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TMUA · Practice Sheet 13

Sheet code: TMUA-S13 · 20 questions

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

    Divide £2,952 between two people in the ratio 6:6. 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 binomial coefficient C(5, 3) — the coefficient of x^3 in (1 + x)^5.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  3. 3.
    Quantitative Aptitude

    A invests £5,000 and B invests £9,000 for the same period. If the total profit is £21,000, 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.
    Mathematics

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

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  5. 5.
    Mathematics

    Find the sum of the first 14 terms of an AP with first term 6 and common difference 3.

    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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  6. 6.
    Quantitative Aptitude

    A vehicle covers 132 km in 2 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  7. 7.
    Quantitative Aptitude

    Divide £3,835 between two people in the ratio 7:6. 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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  8. 8.
    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 4.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  9. 9.
    Mathematics

    If f(x) = 1x³ + 6x² + 3x, find f′(3).

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
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  10. 10.
    Mathematics

    For the quadratic 4x² − 8x − 2 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)
    α+β=−ba,  αβ=ca\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}
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  11. 11.
    Quantitative Aptitude

    The marked price of an item is £1,900. After a 20% 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.
    Quantitative Aptitude

    The sum of the ages of two people is 51 years, and one is 3 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  13. 13.
    Mathematics

    Evaluate log base 5 of 3,125.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  14. 14.
    Mathematics

    Find the sum of the first 7 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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  15. 15.
    Quantitative Aptitude

    A invests £10,000 and B invests £2,000 for the same period. If the total profit is £30,000, 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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  16. 16.
    Mathematics

    Find the sum of the first 13 terms of an AP with first term 3 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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  17. 17.
    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 3.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  18. 18.
    Quantitative Aptitude

    Find the compound interest on £6,000 at 10% per annum compounded annually for 3 years.

    Formula:Compound Interest
    A=P(1+R100)TA = P\left(1+\dfrac{R}{100}\right)^{T}
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  19. 19.
    Mathematics

    Find the distance between the points (-8, 3) and (-3, 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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  20. 20.
    Mathematics

    Evaluate log base 10 of 100,000.

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