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TMUA · Practice Sheet 50

Sheet code: TMUA-S50 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
In an arithmetic progression with first term 18 and common difference 2, find term number 9.
Formula:AP nth Term
$a_n = a + (n-1)d$
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2.
Quantitative Aptitude
Divide £1,820 between two people in the ratio 6:4. How much does each receive?
Formula:Sharing in a Ratio
$\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$
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3.
Mathematics
In an arithmetic progression with first term 16 and common difference 3, find term number 27.
Formula:AP nth Term
$a_n = a + (n-1)d$
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4.
Quantitative Aptitude
The marked price of an item is £300. After a 25% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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5.
Mathematics
Find the sum of the first 23 terms of an AP with first term 15 and common difference 2.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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6.
Mathematics
If f(x) = 1x³ + 2x² + 7x, find f′(5).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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7.
Mathematics
For the quadratic 3x² − 7x − 1 = 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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8.
Quantitative Aptitude
Divide £3,000 between two people in the ratio 6:4. How much does each receive?
Formula:Sharing in a Ratio
$\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$
View formula →
9.
Quantitative Aptitude
The marked price of an item is £1,900. After a 5% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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10.
Quantitative Aptitude
A invests £8,000 and B invests £7,000 for the same period. If the total profit is £19,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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11.
Quantitative Aptitude
Pipe A fills a tank in 5 hours and pipe B in 6 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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12.
Mathematics
For the quadratic 3x² − 6x − 3 = 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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13.
Mathematics
Find the distance between the points (-8, -6) and (-8, 3).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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14.
Quantitative Aptitude
Pipe A fills a tank in 15 hours and pipe B in 14 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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15.
Quantitative Aptitude
Divide £2,160 between two people in the ratio 5:7. How much does each receive?
Formula:Sharing in a Ratio
$\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$
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16.
Quantitative Aptitude
A vehicle covers 108 km in 2 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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17.
Quantitative Aptitude
Pipe A fills a tank in 14 hours and pipe B in 15 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
View formula →
18.
Quantitative Aptitude
Divide £776 between two people in the ratio 6:2. How much does each receive?
Formula:Sharing in a Ratio
$\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$
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19.
Mathematics
Find the sum of the first 3 terms of a GP with first term 2 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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20.
Mathematics
Find the slope of the line through (8, 4) and (-8, 2).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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