Police & Armed Forces · Practice Sheet 44

1. 1.

   Physics

   Find the kinetic energy of a 8 kg object moving at 21 m/s.

   Formula:Kinetic Energy

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

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2. 2.

   Physics

   An object starts at 6 m/s and accelerates at 6 m/s² for 12 s. Find its final velocity.

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

   $v = u + at$

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3. 3.

   Physics

   A body moving at 1 m/s accelerates at 5 m/s² for 5 s. Find the distance travelled.

   Formula:Equation of Motion (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^{2}$

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4. 4.

   Physics

   A force of 190 N acts on an area of 11 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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5. 5.

   Quantitative Aptitude

   In how many ways can 3 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 3.)

   Formula:Permutations

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

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6. 6.

   Quantitative Aptitude

   In how many ways can 3 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 3.)

   Formula:Combinations

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

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7. 7.

   Quantitative Aptitude

   The sum of the ages of two people is 42 years, and one is 12 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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8. 8.

   Quantitative Aptitude

   Two varieties costing AED 37 and AED 77 per kg are mixed to give a mixture worth AED 49 per kg. Find the mixing ratio.

   Formula:Alligation (Mixtures)

   $\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$

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9. 9.

   Quantitative Aptitude

   A can finish a job in 12 days and B in 8 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

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10. 10.

    Quantitative Aptitude

    Find the average of these 5 numbers: 68, 30, 90, 20, 32.

    Formula:Arithmetic Mean

    $\bar{x} = \dfrac{\sum x}{n}$

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11. 11.

    Physics

    Find the momentum of a 15 kg body moving at 12 m/s.

    Formula:Linear Momentum

    $p = mv$

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12. 12.

    Physics

    If 1,138 J of work is done in 45 s, find the power.

    Formula:Power

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

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13. 13.

    Physics

    Find the voltage across a 24 Ω resistor carrying a current of 1 A.

    Formula:Ohm's Law

    $V = IR$

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14. 14.

    Quantitative Aptitude

    A vehicle covers 424 km in 8 hours. Find its average speed.

    Formula:Speed, Distance & Time

    $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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15. 15.

    Quantitative Aptitude

    Find the average of these 5 numbers: 87, 64, 89, 51, 87.

    Formula:Arithmetic Mean

    $\bar{x} = \dfrac{\sum x}{n}$

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16. 16.

    Physics

    If 221 J of work is done in 6 s, find the power.

    Formula:Power

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

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17. 17.

    Physics

    A constant force of 89 N moves an object 39 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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18. 18.

    Quantitative Aptitude

    Find the simple interest on AED 13,000 at 12% per annum for 2 year(s).

    Formula:Simple Interest

    $SI = \dfrac{P\times R\times T}{100}$

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19. 19.

    Physics

    Find the momentum of a 31 kg body moving at 28 m/s.

    Formula:Linear Momentum

    $p = mv$

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20. 20.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 10?

    Formula:Probability (two dice)

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

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