TMUA · Practice Sheet 3

1. 1.

   Quantitative Aptitude

   A invests £5,000 and B invests £10,000 for the same period. If the total profit is £31,000, find A's share.

   Formula:Partnership (profit share)

   $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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2. 2.

   Mathematics

   Find the slope of the line through (8, 1) and (0, -7).

   Formula:Slope of a Line

   $m = \dfrac{y_2-y_1}{x_2-x_1}$

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3. 3.

   Quantitative Aptitude

   An item is bought for £200 and sold for £280. Find the profit percentage.

   Formula:Profit Percentage

   $\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$

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4. 4.

   Mathematics

   Find the binomial coefficient C(5, 2) — the coefficient of x^2 in (1 + x)^5.

   Formula:Binomial Coefficient

   $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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5. 5.

   Mathematics

   Find the slope of the line through (-8, -3) and (-6, 3).

   Formula:Slope of a Line

   $m = \dfrac{y_2-y_1}{x_2-x_1}$

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6. 6.

   Mathematics

   Evaluate ∫ from 2 to 3 of 5x^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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7. 7.

   Quantitative Aptitude

   In how many ways can 2 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 2.)

   Formula:Permutations

   $^{n}P_{r} = \dfrac{n!}{(n-r)!}$

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8. 8.

   Quantitative Aptitude

   Two varieties costing £38 and £65 per kg are mixed to give a mixture worth £48 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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9. 9.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 2.)

   Formula:Combinations

   $^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$

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10. 10.

    Mathematics

    Evaluate ∫ from 0 to 4 of 1x^3 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. 11.

    Quantitative Aptitude

    A can finish a job in 14 days and B in 13 days. Working together, how long will they take?

    Formula:Time & Work (combined)

    $T = \dfrac{xy}{x+y}$

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12. 12.

    Mathematics

    In an arithmetic progression with first term 13 and common difference 1, find term number 24.

    Formula:AP nth Term

    $a_n = a + (n-1)d$

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13. 13.

    Mathematics

    Evaluate log base 3 of 243.

    Formula:Logarithm Evaluation

    $\log_{b}(b^{k}) = k$

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14. 14.

    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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15. 15.

    Quantitative Aptitude

    A can finish a job in 14 days and B in 10 days. Working together, how long will they take?

    Formula:Time & Work (combined)

    $T = \dfrac{xy}{x+y}$

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16. 16.

    Mathematics

    If f(x) = 5x³ + 4x² + 3x, find f′(2).

    Formula:Derivative of a Polynomial

    $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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17. 17.

    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 3.)

    Formula:Permutations

    $^{n}P_{r} = \dfrac{n!}{(n-r)!}$

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18. 18.

    Quantitative Aptitude

    A invests £2,000 and B invests £10,000 for the same period. If the total profit is £18,000, find A's share.

    Formula:Partnership (profit share)

    $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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19. 19.

    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 2.)

    Formula:Combinations

    $^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$

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20. 20.

    Quantitative Aptitude

    Find the compound interest on £10,000 at 20% per annum compounded annually for 2 years.

    Formula:Compound Interest

    $A = P\left(1+\dfrac{R}{100}\right)^{T}$

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