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TMUA · Practice Sheet 2

Sheet code: TMUA-S02 · 20 questions

Name: ______________

Date: ______________

1.
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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2.
Quantitative Aptitude
Two varieties costing £14 and £64 per kg are mixed to give a mixture worth £59 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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3.
Quantitative Aptitude
An item is bought for £200 and sold for £230. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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4.
Mathematics
Evaluate log base 2 of 32.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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5.
Quantitative Aptitude
The sum of the ages of two people is 81 years, and one is 3 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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6.
Quantitative Aptitude
In how many ways can 4 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 4.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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7.
Quantitative Aptitude
Divide £553 between two people in the ratio 4:3. 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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8.
Mathematics
Find term number 5 of a geometric progression with first term 1 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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9.
Quantitative Aptitude
An item is bought for £500 and sold for £650. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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10.
Mathematics
Evaluate ∫ from 1 to 4 of 2x^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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11.
Mathematics
If f(x) = 4x³ + 1x² + 7x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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12.
Mathematics
For the quadratic 2x² − 2x − 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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13.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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14.
Mathematics
Find term number 6 of a geometric progression with first term 3 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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15.
Quantitative Aptitude
What is 25% of 440?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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16.
Quantitative Aptitude
Find the simple interest on £50,000 at 12% per annum for 3 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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17.
Quantitative Aptitude
Find the compound interest on £20,000 at 20% per annum compounded annually for 3 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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18.
Quantitative Aptitude
Find the HCF and LCM of 6 and 27.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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19.
Quantitative Aptitude
An item is bought for £800 and sold for £1,000. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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20.
Quantitative Aptitude
Divide £1,200 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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