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11+ · Practice Sheet 44

Sheet code: ELEVEN-PLUS-S44 · 20 questions

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

    A vehicle covers 180 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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  2. 2.
    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 2.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  3. 3.
    Mathematics

    In an arithmetic progression with first term 16 and common difference 2, find term number 18.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  4. 4.
    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 2.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  5. 5.
    Mathematics

    For the quadratic 1x² + 2x − 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}
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  6. 6.
    Quantitative Aptitude

    A vehicle covers 112 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

    The sum of the ages of two people is 76 years, and one is 6 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  8. 8.
    Quantitative Aptitude

    A can finish a job in 4 days and B in 18 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  9. 9.
    Quantitative Aptitude

    A invests £7,000 and B invests £3,000 for the same period. If the total profit is £6,000, 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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  10. 10.
    Mathematics

    Evaluate log base 5 of 25.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  11. 11.
    Quantitative Aptitude

    Find the HCF and LCM of 20 and 25.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  12. 12.
    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 2.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
    View formula →
  13. 13.
    Quantitative Aptitude

    A invests £4,000 and B invests £9,000 for the same period. If the total profit is £13,000, 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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  14. 14.
    Mathematics

    In an arithmetic progression with first term 11 and common difference 8, find term number 21.

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

    Divide £1,328 between two people in the ratio 5:3. 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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  16. 16.
    Quantitative Aptitude

    The marked price of an item is £1,600. After a 40% 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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  17. 17.
    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 3.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  18. 18.
    Quantitative Aptitude

    The marked price of an item is £200. After a 50% 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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  19. 19.
    Quantitative Aptitude

    Find the simple interest on £16,000 at 12% per annum for 4 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  20. 20.
    Quantitative Aptitude

    Two varieties costing £20 and £86 per kg are mixed to give a mixture worth £54 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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