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TMUA · Practice Sheet 34

Sheet code: TMUA-S34 · 20 questions

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

    Two varieties costing £26 and £89 per kg are mixed to give a mixture worth £36 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)
    q1q2=p2−mm−p1\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}
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  2. 2.
    Mathematics

    Find the binomial coefficient C(6, 3) — the coefficient of x^3 in (1 + x)^6.

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

    Find the simple interest on £34,000 at 12% per annum for 5 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  4. 4.
    Quantitative Aptitude

    Find the average of these 10 numbers: 42, 39, 84, 87, 69, 78, 62, 65, 90, 84.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  5. 5.
    Quantitative Aptitude

    Pipe A fills a tank in 4 hours and pipe B in 15 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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  6. 6.
    Quantitative Aptitude

    Find the HCF and LCM of 32 and 17.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  7. 7.
    Mathematics

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

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
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  8. 8.
    Quantitative Aptitude

    What is 20% of 460?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  9. 9.
    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 4.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  10. 10.
    Quantitative Aptitude

    A vehicle covers 275 km in 5 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  11. 11.
    Mathematics

    Find the slope of the line through (-3, 0) and (-5, 7).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  12. 12.
    Mathematics

    Evaluate ∫ from 2 to 5 of 1x^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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  13. 13.
    Quantitative Aptitude

    Pipe A fills a tank in 11 hours and pipe B in 5 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.
    Mathematics

    In an arithmetic progression with first term 6 and common difference 3, find term number 22.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  15. 15.
    Mathematics

    For the quadratic 1x² − 1x − 9 = 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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  16. 16.
    Quantitative Aptitude

    An item is bought for £400 and sold for £500. 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

    The marked price of an item is £600. After a 25% 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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  18. 18.
    Quantitative Aptitude

    Divide £1,722 between two people in the ratio 4:2. 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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  19. 19.
    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 4.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  20. 20.
    Quantitative Aptitude

    Find the HCF and LCM of 21 and 7.

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