Stop Reading. Start Scoring.

Sections 1 to 9 taught you this chapter — scalars and vectors, the triangle and parallelogram laws, resolution into components, the analytical method, plane motion with constant acceleration, projectiles, uniform circular motion, relative velocity in two dimensions, and the JEE-only extensions in Section 9. This section finds out whether you can use any of it with a clock running, which is a completely different skill.

There is no new theory below. There are 27 questions built to the JEE Main pattern, and a marking scheme that punishes the thing students do most: guessing.

The rules of engagement

Key Point: Do not treat this as a reading exercise. Sit down with a blank sheet, a pen and a timer, and attempt all 27 questions in one unbroken sitting before you look at a single explanation.

The setup What it is
Number of questions 27
Marking scheme +4+4 correct, 1-1 incorrect, 00 unattempted
Maximum score 27×4=10827 \times 4 = 108 marks
Minimum possible score 27×(1)=2727 \times (-1) = -27 marks
Suggested time limit 30 minutes (JEE Main pace is a little over 1 minute per question)
Take gg as 10 m/s^2 unless a question says otherwise
Allowed rough sheet, your own brain
Not allowed calculator, formula sheet, looking back at Sections 1 to 9

[Exam Tip] That 1-1 is not decoration. Four wild guesses that produce one lucky hit earn you 43=+14 - 3 = +1 mark for four minutes of work — a terrible trade. But a question you have narrowed to two options is worth attempting: on average that returns 412=+1.5\frac{4 - 1}{2} = +1.5 marks. Narrow first, then commit. Leave blank only what you could not narrow at all.

What this set covers

Topic map and self-scoring card for the 27-question JEE Main drill

Topic Questions How many
Vector algebra: resultants, bounds, components, the quadrant trap, dot and cross products Q1 to Q5 5
Motion in a plane: differentiating a position vector, constant acceleration, the angle between velocity and acceleration Q6 to Q9 4
Projectile motion, including inclines, moving platforms and the radius of curvature Q10 to Q16 7
Circular motion: uniform, non-uniform, and angular kinematics Q17 to Q21 5
Relative velocity in two dimensions, including a two-projectile collision Q22 to Q24 3
Hard multi-concept chains Q25 to Q27 3

That spread is deliberate — it mirrors how JEE Main actually samples Motion in a Plane. Projectiles alone are 7 of the 27, because in the real paper they carry more marks from this chapter than anything else. Vectors and circular motion take another 10 between them, and they are where the fast marks are, because most candidates over-think them.

The difficulty mix is roughly 25% easy, 45% medium and 30% hard, so do not panic if a handful feel brutal. They are meant to.

[Exam Tip] Before you start, write your axes at the top of the sheet — +x+x to the right, +y+y up — and resolve everything into components before you reach for a single formula. More marks are lost in this chapter to a vector added as a magnitude, or to a tan1\tan^{-1} dropped into the wrong quadrant, than to any forgotten formula.

Scoring Yourself Honestly

Mark your sheet with the real scheme — +4+4, 1-1, 00 — and total it. No half marks for "I knew that one really". The number you get is the number that matters.

The bands

Your score (out of 108) Verdict What to do next
87 to 108 Exam ready. 80% or more on a hard set, inside the time. Move on. This chapter will not cost you marks. Revisit only the specific items you missed.
65 to 86 Solid, but leaking marks. These are almost always slips, not gaps — a quadrant not corrected, a sin\sin where a cos\cos belonged, an angle measured from the wrong line. Redo every wrong question without the explanation first.
40 to 64 Shaky. The ideas are there; the execution is not. For each wrong answer, go back to the section it came from (use the topic map above) and rework its solved examples before re-attempting.
Below 40 Start again. Work Sections 1 to 9 properly, then Section 8's solved examples, then come back. Re-attempting this set now teaches you nothing.

Read your own answer sheet

Before you touch the explanations, sort your mistakes into three piles. This is the most valuable ten minutes in the whole section.

  1. Concept errors — you did not know that the horizontal velocity of a projectile never changes, or that a body in uniform circular motion is accelerating, or that the linear kinematic equations are illegal on a circle. Fixable by revision, and quickly.
  2. Execution errors — right method, wrong arithmetic, or you resolved along the wrong pair of axes. Fixable by slowing down for four seconds at the last line.
  3. Reading errors — the angle was measured from the incline and you took it from the horizontal, the speed was relative to the trolley and you used it as a ground speed, the question wanted the shortest path and you gave the shortest time. These are the cheapest marks in the paper to win back, and the ones students refuse to take seriously.

Key Point: In this chapter specifically, pile 3 is dominated by four traps: an angle measured from the wrong reference line, a velocity quoted in the wrong frame, "displacement" answered where "distance along the path" was asked, and a tan1\tan^{-1} read straight off the calculator without the quadrant check. Check which of the four caught you, every single time.

The six habits this set is drilling

  • Resolve first, think second. Two components and a sketch beat any amount of staring at a geometry problem. Add components, never magnitudes.
  • Fix the reference line before you write an angle. From the horizontal, from the incline, from the vertical, from A\vec{A} — four different numbers for the same picture.
  • In every projectile question, sort the data into an x-column and a y-column. The only thing shared between them is the clock. "When?" is a y-question; "how far?" is an x-question that spends the y-answer.
  • On a circle, never reach for v=v0+atv = v_0 + at. The acceleration vector is turning, so it is not constant even when the speed is. Use v=ωRv = \omega R, ac=v2/Ra_c = v^2/R, and — only if α\alpha is constant — the angular equations.
  • In any two-body problem, sit in the other body's frame. vAB=vAvB\vec{v}_{AB} = \vec{v}_A - \vec{v}_B turns two moving objects into one. For two projectiles the relative acceleration is exactly zero, so the relative motion is a straight line at constant velocity.
  • Sanity-check the size of the answer. A range of 4 km from a hand throw, or a radius of curvature of 2 mm for a cricket ball, is telling you something before you check the algebra.

[Exam Tip] Every explanation below is a full step-by-step solution, so this set doubles as revision material. Read the explanation even for the questions you got right — sometimes you got there the slow way, and the fast way is what you will need in the hall.