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TMUA · Practice Sheet 30

Sheet code: TMUA-S30 · 20 questions

Name: ______________

Date: ______________

1.
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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2.
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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3.
Quantitative Aptitude
A vehicle covers 325 km in 5 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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4.
Quantitative Aptitude
Two varieties costing £10 and £76 per kg are mixed to give a mixture worth £50 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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5.
Mathematics
Find the slope of the line through (-2, 1) and (1, 7).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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6.
Mathematics
Find the binomial coefficient C(6, 2) — the coefficient of x^2 in (1 + x)^6.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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7.
Quantitative Aptitude
A invests £3,000 and B invests £4,000 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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8.
Mathematics
Find the binomial coefficient C(9, 3) — the coefficient of x^3 in (1 + x)^9.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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9.
Mathematics
Evaluate ∫ from 2 to 4 of 5x^1 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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10.
Quantitative Aptitude
Divide £1,672 between two people in the ratio 6:5. 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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11.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 7?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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12.
Quantitative Aptitude
A invests £6,000 and B invests £2,000 for the same period. If the total profit is £29,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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13.
Mathematics
Evaluate log base 10 of 100,000.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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14.
Quantitative Aptitude
The sum of the ages of two people is 50 years, and one is 2 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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15.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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16.
Quantitative Aptitude
Pipe A fills a tank in 5 hours and pipe B in 13 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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17.
Quantitative Aptitude
Find the HCF and LCM of 31 and 21.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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18.
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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19.
Mathematics
If f(x) = 2x³ + 4x² + 2x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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20.
Quantitative Aptitude
Find the simple interest on £7,000 at 6% per annum for 3 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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