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  1. Prepare for an exam
  2. /CMI Entrance
Exam preparation

CMI Entrance preparation

The CMI entrance for the BS (Hons) programmes is one Mathematics test for everyone. Part A is quick objective questions and Part B is six problems where you must write your full reasoning. It rewards clear thinking more than memory of formulas, and it uses school topics.

951 questions · 581 problems

With a Standard plan

Paper pattern

The CMI Entrance exams follow this pattern.

The real exam: One common Mathematics aptitude test for all BS (Hons) programmes: Part A objective screening, 40 points, no negative marking; Part B six written problems, 80 points (2024 and 2025 papers).

CMI Entrance syllabus

12 units in Mathematics. Source: Chennai Mathematical Institute, 'Information about BSc Entrance Examination', https://www.cmi.ac.in//admissions/syllabus/ugmath-syllabus.pdf (opened 2026-11-09), linked from https://www.cmi.ac.in/admissions/syllabus.php. One common entrance examination serves all B.S. (Hons.) programmes and it is a Mathematics aptitude test; neither page lists a Physics or a Computer Science section for it, so only the mathematics subject is listed. Units follow the document's bullet list of what students are expected to know.

Mathematics · 12 units

NCERT mathematics up to Class 12

  • Relations and functions
  • Algebra
  • Calculus
  • Coordinate geometry
  • Vectors and matrices (up to 3 dimensions)
  • Counting
  • Probability

Topics up to Class 10

  • Euclidean geometry
  • Basic number theory

Standard real valued functions

  • Standard real valued functions: roots and graphs

Number theory

  • Unique factorization, GCD and modular arithmetic

Complex numbers

Question sets

No timer. Work at your own pace.

  • PhysicsJEE Advanced Physics: Electrostatic Potential and Capacitance12 questions
  • PhysicsJEE Advanced Physics: Moving Charges and Magnetism12 questions
  • PhysicsJEE Advanced Physics: Electric Charges and Fields

Practice questions and problems

Hardest first. Try each one on paper before you see the answer.

Physics

Questions

  • AdvancedA 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?
  • AdvancedIn 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?

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12 questions
  • MathematicsMaths Olympiad: Combinatorics, Geometry and Inequalities6 questions
  • MathematicsJEE Advanced Maths: Integrals and Their Applications12 questions
  • MathematicsJEE Advanced Maths: Derivatives and Their Applications12 questions

    • All CMI Entrance question sets →

    Advanced
    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?
  • AdvancedA 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?
  • AdvancedA 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?
    • More Physics questions for CMI Entrance →

    Problems with worked solutions

    • AdvancedA radio antenna stands on the edge of a cliff, at a height h = 120 m above a calm sea, and points…
    • AdvancedA large flat coil of 500 turns and radius R = 20 cm carries a steady current of 4.0 A…
    • AdvancedIn a vacuum chamber there is a uniform electric field of 2.0 × 10⁴ V/m along +y and a uniform…
    • AdvancedTwo equal capacitors, each of C = 100 µF, and two equal resistors, each of R = 10 kΩ, make a…
    • AdvancedA metal sphere of radius R = 10.0 cm stands on an insulating stand in a large empty room…
    More Physics problems for CMI Entrance →

    Mathematics

    Questions

    • AdvancedEach 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.
    • AdvancedPositive 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?
    • AdvancedThe figure shows a regular polygon with 12 vertices, all on one circle. Any three of the vertices form a triangle, which gives C(12, 3) = 220 triangles in all. How many of these triangles are acute-angled, that is, have all three angles less than 90°?
    • AdvancedFour married couples, eight people in all, sit at a round table with eight equal chairs. Two seatings count as the same when one is a rotation of the other, but a seating and its mirror image count as different. In how many seatings does no husband sit next to his own wife?
    • AdvancedThe figure shows the graph of a function f on [0, 12]. It is made of three straight pieces joining the points (0, 0), (3, 6), (9, 0) and (12, -3): a steep rise, a slow fall, and a dip below the axis. For 0 ≤ x ≤ 9 let F(x) = ∫xˣ⁺³ f(t) dt, the area under the graph over a window of width 3 that slides along the axis. The window catches the most area when its two ends are at the same height, but the peak of f need not sit in the middle of the window. What is the greatest value of F(x) for 0 ≤ x ≤ 9?
    More Mathematics questions for CMI Entrance →

    Problems with worked solutions

    • AdvancedA ranger in Cornwall is protecting a sand dune from walkers…
    • AdvancedIn a round-robin tournament every two teams play each other exactly once, and every match has a…
    • AdvancedA 7 × 7 board has its rows numbered 0 to 6 from the top and its columns numbered 0 to 6 from the…
    • AdvancedLet f(x) = x³ + x. Since f'(x) = 3x² + 1 > 0, the function f increases on the whole real line, and…
    • All 581 CMI Entrance problems →
    • All 951 CMI Entrance questions →
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    • Advanced
    A definite integral is a limit of sums, and this works in both directions…
    More Mathematics problems for CMI Entrance →