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TMUA · Practice Sheet 40

Sheet code: TMUA-S40 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    Find the distance between the points (2, -3) and (-6, -7).

    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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  2. 2.
    Mathematics

    Find the slope of the line through (-1, 3) 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

    The sum of the ages of two people is 65 years, and one is 9 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  4. 4.
    Quantitative Aptitude

    What is 15% of 820?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  5. 5.
    Quantitative Aptitude

    A value changes from 300 to 225. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  6. 6.
    Quantitative Aptitude

    A can finish a job in 4 days and B in 20 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  7. 7.
    Quantitative Aptitude

    The sum of the ages of two people is 78 years, and one is 18 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  8. 8.
    Mathematics

    Find the binomial coefficient C(8, 3) — the coefficient of x^3 in (1 + x)^8.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  9. 9.
    Mathematics

    Find the sum of the first 3 terms of a GP with first term 1 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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  10. 10.
    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 3.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  11. 11.
    Quantitative Aptitude

    The marked price of an item is £200. After a 40% discount, find the selling price.

    Formula:Discount & Selling Price
    SP=MP(1−d100)SP = MP\left(1-\dfrac{d}{100}\right)
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  12. 12.
    Mathematics

    Evaluate log base 10 of 1,000,000.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  13. 13.
    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 4.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  14. 14.
    Quantitative Aptitude

    An item is bought for £400 and sold for £520. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  15. 15.
    Mathematics

    Find term number 7 of a geometric progression with first term 4 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  16. 16.
    Quantitative Aptitude

    Find the HCF and LCM of 8 and 14.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  17. 17.
    Mathematics

    In an arithmetic progression with first term 5 and common difference 6, find term number 6.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  18. 18.
    Mathematics

    Find the sum of the first 3 terms of a GP with first term 2 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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  19. 19.
    Mathematics

    In an arithmetic progression with first term 19 and common difference 4, find term number 30.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  20. 20.
    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 2.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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