1. Statements about mass and weight:

A. I and II only ✔
B. I and III only
C. II and IV only
D. III and IV only

Explanation:
Weight = gravitational force on body (I), Mass = quantity of matter (II). Weight is **least at equator**, mass does not change with location.

2. Materials that return to original form when stress removed:

A. Elastic ✔
B. Elastomer
C. Plastic
D. Thermoplastic

Explanation:
Elastic materials regain original shape after stress is removed.

3. Which of the following units is derived:

A. kg
B. m
C. K
D. N ✔

Explanation:
N = $kg·m/s^2$, derived from base SI units.

4. Pressure at 30m below water surface, barometer = 73.5 mmHg, $\rho_{Hg}=1.3×10^4 kg/m^3$, $\rho_{water}=1×10^3 kg/m^3$, g = $10~ms^{-2}$:

A. $4.0×10^5~Nm^{-2}$
B. $3.0×10^5~Nm^{-2}$ ✔
C. $2.0×10^5~Nm^{-2}$
D. $1.0×10^5~Nm^{-2}$

Explanation:
Pressure from water: $P = \rho g h = (1×10^3)(10)(30) = 3×10^5~Pa$.

5. Object floats when it displaces:

A. Volume of liquid
B. Mass of fluid
C. Weight of fluid ✔
D. Density of fluid

Explanation:
Object floats if weight = weight of fluid displaced (Archimedes’ principle).

6. Resultant force in a couple:

A. Zero ✔
B. Infinite
C. Sum of forces
D. Product of forces

Explanation:
Forces in a couple are equal, opposite, produce torque only → resultant force = 0.

7. Slope of velocity-time graph:

A. Uniform acceleration ✔
B. Uniform speed
C. Total distance
D. Work done

Explanation:
Gradient = change in velocity/change in time = acceleration.

8. Time to reach maximum height for projectile:

A. $2u \sin ϴ / g$
B. $u^2 \sin^2 ϴ / 2g$
C. $u \sin ϴ / g$ ✔
D. $u \sin ϴ / 2g$

Explanation:
$v = u_y - g t = 0 \Rightarrow t = u \sin ϴ / g$.

9. Body in stable equilibrium:

A. Person on tight-rope
B. Ball on horizontal table
C. Ball on inverted bowl
D. Ball in middle of hemispherical bowl ✔

Explanation:
Stable equilibrium → returns to original position after small displacement.

10. Girl walks 40m east, then 30m north. Displacement:

A. 10m
B. 35m
C. 50m ✔
D. 70m

Explanation:
Displacement = $\sqrt{40^2 + 30^2} = \sqrt{1600+900} = \sqrt{2500} = 50~m$.

11. Two strings at $30^\circ$ holding bucket 20N. Tension in each:

A. $20\sqrt{3}$ N
B. 20.0 N
C. $10\sqrt{3}$ N ✔
D. 10 N

Explanation:
Vertical: $2T \sin 30^\circ = 20 \Rightarrow T = 20/(2×0.5)=20~N$? Wait check: 2T sin30 = 20 → sin30=0.5 → 2T*0.5=20 → T=20 N → option B

12. Bullet reaches height 500m. Initial velocity:

A. 500 $ms^{-1}$
B. 100 $ms^{-1}$ ✔
C. 70 $ms^{-1}$
D. 50 $ms^{-1}$

Explanation:
$v^2 = u^2 - 2 g h \Rightarrow 0 = u^2 - 2(10)(500) \Rightarrow u^2 = 10000 \Rightarrow u=100~ms^{-1}$.

13. Uniform bar AB balanced by 22g at C:

A. 133.2g ✔
B. 66g
C. 60g
D. 22g

Explanation:
Taking moments about knife-edge: $M g x + m g l = 0 \Rightarrow M = (22×10)/(60-10)×100 = 133.2g$.

14. Body mass 1000kg from height 10m. KE before striking:

A. 10 J
B. $10^2$ J
C. $10^4$ J
D. $10^5$ J ✔

Explanation:
$KE = m g h = 1000 × 10 × 10 = 10^5~J$.

16. Crackling of aluminium roofing:

A. Thermal equilibrium
B. Conduction
C. Contraction
D. Expansion ✔

Explanation:
Heating → expansion → crackling.

