Police & Armed Forces · Practice Sheet 45

1. 1.

   Quantitative Aptitude

   An item is bought for AED 800 and sold for AED 1,120. Find the profit percentage.

   Formula:Profit Percentage

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

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2. 2.

   Physics

   Find the voltage across a 7 Ω resistor carrying a current of 16 A.

   Formula:Ohm's Law

   $V = IR$

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3. 3.

   Quantitative Aptitude

   In how many ways can 4 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 4.)

   Formula:Permutations

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

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4. 4.

   Quantitative Aptitude

   What is 15% of 400?

   Formula:Percentage of a Number

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

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5. 5.

   Physics

   A projectile is launched at 21 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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6. 6.

   Quantitative Aptitude

   Two varieties costing AED 30 and AED 74 per kg are mixed to give a mixture worth AED 45 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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7. 7.

   Physics

   A constant force of 110 N moves an object 48 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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8. 8.

   Quantitative Aptitude

   The sum of the ages of two people is 83 years, and one is 9 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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9. 9.

   Physics

   An object starts at 11 m/s and accelerates at 7 m/s² for 4 s. Find its final velocity.

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

   $v = u + at$

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10. 10.

    Physics

    A force of 122 N acts on an area of 18 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    Physics

    A constant force of 132 N moves an object 24 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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12. 12.

    Physics

    Calculate the potential energy of a 43 kg object at a height of 13 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Physics

    A projectile is launched at 41 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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14. 14.

    Physics

    A body moving at 1 m/s accelerates at 2 m/s² for 6 s. Find the distance travelled.

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

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

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15. 15.

    Physics

    Find the force required to accelerate a 35 kg mass at 14 m/s².

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

    $F = ma$

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16. 16.

    Quantitative Aptitude

    Find the compound interest on AED 1,000 at 20% per annum compounded annually for 2 years.

    Formula:Compound Interest

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

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17. 17.

    Physics

    Find the momentum of a 46 kg body moving at 28 m/s.

    Formula:Linear Momentum

    $p = mv$

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18. 18.

    Quantitative Aptitude

    The marked price of an item is AED 400. After a 40% discount, find the selling price.

    Formula:Discount & Selling Price

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

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19. 19.

    Quantitative Aptitude

    Two varieties costing AED 23 and AED 95 per kg are mixed to give a mixture worth AED 34 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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20. 20.

    Quantitative Aptitude

    Find the average of these 5 numbers: 22, 26, 47, 42, 70.

    Formula:Arithmetic Mean

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

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