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TMUA · Practice Sheet 23

Sheet code: TMUA-S23 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 10?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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2.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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3.
Quantitative Aptitude
The sum of the ages of two people is 56 years, and one is 18 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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4.
Quantitative Aptitude
Two varieties costing £40 and £73 per kg are mixed to give a mixture worth £49 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
If f(x) = 1x³ + 3x² + 3x, find f′(4).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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6.
Mathematics
Evaluate ∫ from 2 to 3 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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7.
Quantitative Aptitude
A value changes from 500 to 300. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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8.
Mathematics
Evaluate log base 3 of 729.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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9.
Mathematics
Find the sum of the first 23 terms of an AP with first term 8 and common difference 10.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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10.
Quantitative Aptitude
A value changes from 900 to 765. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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11.
Quantitative Aptitude
The marked price of an item is £400. After a 25% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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12.
Mathematics
Find term number 5 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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13.
Quantitative Aptitude
Find the compound interest on £15,000 at 10% per annum compounded annually for 3 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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14.
Quantitative Aptitude
Pipe A fills a tank in 13 hours and pipe B in 15 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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15.
Quantitative Aptitude
A can finish a job in 20 days and B in 5 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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16.
Mathematics
Evaluate ∫ from 2 to 5 of 3x^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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17.
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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18.
Mathematics
For the quadratic 1x² − 9x + 4 = 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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19.
Mathematics
Find the slope of the line through (-2, -6) and (0, -1).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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20.
Quantitative Aptitude
In how many ways can 4 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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