Police & Armed Forces · Practice Sheet 28

1. 1.

   Quantitative Aptitude

   Pipe A fills a tank in 9 hours and pipe B in 3 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

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2. 2.

   Physics

   Find the momentum of a 10 kg body moving at 35 m/s.

   Formula:Linear Momentum

   $p = mv$

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3. 3.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 2.)

   Formula:Combinations

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

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4. 4.

   Physics

   A force of 123 N acts on an area of 35 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   Quantitative Aptitude

   A value changes from 600 to 510. Find the percentage decrease.

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$

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6. 6.

   Quantitative Aptitude

   Pipe A fills a tank in 8 hours and pipe B in 4 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

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7. 7.

   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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8. 8.

   Physics

   Find the density of an object with mass 391 g and volume 38 cm³.

   Formula:Density

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

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9. 9.

   Quantitative Aptitude

   Find the average of these 8 numbers: 37, 68, 51, 62, 27, 53, 89, 68.

   Formula:Arithmetic Mean

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

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10. 10.

    Quantitative Aptitude

    A can finish a job in 16 days and B in 14 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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11. 11.

    Physics

    Find the momentum of a 37 kg body moving at 31 m/s.

    Formula:Linear Momentum

    $p = mv$

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12. 12.

    Quantitative Aptitude

    Find the average of these 5 numbers: 72, 40, 45, 79, 52.

    Formula:Arithmetic Mean

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

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13. 13.

    Physics

    Find the voltage across a 7 Ω resistor carrying a current of 8 A.

    Formula:Ohm's Law

    $V = IR$

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14. 14.

    Quantitative Aptitude

    Two varieties costing AED 17 and AED 63 per kg are mixed to give a mixture worth AED 32 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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15. 15.

    Quantitative Aptitude

    What is 30% of 680?

    Formula:Percentage of a Number

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

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16. 16.

    Physics

    Find the force required to accelerate a 3 kg mass at 19 m/s².

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

    $F = ma$

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17. 17.

    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 2.)

    Formula:Permutations

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

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18. 18.

    Physics

    Find the momentum of a 2 kg body moving at 10 m/s.

    Formula:Linear Momentum

    $p = mv$

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19. 19.

    Physics

    Find the density of an object with mass 338 g and volume 13 cm³.

    Formula:Density

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

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20. 20.

    Physics

    A force of 189 N acts on an area of 41 m². Find the pressure.

    Formula:Pressure

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

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