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TMUA · Practice Sheet 36

Sheet code: TMUA-S36 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Find the distance between the points (4, 3) and (8, -1).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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2.
Quantitative Aptitude
An item is bought for £500 and sold for £750. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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3.
Mathematics
In an arithmetic progression with first term 5 and common difference 10, find term number 7.
Formula:AP nth Term
$a_n = a + (n-1)d$
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4.
Quantitative Aptitude
A can finish a job in 16 days and B in 7 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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5.
Quantitative Aptitude
Two varieties costing £28 and £66 per kg are mixed to give a mixture worth £44 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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6.
Quantitative Aptitude
A invests £3,000 and B invests £9,000 for the same period. If the total profit is £30,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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7.
Quantitative Aptitude
A value changes from 200 to 120. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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8.
Quantitative Aptitude
The marked price of an item is £1,400. After a 5% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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9.
Quantitative Aptitude
Find the average of these 8 numbers: 52, 61, 57, 60, 87, 88, 54, 48.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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10.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 9?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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11.
Quantitative Aptitude
The marked price of an item is £2,000. After a 15% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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12.
Mathematics
Evaluate ∫ from 2 to 4 of 5x^2 dx.
Formula:Definite Integral of a Power
$\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$
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13.
Mathematics
In an arithmetic progression with first term 17 and common difference 10, find term number 7.
Formula:AP nth Term
$a_n = a + (n-1)d$
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14.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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15.
Quantitative Aptitude
A value changes from 800 to 560. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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16.
Mathematics
Find the sum of the first 3 terms of a GP with first term 4 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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17.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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18.
Quantitative Aptitude
Pipe A fills a tank in 9 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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19.
Quantitative Aptitude
A can finish a job in 20 days and B in 22 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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20.
Quantitative Aptitude
What is 50% of 680?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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