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TMUA · Practice Sheet 4

Sheet code: TMUA-S04 · 20 questions

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

    A invests £4,000 and B invests £9,000 for the same period. If the total profit is £34,000, 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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  2. 2.
    Mathematics

    For the quadratic 1x² − 8x − 8 = 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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  3. 3.
    Quantitative Aptitude

    Divide £909 between two people in the ratio 4:5. 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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  4. 4.
    Quantitative Aptitude

    An item is bought for £300 and sold for £420. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  5. 5.
    Mathematics

    Find the distance between the points (4, -6) and (3, -6).

    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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  6. 6.
    Quantitative Aptitude

    Find the compound interest on £14,000 at 10% per annum compounded annually for 2 years.

    Formula:Compound Interest
    A=P(1+R100)TA = P\left(1+\dfrac{R}{100}\right)^{T}
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  7. 7.
    Quantitative Aptitude

    Two varieties costing £12 and £79 per kg are mixed to give a mixture worth £41 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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  8. 8.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 4?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  9. 9.
    Quantitative Aptitude

    Find the HCF and LCM of 29 and 37.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  10. 10.
    Quantitative Aptitude

    A can finish a job in 8 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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  11. 11.
    Mathematics

    Evaluate ∫ from 0 to 4 of 2x^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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  12. 12.
    Mathematics

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

    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.
    Mathematics

    Find term number 4 of a geometric progression with first term 6 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  14. 14.
    Quantitative Aptitude

    A vehicle covers 600 km in 8 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  15. 15.
    Quantitative Aptitude

    What is 25% of 780?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  16. 16.
    Quantitative Aptitude

    A value changes from 900 to 990. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  17. 17.
    Quantitative Aptitude

    What is 15% of 180?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  18. 18.
    Mathematics

    If f(x) = 3x³ + 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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  19. 19.
    Mathematics

    Evaluate log base 3 of 81.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  20. 20.
    Quantitative Aptitude

    The marked price of an item is £200. After a 10% 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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