CMI Entrance problems

581 problems for CMI Entrance practice, in Mathematics and Physics, each with a worked solution. Try each one on paper first, then check your answer.

All SubjectsPhysicsChemistryMathematicsBiologyPython ProgrammingStatistics & Data Science

All LevelsHigh School (9–10)High School (11–12)General

All TopicsMechanicsHeat & ThermodynamicsWaves & SoundOpticsElectricity & MagnetismElectronicsAtomic PhysicsQuantum MechanicsModern PhysicsAstrophysics

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Type:AnyConceptualNumerical

1.

A student measures a silicon transistor in the common-emitter circuit… New

High School (11–12) · Transistors and Logic GatesJEE MainAEEE (Amrita)AMUEEE+23StemPy Lab

Hard

2.

A common-emitter amplifier is built with a supply of 12 V and a collector resistor of 3.0 kΩ… New

High School (11–12) · Transistors and Logic GatesJEE MainAEEE (Amrita)AMUEEE+23StemPy Lab

Hard

3.

A logic circuit has two inputs A and B. Gate 1 is a NAND gate with inputs A and B… New

High School (11–12) · Transistors and Logic GatesJEE MainAEEE (Amrita)AMUEEE+23StemPy Lab

Hard

4.

A thin rod of pure germanium is used to sense temperature… New

High School (11–12) · Semiconductors and DiodesAEEE (Amrita)AMUEEEAP EAPCET+22StemPy Lab

Hard

5.

A silicon wafer is doped with both kinds of impurity… New

High School (11–12) · Semiconductors and DiodesAEEE (Amrita)AMUEEEAP EAPCET+22StemPy Lab

Hard

6.

A resistor is cut from n-type silicon in which ne = 1.0 × 10²¹ m⁻³… New

High School (11–12) · Semiconductors and DiodesAEEE (Amrita)AMUEEEAP EAPCET+22StemPy Lab

Hard

7.

A silicon diode follows the equation I = Is(e^(V/VT) - 1) with η = 1, Is = 1.0 pA and VT = 25.85 mV… New

High School (11–12) · Semiconductors and DiodesAEEE (Amrita)AMUEEEAP EAPCET+22StemPy Lab

Hard

8.

A bench supply is built with a full-wave bridge on a 50 Hz mains transformer… New

High School (11–12) · Semiconductors and DiodesJEE MainAEEE (Amrita)AMUEEE+23StemPy Lab

Hard

9.

A sensor circuit needs a steady 5.1 V from a supply whose voltage is not steady… New

High School (11–12) · Semiconductors and DiodesJEE MainAEEE (Amrita)AMUEEE+23StemPy Lab

Hard

10.

A green LED has a semiconductor with a band gap of 2.3 eV, and each photon that it gives out has… New

High School (11–12) · Semiconductors and DiodesJEE MainAEEE (Amrita)AMUEEE+23StemPy Lab

Hard

11.

A farmer plans a solar panel for a small water pump… New

High School (11–12) · Semiconductors and DiodesJEE MainAEEE (Amrita)AMUEEE+23StemPy Lab

Hard

12.

The energy needed to remove one neutron from a nucleus is its neutron separation energy… New

High School (11–12) · Nuclei and RadioactivityJEE AdvancedAPA-Level+26APA-LevelIBStemPy Lab

Hard

13.

Carbon-12 can be pictured as three helium-4 nuclei bound together, and oxygen-16 as four… New

High School (11–12) · Nuclei and RadioactivityJEE AdvancedAPA-Level+26APA-LevelIBStemPy Lab

Hard

14.

Cobalt-60 (mass 59.933817 u) decays by beta-minus to an excited state of nickel-60 (ground-state… New

High School (11–12) · Nuclei and RadioactivityJEE MainJEE AdvancedAP+27APA-LevelIBStemPy Lab

Hard

15.

A radioactive nucleus can decay in two ways… New

High School (11–12) · Nuclei and RadioactivityJEE MainJEE AdvancedAP+27APA-LevelIBStemPy Lab

Hard

16.

A sample of rock contains 5.00 mg of uranium-238 and 0.90 mg of lead-206… New

High School (11–12) · Nuclei and RadioactivityJEE MainJEE AdvancedAP+27APA-LevelIBStemPy Lab

Hard

17.

A slow neutron, with almost no kinetic energy, is taken in by lithium-6… New

High School (11–12) · Nuclei and RadioactivityJEE AdvancedNEETAP+27APA-LevelIBStemPy Lab

Hard

18.

In a block of fuel the multiplication factor is k = 1.01, and in another it is k = 1.10… New

High School (11–12) · Nuclei and RadioactivityJEE AdvancedNEETAP+27APA-LevelIBStemPy Lab

Hard

19.

A neutron of mass number 1 and kinetic energy 2.0 MeV hits a stationary nucleus of mass number a… New

High School (11–12) · Nuclei and RadioactivityJEE AdvancedNEETAP+27APA-LevelIBStemPy Lab

Hard

20.

A fusion plant makes 500 MW of heat from the reaction ²H + ³H → ⁴He + n, which releases 17.59 MeV… New

High School (11–12) · Nuclei and RadioactivityJEE AdvancedNEETAP+27APA-LevelIBStemPy Lab

Hard

21.

A glass-maker is checking a thin plate that will be used as a camera filter… New

High School (11–12) · Wave OpticsJEE AdvancedAPA-Level+26APA-LevelIBStemPy Lab

Hard

22.

In a laboratory, a laser beam is split into two beams by a thin glass plate… New

High School (11–12) · Wave OpticsJEE AdvancedAPA-Level+26APA-LevelIBStemPy Lab

Hard

23.

A student sets up a double-slit experiment… New

High School (11–12) · Wave OpticsJEE AdvancedAPA-Level+26APA-LevelIBStemPy Lab

Hard

24.

A student has a single slit that is 0.15 mm wide, cut in a thin metal foil… New

High School (11–12) · Wave OpticsJEE MainJEE AdvancedAP+27APA-LevelIBStemPy Lab

Hard

25.

A physics club is testing a diffraction grating that is marked with 450 lines in each millimetre… New

High School (11–12) · Wave OpticsJEE MainJEE AdvancedAP+27APA-LevelIBStemPy Lab

Hard