Police & Armed Forces · Practice Sheet 4

1. 1.

   Physics

   If 754 J of work is done in 33 s, find the power.

   Formula:Power

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

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2. 2.

   Physics

   Calculate the potential energy of a 25 kg object at a height of 22 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   Physics

   If 1,162 J of work is done in 31 s, find the power.

   Formula:Power

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

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4. 4.

   Quantitative Aptitude

   A value changes from 400 to 440. Find the percentage increase.

   Formula:Percentage Change

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

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5. 5.

   Quantitative Aptitude

   Find the compound interest on AED 1,000 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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6. 6.

   Physics

   Find the momentum of a 13 kg body moving at 34 m/s.

   Formula:Linear Momentum

   $p = mv$

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7. 7.

   Quantitative Aptitude

   Find the compound interest on AED 2,000 at 20% per annum compounded annually for 3 years.

   Formula:Compound Interest

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

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8. 8.

   Quantitative Aptitude

   Pipe A fills a tank in 13 hours and pipe B in 10 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

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9. 9.

   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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10. 10.

    Physics

    A force of 140 N acts on an area of 50 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    Quantitative Aptitude

    The marked price of an item is AED 700. After a 25% discount, find the selling price.

    Formula:Discount & Selling Price

    $SP = MP\left(1-\dfrac{d}{100}\right)$

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12. 12.

    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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13. 13.

    Physics

    Find the force required to accelerate a 48 kg mass at 20 m/s².

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

    $F = ma$

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14. 14.

    Physics

    Find the kinetic energy of a 13 kg object moving at 6 m/s.

    Formula:Kinetic Energy

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

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15. 15.

    Physics

    A projectile is launched at 18 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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16. 16.

    Quantitative Aptitude

    A vehicle covers 621 km in 9 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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17. 17.

    Quantitative Aptitude

    Find the HCF and LCM of 27 and 11.

    Formula:LCM & HCF

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

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18. 18.

    Physics

    A constant force of 57 N moves an object 17 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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19. 19.

    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 2.)

    Formula:Combinations

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

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20. 20.

    Quantitative Aptitude

    An item is bought for AED 400 and sold for AED 600. Find the profit percentage.

    Formula:Profit Percentage

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

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