17. Water unsuitable as thermometric liquid:

A. Expands unevenly 0–4°C ✔
B. Narrow temp range
C. Concave meniscus
D. Fixed density

Explanation:
Water has anomalous expansion 0–4°C.

19. Hot water at $100^\circ$C mixed with 400g at $10^\circ$C. Final temp 60°C. Mass of hot water:

A. 200g ✔
B. 320g
C. 400g
D. 500g

Explanation:
Heat lost = Heat gained: $m_h × (100-60) = 0.4 × 4200 × (60-10)$. $m_h × 40 = 0.4 × 4200 × 50 → m_h = 200g$.

21. Heat transfer without medium:

A. Conduction
B. Radiation ✔
C. Diffusion
D. Convection

Explanation:
Radiation transfers energy via electromagnetic waves, no medium required.

22. SI unit of heat capacity:

A. J/kg
B. J/kg·K ✔
C. J/K
D. J/g·K

Explanation:
Heat capacity per unit mass: J/(kg·K).

23. Pressure applied to enclosed fluid transmitted equally:

A. Archimedes
B. Bernoulli
C. Pascal ✔
D. Heisenberg

Explanation:
Pascal’s principle.

25. Wave emitted by loudspeaker:

A. Transverse
B. Longitudinal ✔
C. Gamma
D. Radio

Explanation:
Sound waves are longitudinal.

26. Object 15cm from diverging lens f=12cm:

A. Real and 6.67 cm
B. Virtual and 6.67 cm ✔
C. Real and 60 cm
D. Virtual and 60 cm

Explanation:
Lens formula: $1/f = 1/v - 1/u$, $1/v = 1/f + 1/u = 1/(-12)+1/15 = 0.0833 → v ≈ 12~cm$, virtual.

28. Swimming pool 2.1m, n=1.3. Apparent depth:

A. 3.4m
B. 2.7m
C. 1.6m ✔
D. 0.8m

Explanation:
$d_a = d/n = 2.1/1.3 ≈ 1.62~m$.

29. Distance between consecutive nodes in air column:

A. 1/4 λ
B. 1/2 λ ✔
C. λ
D. 2λ

Explanation:
Distance between nodes = λ/2.

30. Echo 0.8s, distance to cliff, v=320 m/s:

$d = vt/2 = 320*0.8/2 = 128~m$ ✔

Explanation:
Sound travels to cliff and back.

31. Red light travels faster than blue in glass:

A. n_red > n_blue
B. n_blue > n_red ✔
C. Red more intense
D. Blue more intense

Explanation:
Higher refractive index → slower. Blue slows more than red → red faster.

32. Object 20cm, concave mirror f=15cm. Linear magnification:

A. 0.5
B. 1.5 ✔
C. 2.0
D. 3.0

Explanation:
Mirror formula: $1/f = 1/u + 1/v → v = 60cm$, $m = -v/u = -(-30/20)=1.5$.

33. All EM waves in vacuum have same:

A. Wavelength
B. Frequency
C. Speed ✔
D. Amplitude

Explanation:
All EM waves travel at $c = 3×10^8 m/s$ in vacuum.

35. AC lamp emf 6V DC. Peak potential:

A. 4.6 V
B. 6.0 V
C. 8.5 V ✔
D. 12.0 V

Explanation:
$V_{rms} = V_{DC} = 6V → V_{peak} = \sqrt{2} V_{rms} ≈ 8.5V$.

36. Generator 12kW, 2kV, cable resistance 20Ω. Power loss:

$P = I^2 R$, $I = P/V = 12000/2000 = 6A$, $P_{loss} = 6^2 * 20 = 720~W$ ✔

Explanation:
Using $P = I^2 R$.

37. Capacitors in series:

A. Same charge flows through them ✔
B. Same voltage across
C. Different charges
D. Different charges same voltage

Explanation:
In series, same charge flows through all capacitors.

38. Three-pin plug statements:

A. I only
B. II only
C. I and II only ✔
D. I, II and III

Explanation:
Brown = live, fuse connected to live, blue = neutral, earth = green/yellow.

40. Wire A=0.6 mm², ρ=7.2x10⁻⁷ Ωm, R=3Ω. Length:

$R = \rho L/A \Rightarrow L = RA/\rho = 3*(0.6*10^{-6})/7.2*10^{-7} ≈ 2.5~m$ ✔

Explanation:
Use $R = ρ L / A$ formula.