View solutions
FormulaWon

TMUA · Practice Sheet 45

Sheet code: TMUA-S45 · 20 questions

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

    In how many ways can 3 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 3.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
    View formula →
  2. 2.
    Quantitative Aptitude

    Find the average of these 6 numbers: 56, 36, 60, 50, 46, 21.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
    View formula →
  3. 3.
    Quantitative Aptitude

    A value changes from 500 to 450. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
    View formula →
  4. 4.
    Mathematics

    Evaluate ∫ from 1 to 4 of 5x^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}
    View formula →
  5. 5.
    Quantitative Aptitude

    A vehicle covers 352 km in 8 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
    View formula →
  6. 6.
    Mathematics

    If f(x) = 2x³ + 6x² + 1x, find f′(2).

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
    View formula →
  7. 7.
    Mathematics

    Find the distance between the points (2, 3) and (-1, 2).

    Formula:Distance Between Two Points
    d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}
    View formula →
  8. 8.
    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}
    View formula →
  9. 9.
    Quantitative Aptitude

    Find the simple interest on £42,000 at 12% per annum for 3 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
    View formula →
  10. 10.
    Quantitative Aptitude

    An item is bought for £500 and sold for £650. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
    View formula →
  11. 11.
    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)!}
    View formula →
  12. 12.
    Quantitative Aptitude

    Find the average of these 6 numbers: 30, 39, 30, 33, 62, 36.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
    View formula →
  13. 13.
    Mathematics

    Find the distance between the points (-3, -4) and (-4, 8).

    Formula:Distance Between Two Points
    d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}
    View formula →
  14. 14.
    Quantitative Aptitude

    Pipe A fills a tank in 6 hours and pipe B in 7 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns
    T=xyx+yT = \dfrac{xy}{x+y}
    View formula →
  15. 15.
    Mathematics

    Evaluate ∫ from 2 to 4 of 2x^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}
    View formula →
  16. 16.
    Quantitative Aptitude

    A invests £3,000 and B invests £9,000 for the same period. If the total profit is £38,000, find A's share.

    Formula:Partnership (profit share)
    ShareA=Profit×AA+B\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}
    View formula →
  17. 17.
    Mathematics

    Find the sum of the first 5 terms of a GP with first term 6 and common ratio 2.

    Formula:GP Sum of n Terms
    Sn=a rn−1r−1S_n = a\,\dfrac{r^{n}-1}{r-1}
    View formula →
  18. 18.
    Mathematics

    Find the slope of the line through (2, 0) and (4, 7).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
    View formula →
  19. 19.
    Mathematics

    For the quadratic 3x² − 5x + 4 = 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}
    View formula →
  20. 20.
    Quantitative Aptitude

    Pipe A fills a tank in 4 hours and pipe B in 6 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns
    T=xyx+yT = \dfrac{xy}{x+y}
    View formula →

© FormulaWon — formulawon.app · Answers & step-by-step working available on the solutions sheet.

Go to full solutions for this sheet