JEE Main 2021 previous year paper practice · PYQ-pattern set

JEE Main 2021 PYQ-pattern questions

Showing 10 of the 15 PYQ-pattern questions in this set — freshly worded in that year's pattern, not the original questions. Answers and solutions open under each question.

1. Q1 · Rotational Motion

   A solid cylinder and a hollow cylinder of the same mass and radius are released from rest at the top of an inclined plane. Which one reaches the bottom first and why?

   • A. Solid cylinder, because it has smaller moment of inertia
   • B. Hollow cylinder, because it has larger moment of inertia
   • C. Both reach at the same time
   • D. Solid cylinder, because it has larger moment of inertia
   Answer and solution

   Answer: A

   For rolling without slipping, acceleration a = g sinθ/(1 + I/MR²). Solid cylinder has I = MR²/2, hollow has I = MR². Smaller I gives larger a, so solid cylinder reaches first.

2. Q2 · Physics and Measurement

   The dimensional formula of physical quantity X is [M¹L²T⁻³]. Which of the following represents X?

   • A. Power
   • B. Energy
   • C. Force
   • D. Momentum
   Answer and solution

   Answer: A

   Power has dimensional formula [M¹L²T⁻³]. Energy is [M¹L²T⁻²], Force is [M¹L¹T⁻²], and Momentum is [M¹L¹T⁻¹].

3. Q3 · Magnetic Effects of Current and Magnetism

   A current-carrying circular loop of radius R is placed in a uniform magnetic field B perpendicular to the plane of the loop. If the current in the loop is I, the magnetic force on the loop is

   • A. BIR
   • B. 2πBIR
   • C. Zero
   • D. πBIR
   Answer and solution

   Answer: C

   The magnetic force on each element of the loop is radially directed. The vector sum of all such forces around a complete circular loop is zero due to symmetry.

4. Q4 · Kinetic Theory of Gases

   The root mean square velocity of molecules of a gas at temperature T is v. If the temperature is increased to 4T and the molecular mass is halved, the new rms velocity will be

   • A. 2v
   • B. 4v
   • C. v√2
   • D. 2√2v
   Answer and solution

   Answer: D

   RMS velocity v_rms = √(3RT/M). New velocity v' = √(3R(4T)/(M/2)) = √(24RT/M) = 2√2 × √(3RT/M) = 2√2v.

5. Q5 · Electronic Devices

   In a p-n junction diode under forward bias, the width of the depletion region:

   • A. Increases
   • B. Decreases
   • C. Remains unchanged
   • D. First increases then decreases
   Answer and solution

   Answer: B

   Under forward bias, the applied voltage opposes the built-in potential barrier, reducing the width of the depletion region and allowing current to flow.

6. Q6 · Experimental Skills

   In a screw gauge, the pitch is 0.5 mm and there are 50 divisions on the circular scale. The least count of the screw gauge is:

   • A. 0.001 mm
   • B. 0.01 mm
   • C. 0.1 mm
   • D. 0.05 mm
   Answer and solution

   Answer: B

   Least count = Pitch / Number of divisions on circular scale = 0.5 mm / 50 = 0.01 mm.

7. Q7 · Classification of Elements and Periodicity in Properties

   Which of the following has the smallest ionic radius?

   • A. O²⁻
   • B. F⁻
   • C. Na⁺
   • D. Mg²⁺
   Answer and solution

   Answer: D

   All are isoelectronic with 10 electrons. Ionic radius decreases with increasing nuclear charge. Mg²⁺ has 12 protons, the highest among the given, hence smallest radius.

8. Q8 · Organic Compounds Containing Oxygen

   Which of the following alcohols will give a positive iodoform test?

   • A. Ethanol
   • B. Methanol
   • C. Propan-1-ol
   • D. 2-Methylpropan-1-ol
   Answer and solution

   Answer: A

   The iodoform test is positive for compounds containing the CH₃CH(OH)- or CH₃CO- group. Ethanol (CH₃CH₂OH) oxidizes to acetaldehyde (CH₃CHO) which gives a positive iodoform test with I₂/NaOH.

9. Q9 · Hydrocarbons

   When 2-methylbut-2-ene is treated with cold dilute alkaline KMnO₄ solution, the product obtained is:

   • A. 2-Methylbutane-2,3-diol
   • B. Acetone and acetic acid
   • C. 2-Methylpropanoic acid
   • D. But-2-ene-1,4-diol
   Answer and solution

   Answer: A

   Cold dilute alkaline KMnO₄ (Baeyer's reagent) hydroxylates alkenes to form vicinal diols (syn-addition). 2-Methylbut-2-ene [(CH₃)₂C=CHCH₃] gives 2-methylbutane-2,3-diol as the product.

10. Q10 · Complex Numbers and Quadratic Equations

    If α and β are the roots of the equation x² - 6x + k = 0 such that α² + β² = 28, then the value of k is:

    • A. 4
    • B. 6
    • C. 8
    • D. 10
    Answer and solution

    Answer: A

    Using Vieta's formulas: α + β = 6, αβ = k. We have α² + β² = (α + β)² - 2αβ = 36 - 2k = 28. Solving: 2k = 8, so k = 4.