BITSAT problems

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

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1.

A refrigerator keeps its inside at 4 °C in a kitchen at 32 °C.

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

Medium

2.

For N₂O₄(g) ⇌ 2NO₂(g), Δ H° = +57.2 kJ/mol and Δ S° = +175.8 J/(K mol). New

High School (11–12) · Entropy, Gibbs Energy and SpontaneityJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IBStemPy 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 Carnot engine works between 450 K and 306 K.

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

Medium

5.

For N₂(g) + 3H₂(g) → 2NH₃(g), Δ H° = -92.4 kJ/mol and Δ S° = -198.7 J/(K mol). New

High School (11–12) · Entropy, Gibbs Energy and SpontaneityJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IBStemPy 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 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

8.

Supercooled water freezes at 263 K. Take Δ H = -6.01 kJ/mol and Δ Ssystem = -22.0 J/(K mol). New

High School (11–12) · Entropy, Gibbs Energy and SpontaneityJEE Main, NEET, BITSAT, WBJEE, Board ExamStemPy Lab

Hard

9.

Three neighbours in a row of Pascal's triangle, ⁿC_(r - 1), ⁿCr and ⁿC_(r + 1), are in the ratio 1… New

High School (11–12) · Permutations and CombinationsJEE Main, BITSAT, WBJEE, Board ExamStemPy Lab

Hard

10.

A gas with γ = 1.40 at 5.5 × 10⁵ Pa fills 1.2 litres.

High School (11–12) · Thermodynamic Processes and Specific Heats of GasesJEE Main, NEET, BITSAT, WBJEE, Board ExamStemPy Lab

Hard

11.

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

12.

There are 15 points in a plane. Exactly 6 of them lie on one straight line, and no other three are… New

High School (11–12) · Permutations and CombinationsJEE Main, BITSAT, WBJEE, Board ExamStemPy Lab

Medium

13.

0.80 mol of a monatomic ideal gas goes from A to C in two steps.

High School (11–12) · Thermodynamic Processes and Specific Heats of GasesJEE Main, NEET, BITSAT, WBJEE, Board ExamStemPy Lab

Hard

14.

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

15.

All the arrangements of the letters of TIGER are listed in dictionary order. New

High School (11–12) · Permutations and CombinationsJEE Main, BITSAT, WBJEE, Board ExamStemPy Lab

Hard

16.

1.2 mol of an ideal gas at 310 K is squeezed slowly at a steady temperature from 24 to 6.0 litres.

High School (11–12) · Thermodynamic Processes and Specific Heats of GasesJEE Main, NEET, BITSAT, WBJEE, Board ExamStemPy Lab

Medium

17.

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

18.

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

19.

0.40 mol of a diatomic ideal gas is at 290 K and 1.5 × 10⁵ Pa.

High School (11–12) · Thermodynamic Processes and Specific Heats of GasesJEE Main, NEET, BITSAT, WBJEE, Board ExamStemPy Lab

Medium

20.

How much heat turns 36.0 g of ice at 273 K into steam at 373 K? New

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

Medium

21.

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

22.

A gas heated at a steady pressure takes in 1540 J.

High School (11–12) · Thermodynamic Processes and Specific Heats of Gases, Kinetic Theory of GasesJEE Main, NEET, BITSAT, WBJEE, Board ExamStemPy Lab

Medium

23.

Quicklime is made by heating limestone: CaCO₃(s) → CaO(s) + CO₂(g). New

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

Medium

24.

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

25.

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