ACT · Practice Sheet 35

1. 1.

   Physics

   If 3,673 J of work is done in 7 s, find the power.

   Formula:Power

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

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2. 2.

   Quantitative Aptitude

   In how many ways can 3 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 3.)

   Formula:Combinations

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

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3. 3.

   Quantitative Aptitude

   A invests $2,000 and B invests $2,000 for the same period. If the total profit is $20,000, find A's share.

   Formula:Partnership (profit share)

   $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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4. 4.

   Quantitative Aptitude

   Pipe A fills a tank in 11 hours and pipe B in 12 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. 5.

   Mathematics

   Find the sum of the first 20 terms of an AP with first term 16 and common difference 4.

   Formula:AP Sum of n Terms

   $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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6. 6.

   Physics

   A body moving at 7 m/s accelerates at 5 m/s² for 2 s. Find the distance travelled.

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

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

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7. 7.

   Mathematics

   In an arithmetic progression with first term 13 and common difference 7, find term number 24.

   Formula:AP nth Term

   $a_n = a + (n-1)d$

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8. 8.

   Mathematics

   Find the sum of the first 6 terms of a GP with first term 1 and common ratio 2.

   Formula:GP Sum of n Terms

   $S_n = a\,\dfrac{r^{n}-1}{r-1}$

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9. 9.

   Physics

   A force of 452 N acts on an area of 19 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    Quantitative Aptitude

    What is 25% of 1,160?

    Formula:Percentage of a Number

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

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11. 11.

    Quantitative Aptitude

    A can finish a job in 17 days and B in 9 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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12. 12.

    Quantitative Aptitude

    A value changes from 200 to 180. Find the percentage decrease.

    Formula:Percentage Change

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

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13. 13.

    Quantitative Aptitude

    What is 75% of 720?

    Formula:Percentage of a Number

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

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14. 14.

    Mathematics

    Find the sum of the first 5 terms of a GP with first term 6 and common ratio 2.

    Formula:GP Sum of n Terms

    $S_n = a\,\dfrac{r^{n}-1}{r-1}$

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15. 15.

    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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16. 16.

    Mathematics

    Find the sum of the first 23 terms of an AP with first term 4 and common difference 4.

    Formula:AP Sum of n Terms

    $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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17. 17.

    Physics

    Find the density of an object with mass 73 g and volume 6 cm³.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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18. 18.

    Physics

    Find the electrical power when 175 V drives a current of 14 A.

    Formula:Electrical Power

    $P = VI$

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19. 19.

    Mathematics

    Find the distance between the points (1, 5) and (2, 7).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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20. 20.

    Quantitative Aptitude

    What is 75% of 420?

    Formula:Percentage of a Number

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

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