ACT · Practice Sheet 12

1. 1.

   Physics

   Find the kinetic energy of a 18 kg object moving at 24 m/s.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2}mv^{2}$

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2. 2.

   Physics

   Find the voltage across a 49 Ω resistor carrying a current of 19 A.

   Formula:Ohm's Law

   $V = IR$

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3. 3.

   Physics

   Find the kinetic energy of a 5 kg object moving at 24 m/s.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2}mv^{2}$

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4. 4.

   Physics

   A constant force of 198 N moves an object 20 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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5. 5.

   Mathematics

   In an arithmetic progression with first term 18 and common difference 6, find term number 12.

   Formula:AP nth Term

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

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6. 6.

   Quantitative Aptitude

   Find the simple interest on $8,000 at 5% per annum for 1 year(s).

   Formula:Simple Interest

   $SI = \dfrac{P\times R\times T}{100}$

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7. 7.

   Quantitative Aptitude

   The marked price of an item is $900. After a 5% discount, find the selling price.

   Formula:Discount & Selling Price

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

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8. 8.

   Physics

   Find the voltage across a 27 Ω resistor carrying a current of 4 A.

   Formula:Ohm's Law

   $V = IR$

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9. 9.

   Quantitative Aptitude

   A vehicle covers 639 km in 9 hours. Find its average speed.

   Formula:Speed, Distance & Time

   $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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10. 10.

    Mathematics

    Find the sum of the first 13 terms of an AP with first term 1 and common difference 4.

    Formula:AP Sum of n Terms

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

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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.

    Mathematics

    Find term number 4 of a geometric progression with first term 3 and common ratio 2.

    Formula:GP nth Term

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

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13. 13.

    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 3.)

    Formula:Permutations

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

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14. 14.

    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 3.)

    Formula:Combinations

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

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15. 15.

    Physics

    Find the voltage across a 43 Ω resistor carrying a current of 10 A.

    Formula:Ohm's Law

    $V = IR$

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16. 16.

    Mathematics

    Find term number 3 of a geometric progression with first term 6 and common ratio 2.

    Formula:GP nth Term

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

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17. 17.

    Mathematics

    Find the slope of the line through (8, -4) and (-1, 5).

    Formula:Slope of a Line

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

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18. 18.

    Quantitative Aptitude

    An item is bought for $200 and sold for $240. Find the profit percentage.

    Formula:Profit Percentage

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

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19. 19.

    Physics

    If 1,052 J of work is done in 3 s, find the power.

    Formula:Power

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

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20. 20.

    Physics

    Find the voltage across a 20 Ω resistor carrying a current of 16 A.

    Formula:Ohm's Law

    $V = IR$

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