Module 1: Mathematical Foundations · Practice · NEET pattern
Forty multiple-choice questions across the eleven Foundations, most of them answerable in under twenty seconds.
How this set differs
A NEET paper allows well under a minute a question. That rewards recognition and elimination over derivation — and most of what Module 1 teaches can be used that way, if you know what to look for.
Four habits do most of the work here. A resultant of two vectors always lies between the difference and the sum of their magnitudes. A projection can never exceed the magnitude of the vector projected. On a graph, slope is a rate and area is an accumulation. And terms that are added must have the same dimensions.
Each question carries the Foundation it tests. Choose the single best answer. Many questions need no calculation at all — if you find yourself computing on most of them, you are working harder than the paper requires.
Coverage
Foundation 1, dimensions — Q1 to 3 · Foundation 2, scalars and vectors — Q4 to 8 · Foundation 3, coordinates — Q9 to 12 · Foundation 4, addition and resolution — Q13 to 17 · Foundation 5, dot product — Q18 to 20 · Foundation 6, cross product — Q21 to 24 · Foundation 7, graphs — Q25 to 28 · Foundation 8, differentiation — Q29 to 32 · Foundation 9, integration — Q33 to 36 · Foundation 10, approximations — Q37 and 38 · Foundation 11, recognition — Q39 and 40
Block I — Dimensions, scalars and vectors
1. [F1] A student writes s = ut + at³ for a displacement. What immediately shows this is wrong?
A. ut does not have units of length B. at³ has units of length C. The two terms on the right have different dimensions D. Acceleration cannot appear in a displacement formula
2. [F1] Which of these is dimensionally possible for a displacement s?
A. s = ut + at B. s = u + at² C. s = ut + ½at² D. s = u/t + at²
3. [F1] A quantity has SI units of m s−2. It could be:
A. Velocity B. Acceleration C. Displacement D. Momentum
4. [F2] A person walks 3 m east and then 4 m north. The distance travelled and the magnitude of the displacement are:
A. 3 m, 4 m B. 4 m, 3 m C. 7 m, 5 m D. 5 m, 7 m
5. [F2] A vector has components 6 N east and 8 N north. Its magnitude is:
A. 2 N B. 10 N C. 14 N D. 48 N
6. [F2] Which statement is always true?
A. Distance can be negative B. The magnitude of displacement is always larger than the distance C. Speed is a scalar D. Velocity is a scalar
7. [F2] A runner completes one full lap of a circular track and returns to the start. The magnitude of the displacement is:
A. The circumference B. The radius C. Zero D. The diameter
8. [F2] A body moves 5 m west and then 5 m east. Its distance travelled and displacement magnitude are:
A. 0 m, 10 m B. 10 m, 0 m C. 5 m, 5 m D. 0 m, 0 m
Block II — Coordinates and vector addition
9. [F3] The point (−3, 3√3) lies in which quadrant?
A. First B. Second C. Third D. Fourth
10. [F3] The polar coordinates (5, π/2) correspond to which Cartesian coordinates?
A. (5, 0) B. (0, 5) C. (−5, 0) D. (0, −5)
11. [F3] A particle sits on the positive x-axis, so θ = 0. In which directions do r̂ and θ̂ point?
A. +x and +y B. +y and −x C. +x and −y D. Both along +x
12. [F3] The polar coordinates of the point (−1, √3) are:
A. (2, π/3) B. (2, 2π/3) C. (√2, 2π/3) D. (2, 5π/3)
13. [F4] A boat moves at 4 m/s east relative to the water, and the water flows at 3 m/s north relative to the ground. The boat’s speed relative to the ground is:
A. 1 m/s B. 3 m/s C. 4 m/s D. 5 m/s
14. [F4] Two perpendicular vectors have magnitudes 5 and 12. Their resultant has magnitude:
A. 7 B. 13 C. 17 D. 60
15. [F4] A 10 N force is resolved into two perpendicular components. Which pair is impossible?
A. 6 N and 8 N B. 10 N and 0 N C. 5√2 N and 5√2 N D. 8 N and 8 N
16. [F4] Two perpendicular vectors each have magnitude A. Their resultant has magnitude:
A. A B. 2A C. A/√2 D. √2 A
17. [F4] Two vectors have magnitudes 5 and 4. Which of these cannot be the magnitude of their resultant?
