ACT · Practice Sheet 36

1. 1.

   Physics

   Find the force required to accelerate a 39 kg mass at 13 m/s².

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

   $F = ma$

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2. 2.

   Physics

   An object starts at 8 m/s and accelerates at 2 m/s² for 8 s. Find its final velocity.

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

   $v = u + at$

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3. 3.

   Quantitative Aptitude

   A can finish a job in 20 days and B in 8 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

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4. 4.

   Physics

   Find the electrical power when 140 V drives a current of 7 A.

   Formula:Electrical Power

   $P = VI$

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5. 5.

   Physics

   A projectile is launched at 19 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

   A can finish a job in 15 days and B in 11 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

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7. 7.

   Physics

   A force of 589 N acts on an area of 37 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Quantitative Aptitude

   The sum of the ages of two people is 41 years, and one is 15 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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9. 9.

   Mathematics

   Find the slope of the line through (-1, 3) and (0, 4).

   Formula:Slope of a Line

   $m = \dfrac{y_2-y_1}{x_2-x_1}$

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10. 10.

    Quantitative Aptitude

    Find the HCF and LCM of 12 and 28.

    Formula:LCM & HCF

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

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11. 11.

    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 2.)

    Formula:Combinations

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

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12. 12.

    Physics

    A constant force of 192 N moves an object 31 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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13. 13.

    Quantitative Aptitude

    Find the compound interest on $6,000 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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14. 14.

    Quantitative Aptitude

    Divide $3,276 between two people in the ratio 7:6. 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 arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 3.)

    Formula:Permutations

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

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16. 16.

    Physics

    An object starts at 15 m/s and accelerates at 9 m/s² for 6 s. Find its final velocity.

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

    $v = u + at$

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17. 17.

    Physics

    Find the momentum of a 37 kg body moving at 12 m/s.

    Formula:Linear Momentum

    $p = mv$

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18. 18.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 10?

    Formula:Probability (two dice)

    $P = \dfrac{\text{favourable}}{\text{total}}$

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19. 19.

    Quantitative Aptitude

    What is 40% of 1,100?

    Formula:Percentage of a Number

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

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20. 20.

    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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