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ACT · Practice Sheet 42

Sheet code: ACT-S42 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
A can finish a job in 20 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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2.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 8?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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3.
Quantitative Aptitude
Find the HCF and LCM of 25 and 9.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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4.
Physics
Find the force required to accelerate a 3 kg mass at 4 m/s².
Formula:Newton's Second Law (F = ma)
$F = ma$
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5.
Physics
An object starts at 1 m/s and accelerates at 8 m/s² for 4 s. Find its final velocity.
Formula:Equation of Motion (v = u + at)
$v = u + at$
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6.
Quantitative Aptitude
Find the simple interest on $2,000 at 4% per annum for 5 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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7.
Quantitative Aptitude
The marked price of an item is $1,500. After a 15% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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8.
Quantitative Aptitude
A invests $3,000 and B invests $3,000 for the same period. If the total profit is $33,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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9.
Mathematics
Find the slope of the line through (-7, 7) and (8, -8).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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10.
Quantitative Aptitude
An item is bought for $800 and sold for $1,200. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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11.
Mathematics
Find the sum of the first 7 terms of a GP with first term 3 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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12.
Quantitative Aptitude
The marked price of an item is $1,600. After a 50% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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13.
Physics
A projectile is launched at 22 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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14.
Physics
Find the momentum of a 46 kg body moving at 27 m/s.
Formula:Linear Momentum
$p = mv$
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15.
Mathematics
Find the sum of the first 5 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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16.
Quantitative Aptitude
Two varieties costing $26 and $95 per kg are mixed to give a mixture worth $82 per kg. Find the mixing ratio.
Formula:Alligation (Mixtures)
$\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$
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17.
Physics
A body moving at 12 m/s accelerates at 6 m/s² for 9 s. Find the distance travelled.
Formula:Equation of Motion (s = ut + ½at²)
$s = ut + \tfrac{1}{2}at^{2}$
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18.
Physics
An object starts at 2 m/s and accelerates at 2 m/s² for 10 s. Find its final velocity.
Formula:Equation of Motion (v = u + at)
$v = u + at$
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19.
Physics
A constant force of 11 N moves an object 13 m in the direction of the force. Calculate the work done.
Formula:Work Done
$W = F\,d$
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20.
Quantitative Aptitude
Pipe A fills a tank in 11 hours and pipe B in 3 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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