Gaokao problems

57 problems for Gaokao practice, in Physics, Chemistry, Mathematics and Biology, each with a worked solution. Try each one on paper first, then check your answer.

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1.

A gas goes round a cycle of three steps.

High School (11–12) · Heat Engines, the Second Law and EntropyJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, IB, GaokaoStemPy Lab

Medium

2.

Breaking one mole of CH₄(g) into atoms takes 1665 kJ. New

High School (11–12) · Enthalpy and Hess's LawJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IB, GaokaoStemPy Lab

Hard

3.

How many 4-letter words, with or without meaning, can be made from the letters of EDUCATION, if… New

High School (11–12) · Permutations and CombinationsJEE Main, BITSAT, WBJEE, Board Exam, A-Level, IB, GaokaoStemPy Lab

Medium

4.

A gas goes clockwise round a triangle ABCA on a pressure-volume graph.

High School (11–12) · Laws of ThermodynamicsJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IB, GaokaoStemPy Lab

Hard

5.

Estimate Δr H for C₂H₄(g) + H₂(g) → C₂H₆(g) from the mean bond enthalpies: C=C 611, H-H 435, C-C… New

High School (11–12) · Enthalpy and Hess's LawJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IB, GaokaoStemPy Lab

Medium

6.

A committee of 5 is chosen from 6 men and 5 women. How many committees have at least 2 women? New

High School (11–12) · Permutations and CombinationsJEE Main, BITSAT, WBJEE, Board Exam, A-Level, IB, GaokaoStemPy Lab

Medium

7.

A polar satellite orbits 800 km above the Earth.

High School (11–12) · GravitationJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IB, GaokaoStemPy Lab

Medium

8.

Methane cannot be made cleanly from carbon and hydrogen, so its Δf Hᵒᵐⁱⁿᵘˢ is found with Hess's law. New

High School (11–12) · Enthalpy and Hess's LawJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IB, GaokaoStemPy Lab

Medium

9.

Four digit numbers are made from the digits 0, 1, 2, 3, 4, 5, with no digit repeated. New

High School (11–12) · Permutations and CombinationsJEE Main, BITSAT, WBJEE, Board Exam, A-Level, IB, GaokaoStemPy Lab

Medium

10.

Encke's comet goes round the Sun every 3.3 years.

High School (11–12) · GravitationJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IB, GaokaoStemPy Lab

Medium

11.

Arrange MgO, CaO, NaF and KBr in order of decreasing lattice enthalpy. Give a reason for each step. New

High School (11–12) · Lewis Structures and Ionic BondsJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IB, GaokaoStemPy Lab

Medium

12.

How many 4-digit even numbers can be made from the digits 0, 1, 2, 3, 4 and 5, if no digit is used… New

High School (11–12) · Permutations and CombinationsJEE Main, BITSAT, WBJEE, Board Exam, A-Level, IB, GaokaoStemPy Lab

Hard

13.

A 9.0 kg shell is fired at 50 m/s at 55° above level ground.

High School (11–12) · Rotational Motion, Momentum and CollisionsJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IB, GaokaoStemPy Lab

Medium

14.

Forming Mg²⁺ and O²⁻ seems costly. In kJ/mol: sublimation of magnesium +148; half the bond enthalpy… New

High School (11–12) · Lewis Structures and Ionic BondsJEE Main, NEET, BITSAT, WBJEE, Board Exam, A-Level, IB, GaokaoStemPy Lab

Hard

15.

How many 3-digit numbers have three different digits? How many of them are odd? New

High School (11–12) · Permutations and CombinationsJEE Main, BITSAT, WBJEE, Board Exam, A-Level, IB, GaokaoStemPy Lab

Medium

16.

A 55 kg boy stands at the front of a 165 kg canoe on still water.

High School (11–12) · Rotational Motion, Momentum and CollisionsJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, GaokaoStemPy Lab

Medium

17.

The first ionisation enthalpy of nitrogen is 1402 kJ mol⁻¹ and that of oxygen is 1314 kJ mol⁻¹… New

High School (11–12) · Periodic TrendsNEET, Board Exam, AP, A-Level, IB, GaokaoStemPy Lab

Medium

18.

Find |((3 - 4i)(8 + 6i))/((1 + i)²)| without multiplying out any brackets. New

High School (11–12) · Complex NumbersBoard Exam, A-Level, IB, GaokaoStemPy Lab

Medium

19.

An 8.0 g bullet is fired into a 1.6 kg block hanging on strings, and stays inside.

High School (11–12) · Momentum and Collisions, Work, Energy and PowerJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IB, GaokaoStemPy Lab

Hard

20.

The first four ionisation enthalpies of an element are 578, 1817, 2745 and 11577 kJ mol⁻¹. New

High School (11–12) · Periodic TrendsNEET, Board Exam, AP, A-Level, IB, GaokaoStemPy Lab

Medium

21.

For which real number k is (2 + ki)/(1 + 3i) a real number? What is its value then? New

High School (11–12) · Complex NumbersBoard Exam, A-Level, IB, GaokaoStemPy Lab

Hard

22.

A small car is let go from rest on a smooth track at a height h, and runs round a vertical loop of…

High School (11–12) · Work, Energy and PowerJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IB, GaokaoStemPy Lab

Hard

23.

A chemist burns 0.230 g of a liquid that holds only carbon, hydrogen and oxygen. New

High School (11–12) · Stoichiometry and Concentration, Molecules, Ions and FormulaeJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IB, GaokaoStemPy Lab

Hard

24.

cos x = -5/13, and x lies between π/2 and π. New

High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesBoard Exam, AP, A-Level, IB, GaokaoStemPy Lab

Medium

25.

A bucket of water, of mass 2.5 kg in all, is whirled on a rope in a vertical circle of radius 1.2 m.

High School (11–12) · Circular Motion, FrictionJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IB, GaokaoStemPy Lab

Hard