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Police & Armed Forces · Practice Sheet 3

Sheet code: UAE-POLICE-S03 · 20 questions

Name: ______________

Date: ______________

1.
Physics
A projectile is launched at 39 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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2.
Physics
Find the kinetic energy of a 9 kg object moving at 16 m/s.
Formula:Kinetic Energy
$KE = \tfrac{1}{2}mv^{2}$
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3.
Physics
Calculate the potential energy of a 16 kg object at a height of 40 m (g = 9.8 m/s²).
Formula:Gravitational Potential Energy
$PE = mgh$
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4.
Quantitative Aptitude
Pipe A fills a tank in 9 hours and pipe B in 7 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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5.
Physics
A constant force of 45 N moves an object 16 m in the direction of the force. Calculate the work done.
Formula:Work Done
$W = F\,d$
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6.
Quantitative Aptitude
Two varieties costing AED 35 and AED 91 per kg are mixed to give a mixture worth AED 86 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.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 7?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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8.
Quantitative Aptitude
A value changes from 900 to 450. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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9.
Physics
Find the force required to accelerate a 23 kg mass at 12 m/s².
Formula:Newton's Second Law (F = ma)
$F = ma$
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10.
Quantitative Aptitude
Divide AED 4,018 between two people in the ratio 7:7. 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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11.
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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12.
Quantitative Aptitude
A can finish a job in 18 days and B in 19 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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13.
Physics
Find the density of an object with mass 303 g and volume 18 cm³.
Formula:Density
$\rho = \dfrac{m}{V}$
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14.
Quantitative Aptitude
Pipe A fills a tank in 7 hours and pipe B in 13 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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15.
Quantitative Aptitude
Two varieties costing AED 18 and AED 98 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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16.
Physics
If 4,044 J of work is done in 20 s, find the power.
Formula:Power
$P = \dfrac{W}{t}$
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17.
Quantitative Aptitude
A invests AED 2,000 and B invests AED 3,000 for the same period. If the total profit is AED 14,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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18.
Quantitative Aptitude
Find the average of these 5 numbers: 80, 67, 80, 44, 75.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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19.
Quantitative Aptitude
What is 60% of 840?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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20.
Physics
If 3,379 J of work is done in 46 s, find the power.
Formula:Power
$P = \dfrac{W}{t}$
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