Police & Armed Forces · Practice Sheet 15

1. 1.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 8?

   Formula:Probability (two dice)

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

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2. 2.

   Physics

   Find the kinetic energy of a 16 kg object moving at 22 m/s.

   Formula:Kinetic Energy

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

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3. 3.

   Physics

   Find the electrical power when 13 V drives a current of 6 A.

   Formula:Electrical Power

   $P = VI$

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4. 4.

   Quantitative Aptitude

   In how many ways can 4 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 4.)

   Formula:Combinations

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

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5. 5.

   Quantitative Aptitude

   In how many ways can 4 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 4.)

   Formula:Permutations

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

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6. 6.

   Physics

   A constant force of 82 N moves an object 3 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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7. 7.

   Quantitative Aptitude

   Find the simple interest on AED 34,000 at 8% per annum for 5 year(s).

   Formula:Simple Interest

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

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8. 8.

   Quantitative Aptitude

   Find the compound interest on AED 9,000 at 10% per annum compounded annually for 2 years.

   Formula:Compound Interest

   $A = P\left(1+\dfrac{R}{100}\right)^{T}$

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9. 9.

   Quantitative Aptitude

   A vehicle covers 123 km in 3 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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10. 10.

    Physics

    If 110 J of work is done in 20 s, find the power.

    Formula:Power

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

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11. 11.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 8?

    Formula:Probability (two dice)

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

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12. 12.

    Quantitative Aptitude

    Two varieties costing AED 24 and AED 71 per kg are mixed to give a mixture worth AED 50 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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13. 13.

    Quantitative Aptitude

    A invests AED 5,000 and B invests AED 9,000 for the same period. If the total profit is AED 26,000, find A's share.

    Formula:Partnership (profit share)

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

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14. 14.

    Physics

    Find the momentum of a 12 kg body moving at 7 m/s.

    Formula:Linear Momentum

    $p = mv$

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15. 15.

    Physics

    A projectile is launched at 12 m/s at 45° 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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16. 16.

    Physics

    A constant force of 68 N moves an object 4 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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17. 17.

    Physics

    If 1,485 J of work is done in 30 s, find the power.

    Formula:Power

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

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18. 18.

    Physics

    Calculate the potential energy of a 43 kg object at a height of 14 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    Physics

    Find the electrical power when 75 V drives a current of 1 A.

    Formula:Electrical Power

    $P = VI$

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20. 20.

    Quantitative Aptitude

    Find the average of these 6 numbers: 59, 76, 71, 75, 30, 34.

    Formula:Arithmetic Mean

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

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