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TMUA · Practice Sheet 48

Sheet code: TMUA-S48 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Quantitative Aptitude

    Divide £660 between two people in the ratio 6:5. How much does each receive?

    Formula:Sharing in a Ratio
    Share=Total×partsum of parts\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}
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  2. 2.
    Mathematics

    Find the slope of the line through (-3, 2) and (6, -2).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  3. 3.
    Quantitative Aptitude

    A invests £9,000 and B invests £6,000 for the same period. If the total profit is £19,000, find A's share.

    Formula:Partnership (profit share)
    ShareA=Profit×AA+B\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}
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  4. 4.
    Quantitative Aptitude

    A value changes from 400 to 380. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  5. 5.
    Quantitative Aptitude

    An item is bought for £700 and sold for £805. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  6. 6.
    Quantitative Aptitude

    A value changes from 700 to 350. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  7. 7.
    Mathematics

    Find term number 5 of a geometric progression with first term 2 and common ratio 3.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  8. 8.
    Mathematics

    Find the sum of the first 6 terms of an AP with first term 18 and common difference 5.

    Formula:AP Sum of n Terms
    Sn=n2 [2a+(n−1)d]S_n = \dfrac{n}{2}\,[2a+(n-1)d]
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  9. 9.
    Mathematics

    Evaluate ∫ from 0 to 3 of 2x^3 dx.

    Formula:Definite Integral of a Power
    ∫pqaxn dx=an+1[xn+1]pq\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}
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  10. 10.
    Mathematics

    Find the distance between the points (6, 7) and (3, 1).

    Formula:Distance Between Two Points
    d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}
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  11. 11.
    Mathematics

    Find the binomial coefficient C(10, 2) — the coefficient of x^2 in (1 + x)^10.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  12. 12.
    Mathematics

    Find the sum of the first 3 terms of a GP with first term 5 and common ratio 2.

    Formula:GP Sum of n Terms
    Sn=a rn−1r−1S_n = a\,\dfrac{r^{n}-1}{r-1}
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  13. 13.
    Quantitative Aptitude

    Pipe A fills a tank in 15 hours and pipe B in 6 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns
    T=xyx+yT = \dfrac{xy}{x+y}
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  14. 14.
    Quantitative Aptitude

    A value changes from 200 to 240. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  15. 15.
    Quantitative Aptitude

    The sum of the ages of two people is 41 years, and one is 5 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  16. 16.
    Quantitative Aptitude

    An item is bought for £400 and sold for £600. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  17. 17.
    Quantitative Aptitude

    A can finish a job in 11 days and B in 13 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  18. 18.
    Quantitative Aptitude

    The sum of the ages of two people is 88 years, and one is 12 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  19. 19.
    Mathematics

    Evaluate ∫ from 1 to 4 of 4x^2 dx.

    Formula:Definite Integral of a Power
    ∫pqaxn dx=an+1[xn+1]pq\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}
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  20. 20.
    Quantitative Aptitude

    Pipe A fills a tank in 6 hours and pipe B in 8 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns
    T=xyx+yT = \dfrac{xy}{x+y}
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