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TMUA · Practice Sheet 7

Sheet code: TMUA-S07 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Evaluate log base 5 of 625.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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2.
Mathematics
For the quadratic 1x² − 7x + 0 = 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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3.
Mathematics
Find the sum of the first 7 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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4.
Quantitative Aptitude
A can finish a job in 13 days and B in 16 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 £34 and £87 per kg are mixed to give a mixture worth £79 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.
Mathematics
In an arithmetic progression with first term 3 and common difference 6, find term number 26.
Formula:AP nth Term
$a_n = a + (n-1)d$
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7.
Mathematics
Find the binomial coefficient C(9, 2) — the coefficient of x^2 in (1 + x)^9.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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8.
Quantitative Aptitude
The marked price of an item is £1,600. After a 15% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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9.
Mathematics
Evaluate log base 2 of 32.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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10.
Quantitative Aptitude
Find the simple interest on £47,000 at 5% per annum for 2 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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11.
Mathematics
Find the binomial coefficient C(8, 3) — the coefficient of x^3 in (1 + x)^8.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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12.
Mathematics
In an arithmetic progression with first term 11 and common difference 4, find term number 28.
Formula:AP nth Term
$a_n = a + (n-1)d$
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13.
Quantitative Aptitude
The marked price of an item is £300. After a 15% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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14.
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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15.
Quantitative Aptitude
The sum of the ages of two people is 56 years, and one is 10 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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16.
Mathematics
Find the distance between the points (0, 6) and (-1, -8).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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17.
Quantitative Aptitude
Two varieties costing £32 and £69 per kg are mixed to give a mixture worth £45 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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18.
Mathematics
Find term number 7 of a geometric progression with first term 6 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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19.
Quantitative Aptitude
An item is bought for £600 and sold for £660. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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20.
Quantitative Aptitude
A value changes from 300 to 225. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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