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TMUA · Practice Sheet 44

Sheet code: TMUA-S44 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
A invests £3,000 and B invests £8,000 for the same period. If the total profit is £27,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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2.
Mathematics
Find the binomial coefficient C(7, 3) — the coefficient of x^3 in (1 + x)^7.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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3.
Mathematics
If f(x) = 5x³ + 2x² + 1x, find f′(3).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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4.
Mathematics
Find term number 6 of a geometric progression with first term 5 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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5.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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6.
Mathematics
Evaluate log base 5 of 3,125.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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7.
Mathematics
Find the binomial coefficient C(8, 4) — the coefficient of x^4 in (1 + x)^8.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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8.
Quantitative Aptitude
Divide £1,768 between two people in the ratio 4:4. 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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9.
Mathematics
Evaluate log base 3 of 243.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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10.
Mathematics
Find the slope of the line through (-7, 1) and (-1, 2).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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11.
Quantitative Aptitude
Find the simple interest on £35,000 at 8% per annum for 2 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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12.
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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13.
Quantitative Aptitude
Find the HCF and LCM of 25 and 26.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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14.
Quantitative Aptitude
The marked price of an item is £1,000. After a 40% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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15.
Quantitative Aptitude
An item is bought for £200 and sold for £300. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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16.
Mathematics
Find the distance between the points (-4, -7) and (-7, -7).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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17.
Quantitative Aptitude
In how many ways can 4 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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18.
Quantitative Aptitude
A invests £2,000 and B invests £9,000 for the same period. If the total profit is £11,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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19.
Mathematics
For the quadratic 4x² − 7x − 2 = 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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20.
Quantitative Aptitude
Find the HCF and LCM of 18 and 6.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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