TMUA · Practice Sheet 11

1. 1.

   Quantitative Aptitude

   What is 15% of 340?

   Formula:Percentage of a Number

   $\text{Value} = \dfrac{P}{100}\times N$

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2. 2.

   Mathematics

   Find the sum of the first 3 terms of a GP with first term 2 and common ratio 3.

   Formula:GP Sum of n Terms

   $S_n = a\,\dfrac{r^{n}-1}{r-1}$

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3. 3.

   Quantitative Aptitude

   The sum of the ages of two people is 24 years, and one is 4 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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4. 4.

   Mathematics

   Find the sum of the first 11 terms of an AP with first term 10 and common difference 9.

   Formula:AP Sum of n Terms

   $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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5. 5.

   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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6. 6.

   Quantitative Aptitude

   What is 15% of 400?

   Formula:Percentage of a Number

   $\text{Value} = \dfrac{P}{100}\times N$

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7. 7.

   Quantitative Aptitude

   A invests £6,000 and B invests £4,000 for the same period. If the total profit is £32,000, find A's share.

   Formula:Partnership (profit share)

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

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8. 8.

   Mathematics

   Find the slope of the line through (2, -2) and (-6, -2).

   Formula:Slope of a Line

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

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9. 9.

   Mathematics

   In an arithmetic progression with first term 3 and common difference 10, find term number 21.

   Formula:AP nth Term

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

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10. 10.

    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 3.)

    Formula:Combinations

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

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11. 11.

    Mathematics

    Evaluate ∫ from 1 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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12. 12.

    Mathematics

    For the quadratic 3x² + 7x + 6 = 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. 13.

    Quantitative Aptitude

    A value changes from 200 to 180. Find the percentage decrease.

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$

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14. 14.

    Mathematics

    Find the slope of the line through (5, -1) and (7, -8).

    Formula:Slope of a Line

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

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15. 15.

    Mathematics

    Evaluate log base 2 of 16.

    Formula:Logarithm Evaluation

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

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16. 16.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 5?

    Formula:Probability (two dice)

    $P = \dfrac{\text{favourable}}{\text{total}}$

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17. 17.

    Mathematics

    Evaluate ∫ from 2 to 3 of 1x^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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18. 18.

    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 2.)

    Formula:Permutations

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

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19. 19.

    Quantitative Aptitude

    Find the average of these 10 numbers: 70, 33, 50, 49, 85, 80, 82, 57, 61, 47.

    Formula:Arithmetic Mean

    $\bar{x} = \dfrac{\sum x}{n}$

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20. 20.

    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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