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TMUA · Practice Sheet 31

Sheet code: TMUA-S31 · 20 questions

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

    Two fair dice are rolled. What is the probability that the sum of the numbers is 8?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  2. 2.
    Mathematics

    In an arithmetic progression with first term 14 and common difference 10, find term number 13.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  3. 3.
    Quantitative Aptitude

    A invests £3,000 and B invests £6,000 for the same period. If the total profit is £26,000, 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

    Find the simple interest on £22,000 at 12% per annum for 6 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  5. 5.
    Mathematics

    Find the distance between the points (-8, 6) and (2, 8).

    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.
    Mathematics

    Evaluate ∫ from 2 to 4 of 1x^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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  7. 7.
    Mathematics

    Find term number 7 of a geometric progression with first term 5 and common ratio 2.

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

    An item is bought for £600 and sold for £750. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  9. 9.
    Quantitative Aptitude

    A value changes from 400 to 340. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  10. 10.
    Quantitative Aptitude

    A vehicle covers 375 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

    For the quadratic 5x² − 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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  12. 12.
    Mathematics

    Evaluate ∫ from 0 to 3 of 3x^1 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

    A value changes from 600 to 780. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  14. 14.
    Quantitative Aptitude

    Find the compound interest on £1,000 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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  15. 15.
    Quantitative Aptitude

    An item is bought for £600 and sold for £900. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  16. 16.
    Mathematics

    In an arithmetic progression with first term 13 and common difference 1, find term number 20.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  17. 17.
    Mathematics

    Find the slope of the line through (-2, -5) and (-3, 0).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  18. 18.
    Mathematics

    Find the sum of the first 25 terms of an AP with first term 16 and common difference 4.

    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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  19. 19.
    Quantitative Aptitude

    Find the average of these 5 numbers: 45, 52, 43, 34, 61.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  20. 20.
    Mathematics

    Evaluate ∫ from 1 to 5 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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