A. 1 B. 3 C. 7 D. 10
Block III — Dot product and cross product
18. [F5] A 10 N force acts at 60° to a 2 m displacement. The work done is:
A. 5 J B. 10 J C. 20 J D. 40 J
19. [F5] A force acts perpendicular to the displacement throughout. The work done is:
A. Maximum B. Zero C. Negative D. Fd
20. [F5] If |A| = 5 and |B| = 4, the largest possible value of A · B is:
A. 0 B. 1 C. 9 D. 20
21. [F6] |A × B| is greatest when the angle between them is:
A. 0° B. 30° C. 90° D. 180°
22. [F6] A 5 N force acts perpendicular to a lever arm of 2 m. The magnitude of the torque is:
A. 0 B. 2.5 N m C. 7 N m D. 10 N m
23. [F6] A force acts along the line joining the pivot to its point of application. The torque about that pivot is:
A. Maximum B. Zero C. Negative D. Equal to rF
24. [F6] The vector A × B is perpendicular to:
A. A only B. B only C. The plane containing A and B D. Neither
Block IV — Graphs and differentiation
25. [F7] A velocity–time graph is a horizontal line above the time axis. The motion has:
A. Constant velocity B. Constant non-zero acceleration C. Zero displacement D. Increasing speed
26. [F7] The area under a velocity–time graph represents:
A. Acceleration B. Displacement C. Force D. Momentum
27. [F7] The slope of a position–time graph represents:
A. Displacement B. Speed only C. Velocity D. Acceleration
28. [F7] A velocity–time graph is a straight line with positive slope. The particle has:
A. Zero acceleration B. Constant positive acceleration C. Constant negative acceleration D. Constant displacement
29. [F8] If x(t) = 4t² metres, the velocity at t = 2 s is:
A. 4 m/s B. 8 m/s C. 16 m/s D. 32 m/s
30. [F8] A smooth position function x(t) has a local maximum at some time t0. Which must be true there?
A. The velocity is zero B. The acceleration is positive C. The velocity is greatest D. The acceleration is zero everywhere
31. [F8] A particle’s velocity changes smoothly from +5 m/s to −5 m/s. What must occur at some instant in between?
A. The displacement becomes zero B. The velocity becomes zero C. The acceleration becomes zero D. The speed becomes negative
32. [F8] If the velocity of a particle is constant, its acceleration is:
A. Constant and non-zero B. Zero C. Infinite D. Equal to the displacement
Block V — Integration, approximation and recognition
33. [F9] In one-dimensional motion, the displacement between two times is given by:
A. The area under the velocity–time graph B. The slope of the velocity–time graph C. The area under the acceleration–time graph D. The maximum velocity
34. [F9] For motion with constant acceleration, the average velocity equals:
A. The average acceleration B. The average speed in every case C. (u + v)/2 D. The displacement
35. [F9] An acceleration–time graph is constant at 2 m/s² for 5 s. The change in velocity is:
A. 0.4 m/s B. 2 m/s C. 7 m/s D. 10 m/s
36. [F9] A particle has positive velocity for 3 s and then negative velocity for 2 s. The signed area under the velocity–time graph gives:
A. The total distance B. The net displacement C. The acceleration D. The speed
37. [F10] For small θ measured in radians, the standard approximation is:
A. sin θ ≈ 1/θ B. sin θ ≈ θ C. sin θ ≈ θ² D. sin θ ≈ 0 for every θ
38. [F10] Which statement about a physical approximation is correct?
A. It is always exact B. It has no range of validity C. Its validity depends on the conditions under which it was derived D. It removes the need for physical reasoning
39. [F11] Before adding B and C in an equation A = B + C, what must be checked?
A. That they have the same dimensions B. That they have different units C. That both are vectors D. That both are positive
40. [F11] Which is the best strategy for a question under time pressure?
A. Recall a formula, substitute, and hope B. Calculate everything before deciding what is needed C. Identify the quantity and its representation, check dimensions or direction, then calculate only what is required D. Use the longest derivation available
When you have finished
Count how many of the forty you answered by calculating rather than by recognising. In a paper with under a minute a question, that number is the one that matters — a student who computes question 17 has spent thirty seconds establishing something the bound between |5 − 4| and 5 + 4 gives away instantly.
Four bounds do most of the elimination in this set: a resultant lies between the difference and the sum of the magnitudes; a projection cannot exceed the vector projected; a dot product cannot exceed the product of the magnitudes; and terms added together must share dimensions. Each rules out options before any arithmetic begins.
Covers: Foundations 1–11 · Type: Forty MCQs, no answers · Pattern: NEET — recognition and elimination rather than derivation