StemPy LabStemPy Lab
Hard
Positive real numbers a, b and c satisfy a + b + c = 12, and apart from this they may be chosen freely. What is the greatest possible value of the product ab²c³, in which b appears squared and c appears cubed? New
High School (11–12) · Sequences and Series
Olympiad, JEE Advanced
StemPy LabStemPy Lab
Advanced
A lightning strike burns out the whole centre of an old tree, but the tree keeps its leaves. Which statement explains this? New
High School (11–12) · Anatomy of Flowering Plants
A-Level, IB
StemPy LabStemPy Lab
Hard
A program writes a file in two steps, then reads it back. What does the program print? New
High School (11–12) · Files and Data Formats
PCAP (Python Institute)
StemPy LabStemPy Lab
Hard
In the hill town, the 3 snowy days had a mean highest temperature of 8.7 °C, and the other 17 days 12.5 °C. What may a report say?
Middle Stage (6–8), High School (9–10), High School (11–12), Undergraduate, General · Averages: Mean, Median and Mode
AP, IB
StemPy LabStemPy Lab
Medium
A uniform magnetic field of 0.20 T fills the region to the right of a straight boundary and points out of the page, as in the figure. A proton moving at 2.0 × 10⁶ m/s crosses the boundary into the field, at 30° to the normal, tilted towards the top of the page. Take the proton's mass as 1.67 × 10⁻²⁷ kg and its charge as 1.6 × 10⁻¹⁹ C. Which of the following statements are correct? New
High School (11–12) · Magnetic Effects of Current
Olympiad, JEE Advanced
StemPy LabStemPy Lab
Advanced
The figure shows a drop of rainwater, pH = 5.60, resting on a clean iron sheet in air at 298 K. Iron is oxidised at one spot under the drop, Fe → Fe²⁺ + 2e⁻. The electrons flow through the metal to the edge of the drop, where oxygen from the air is reduced: O₂ + 4H⁺ + 4e⁻ → 2H₂O. The partial pressure of oxygen is 0.21 bar, and near the iron [Fe²⁺] = 1.0 × 10⁻⁶ mol L⁻¹. Take the drop as a small cell in which the iron sheet is both electrodes. Use NCERT's values: E°(O₂/H₂O) = 1.23 V, E°(Fe²⁺/Fe) = -0.44 V, E°(Zn²⁺/Zn) = -0.76 V and E°(Sn²⁺/Sn) = -0.14 V, with 2.303RT/F = 0.059 V. Which of the following statements are correct? New
High School (11–12) · Galvanic Cells, Electrode Potential and the Nernst Equation
JEE Advanced
StemPy LabStemPy Lab
Advanced
In triangle ABC, AB = 8, AC = 12 and BC = 10. The bisector of the angle BAC meets BC at D, and it meets the circumcircle of the triangle again at M, as in the figure. What is the length AM? New
High School (11–12) · Circles
Olympiad
StemPy LabStemPy Lab
Advanced
A forester looks at the bark of a young tree and sees many tiny, raised patches. Through them air can reach the living cells beneath. What are these patches? New
High School (11–12) · Anatomy of Flowering Plants
A-Level, IB
StemPy LabStemPy Lab
Easy
A map is built on a filter, and the list changes before the results are read. What does the program print? New
High School (11–12) · Functions
PCAP (Python Institute)
StemPy LabStemPy Lab
Advanced
The chance of a snowy day is 0.15. If each day's weather did not depend on the day before, what would be the chance of two snowy days in a row?
Middle Stage (6–8), High School (9–10), High School (11–12), Undergraduate, General · Averages: Mean, Median and Mode
AP, IB
StemPy LabStemPy Lab
Hard
A metal sphere of radius 12 cm carries no net charge. Inside it there is a small spherical cavity, not at the centre, and a point charge q = +3.0 nC sits inside the cavity, away from the cavity's centre. A second point charge Q = +5.0 nC is held outside, 40 cm from the centre of the sphere. Take 1/4πε₀ = 9.0 × 10⁹ N m²/C². Which of the following statements are correct? New
High School (11–12) · Electrostatics
Olympiad, JEE Advanced
StemPy LabStemPy Lab
Advanced
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