Police & Armed Forces · Practice Sheet 9

1. 1.

   Quantitative Aptitude

   Two varieties costing AED 37 and AED 63 per kg are mixed to give a mixture worth AED 42 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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2. 2.

   Quantitative Aptitude

   Find the HCF and LCM of 10 and 39.

   Formula:LCM & HCF

   $\text{LCM}\times\text{HCF} = a\times b$

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3. 3.

   Physics

   Find the electrical power when 237 V drives a current of 6 A.

   Formula:Electrical Power

   $P = VI$

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4. 4.

   Quantitative Aptitude

   Divide AED 2,016 between two people in the ratio 4:4. 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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5. 5.

   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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6. 6.

   Physics

   Find the density of an object with mass 391 g and volume 47 cm³.

   Formula:Density

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

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7. 7.

   Quantitative Aptitude

   Pipe A fills a tank in 14 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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8. 8.

   Quantitative Aptitude

   In how many ways can 4 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 4.)

   Formula:Permutations

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

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9. 9.

   Quantitative Aptitude

   Find the HCF and LCM of 8 and 20.

   Formula:LCM & HCF

   $\text{LCM}\times\text{HCF} = a\times b$

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10. 10.

    Physics

    A body moving at 10 m/s accelerates at 2 m/s² for 3 s. Find the distance travelled.

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

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

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11. 11.

    Quantitative Aptitude

    Two varieties costing AED 38 and AED 92 per kg are mixed to give a mixture worth AED 72 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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12. 12.

    Physics

    Calculate the potential energy of a 21 kg object at a height of 6 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Physics

    An object starts at 19 m/s and accelerates at 4 m/s² for 5 s. Find its final velocity.

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

    $v = u + at$

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14. 14.

    Quantitative Aptitude

    Divide AED 1,836 between two people in the ratio 3:6. 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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15. 15.

    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 3.)

    Formula:Combinations

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

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16. 16.

    Physics

    Calculate the potential energy of a 44 kg object at a height of 25 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Physics

    Find the momentum of a 2 kg body moving at 13 m/s.

    Formula:Linear Momentum

    $p = mv$

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18. 18.

    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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19. 19.

    Quantitative Aptitude

    Divide AED 666 between two people in the ratio 4:5. 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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20. 20.

    Quantitative Aptitude

    An item is bought for AED 900 and sold for AED 1,125. Find the profit percentage.

    Formula:Profit Percentage

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

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