Police & Armed Forces · Practice Sheet 38

1. 1.

   Quantitative Aptitude

   In how many ways can 4 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 4.)

   Formula:Combinations

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

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2. 2.

   Physics

   A constant force of 14 N moves an object 25 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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3. 3.

   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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4. 4.

   Physics

   If 2,504 J of work is done in 2 s, find the power.

   Formula:Power

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

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5. 5.

   Physics

   Find the momentum of a 19 kg body moving at 25 m/s.

   Formula:Linear Momentum

   $p = mv$

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6. 6.

   Physics

   Find the electrical power when 192 V drives a current of 16 A.

   Formula:Electrical Power

   $P = VI$

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7. 7.

   Quantitative Aptitude

   Divide AED 2,150 between two people in the ratio 6:4. How much does each receive?

   Formula:Sharing in a Ratio

   $\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$

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8. 8.

   Quantitative Aptitude

   A can finish a job in 13 days and B in 5 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

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9. 9.

   Quantitative Aptitude

   In how many ways can 3 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 3.)

   Formula:Permutations

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

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10. 10.

    Physics

    A constant force of 199 N moves an object 41 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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11. 11.

    Physics

    Find the force required to accelerate a 22 kg mass at 15 m/s².

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

    $F = ma$

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12. 12.

    Physics

    A projectile is launched at 22 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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13. 13.

    Physics

    Find the density of an object with mass 362 g and volume 22 cm³.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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14. 14.

    Physics

    A force of 553 N acts on an area of 25 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    Physics

    If 2,539 J of work is done in 17 s, find the power.

    Formula:Power

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

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16. 16.

    Physics

    A force of 751 N acts on an area of 40 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Quantitative Aptitude

    A vehicle covers 264 km in 3 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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18. 18.

    Physics

    A projectile is launched at 48 m/s at 60° 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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19. 19.

    Quantitative Aptitude

    What is 15% of 80?

    Formula:Percentage of a Number

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

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20. 20.

    Physics

    Find the electrical power when 93 V drives a current of 3 A.

    Formula:Electrical Power

    $P = VI$

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