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ACT · Practice Sheet 29

Sheet code: ACT-S29 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 5?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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2.
Mathematics
Find the sum of the first 3 terms of a GP with first term 3 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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3.
Physics
Find the kinetic energy of a 16 kg object moving at 13 m/s.
Formula:Kinetic Energy
$KE = \tfrac{1}{2}mv^{2}$
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4.
Quantitative Aptitude
The marked price of an item is $1,500. After a 20% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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5.
Mathematics
Evaluate log base 10 of 10,000.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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6.
Physics
Find the electrical power when 103 V drives a current of 8 A.
Formula:Electrical Power
$P = VI$
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7.
Quantitative Aptitude
Find the simple interest on $21,000 at 4% per annum for 2 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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8.
Mathematics
For the quadratic 4x² − 7x + 8 = 0, find the sum and product of its roots.
Formula:Vieta's Formulas (roots)
$\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$
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9.
Quantitative Aptitude
A invests $5,000 and B invests $10,000 for the same period. If the total profit is $9,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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10.
Quantitative Aptitude
Find the simple interest on $36,000 at 12% per annum for 6 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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11.
Physics
A constant force of 44 N moves an object 45 m in the direction of the force. Calculate the work done.
Formula:Work Done
$W = F\,d$
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12.
Physics
Find the force required to accelerate a 21 kg mass at 7 m/s².
Formula:Newton's Second Law (F = ma)
$F = ma$
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13.
Quantitative Aptitude
A can finish a job in 18 days and B in 13 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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14.
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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15.
Mathematics
Find term number 6 of a geometric progression with first term 5 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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16.
Quantitative Aptitude
Pipe A fills a tank in 12 hours and pipe B in 8 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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17.
Quantitative Aptitude
Find the simple interest on $3,000 at 10% per annum for 2 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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18.
Quantitative Aptitude
In how many ways can 2 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 2.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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19.
Quantitative Aptitude
A can finish a job in 11 days and B in 10 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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20.
Quantitative Aptitude
A vehicle covers 469 km in 7 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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