Police & Armed Forces · Practice Sheet 6

1. 1.

   Physics

   Find the kinetic energy of a 9 kg object moving at 25 m/s.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2}mv^{2}$

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2. 2.

   Quantitative Aptitude

   An item is bought for AED 600 and sold for AED 750. Find the profit percentage.

   Formula:Profit Percentage

   $\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$

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3. 3.

   Quantitative Aptitude

   In how many ways can 4 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 4.)

   Formula:Combinations

   $^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$

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4. 4.

   Physics

   Calculate the potential energy of a 5 kg object at a height of 6 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Quantitative Aptitude

   Pipe A fills a tank in 5 hours and pipe B in 6 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

   $T = \dfrac{xy}{x+y}$

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6. 6.

   Physics

   Find the voltage across a 7 Ω resistor carrying a current of 11 A.

   Formula:Ohm's Law

   $V = IR$

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7. 7.

   Physics

   Find the momentum of a 2 kg body moving at 34 m/s.

   Formula:Linear Momentum

   $p = mv$

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8. 8.

   Quantitative Aptitude

   An item is bought for AED 400 and sold for AED 560. Find the profit percentage.

   Formula:Profit Percentage

   $\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$

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9. 9.

   Physics

   A projectile is launched at 13 m/s at 30° to the horizontal. Find its range (g = 9.8 m/s²).

   Formula:Projectile Range

   $R = \dfrac{u^{2}\sin 2\theta}{g}$

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10. 10.

    Physics

    Find the force required to accelerate a 5 kg mass at 20 m/s².

    Formula:Newton's Second Law (F = ma)

    $F = ma$

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11. 11.

    Physics

    Calculate the potential energy of a 45 kg object at a height of 4 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    Quantitative Aptitude

    A invests AED 3,000 and B invests AED 4,000 for the same period. If the total profit is AED 30,000, find A's share.

    Formula:Partnership (profit share)

    $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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13. 13.

    Quantitative Aptitude

    What is 10% of 840?

    Formula:Percentage of a Number

    $\text{Value} = \dfrac{P}{100}\times N$

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14. 14.

    Physics

    A projectile is launched at 28 m/s at 30° to the horizontal. Find its range (g = 9.8 m/s²).

    Formula:Projectile Range

    $R = \dfrac{u^{2}\sin 2\theta}{g}$

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15. 15.

    Physics

    Calculate the potential energy of a 26 kg object at a height of 6 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    Physics

    Find the voltage across a 42 Ω resistor carrying a current of 4 A.

    Formula:Ohm's Law

    $V = IR$

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17. 17.

    Physics

    If 3,414 J of work is done in 15 s, find the power.

    Formula:Power

    $P = \dfrac{W}{t}$

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18. 18.

    Physics

    An object starts at 16 m/s and accelerates at 7 m/s² for 2 s. Find its final velocity.

    Formula:Equation of Motion (v = u + at)

    $v = u + at$

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19. 19.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 4?

    Formula:Probability (two dice)

    $P = \dfrac{\text{favourable}}{\text{total}}$

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20. 20.

    Physics

    Calculate the potential energy of a 36 kg object at a height of 37 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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