Practice NAT questions with answers and explanations.
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The common ratio is 3, so a₆ = 2 × 3⁵.
This equals 2 × 243 = 486.
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Substitute x = 5 into the function.
Then f(5) = 2(5) + 1 = 11.
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The three interior angles of every Euclidean triangle sum to 180°.
This is a fundamental angle property.
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Let total distance be 3d; time is d/30 + 2d/60 = d/15.
Average speed is 3d ÷ (d/15) = 45 km/h.
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The quadratic factors as (x - 2)(x - 3) = 0.
Therefore, x is 2 or 3.
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Travel time is 210 ÷ 70 = 3 hours.
Three hours after 8:00 a.m. is 11:00 a.m.
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Their closing speed is 20 + 25 = 45 km/h.
Time = 90 ÷ 45 = 2 hours.
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The path forms a right triangle with legs 5 and 12.
By Pythagoras, distance is √(25 + 144) = 13 km.
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The first part takes 2 hours and the second takes 1 hour.
The total travel time is 3 hours.
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The speed is 90 × 5/18 = 25 m/s, so total distance is 25 × 24 = 600 m.
Subtracting the train length gives a bridge length of 400 m.
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Downwind speed is 300 km/h and upwind speed is 200 km/h.
Wind speed is half their difference: 50 km/h.
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Subtract 7 from both sides of the equation.
This gives x = 19 - 7 = 12.
