Qpt mathongo

Mathongo Paper-1 — Physics Section

Marking Scheme: +4 for correct, −1 for wrong, 0 unattempted

Q1. Given y = A sin[(ct - x)], where y and x are measured in metres. Which statement is true?

A. Unit of A is same as that of x and A B. Unit of (ct - x) is same as that of (2π/λ) C. Unit of c is same as that of 2λ D. Unit of A is same as that of x but not of A

Q2. Two trains moving in opposite directions are mistakenly put on the same track. When the trains are 300 m apart, they start slowing down. The separation when both have stopped is:

A. 120 m B. 20 m C. 60 m D. 280 m

Q3. A body is projected vertically upwards. The times for reaching a certain height during ascending and descending are t₁ and t₂ respectively. Velocity of projection is:

A. g√(t₁t₂) B. (g t₁ t₂) / (t₁ + t₂) C. (g√(t₁t₂)) / 2 D. g(t₁ + t₂) / 2

Q4. Assertion: A stone and a feather dropped from the same height do not reach ground at the same time. Reason: g depends on mass.

A. Both true, reason correct explanation B. Both true, reason not correct explanation C. Assertion true, reason false D. Both false

Q5. In a cube of side a, vector from the face-centre of ABOD to BEFO is:

A. (a/2) k − i B. a(−k)/2 C. a j D. a(−k)

Q6. If energy E = Gᵖ hᑫ cʳ, with G=gravitational constant, h=Planck's, c=velocity of light, find p,q,r:

A. −½ , ½ , 5/2 B. ½ , −½ , −5/2 C. −½ , ½ , 3/2 D. ½ , −½ , −3/2

Q7. Girl runs 6 km/h, swims 4 km/h, must reach point in sea fastest. Path should be:

A. PAQ B. PBQ C. PCQ D. PDQ

Q8. Person can throw stone max range 100 m; greatest height possible is:

A. 100 m B. 75 m C. 50 m D. 25 m

Q9. Three 1 kg balls on 1 m strings, rotated at 4 rad/s. Match T₁, T₂, T₃ with given values:

A. A–P, B–R, C–Q,T B. A–T, B–R, C–Q,P C. A–S, B–P, C–Q,T D. A–Q, B–R, C–S,T

Q10. A body from rest moved by constant-power machine; distance ∝ ?

A. t^(1/2) B. t^(3/4) C. t^(3/2) D. t^(1/4)

Q11. Falling ball with air resistance ∝ speed. u₁ = u₂, accelerations a₁,a₂:

A. a₁ < a₂ B. a₁ > a₂ C. a₁ = a₂ ≠ g D. a₁ = a₂ = g

Q12. Particle in uniform circular motion — which statement is incorrect?

A. Avg accel = 0 B. Displacement = 0 C. Avg speed = 0 D. Avg velocity = 0

Q13. Quantum Hall Resistance dimensions equal to:

A. e²/h B. h/e² C. h²/e D. e/h²

Q14. Skater P throws 2 m/s balls to Q every 5s. Compare cases: (i) P moves 1 m/s, Q stationary (ii) Q moves 1 m/s, P stationary. Balls reach Q as:

A. 1 every 2s in (i), 1 every 4s in (ii) B. 1 every 5s in (i), 1 every 3s in (ii) C. 1 every 3s in (i), 1 every 5s in (ii) D. None of these

Q15. Dimension of C V² is:

A. [M L² T⁻² A⁰] B. [M L T⁻² A⁻¹] C. [M⁰ L T² A⁰] D. [M L³ T A]

Q16. Guns fire 2 km/s and 4 km/s in all directions; ratio of ground areas covered:

A. 1:2 B. 1:4 C. 1:8 D. 1:16

Q17. Stone’s last‑second fall distance equals distance in first 5 seconds. Total time of fall is:

A. 12 B. 13 C. 25 D. 26

Q18. Max range of a gun is 16 km, g = 10 m/s². Muzzle velocity is:

A. 160 m/s B. 200√2 m/s C. 400 m/s D. 800 m/s

Q19. Significant figures in: 161 cm, 0.161 cm, 0.0161 cm:

A. 3,4,5 B. 3,3,4 C. 3,3,3 D. 3,4,4

Q20. A girl drops an apple from an accelerating train – trajectory in her frame?

A. Parabola in train’s direction B. Parabola opposite direction C. Inclined straight line, direction of train D. Inclined straight line, opposite train