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11+ · Practice Sheet 49

Sheet code: ELEVEN-PLUS-S49 · 20 questions

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

    In how many ways can 2 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 2.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  2. 2.
    Mathematics

    Find the distance between the points (5, -3) and (-2, -7).

    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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  3. 3.
    Quantitative Aptitude

    What is 10% of 1,180?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  4. 4.
    Mathematics

    For the quadratic 3x² − 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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  5. 5.
    Mathematics

    Find the distance between the points (1, 8) and (-6, 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.
    Mathematics

    Find term number 6 of a geometric progression with first term 5 and common ratio 3.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  7. 7.
    Mathematics

    Find the binomial coefficient C(7, 3) — the coefficient of x^3 in (1 + x)^7.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  8. 8.
    Mathematics

    Find the distance between the points (-5, -3) and (8, -4).

    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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  9. 9.
    Mathematics

    Find the binomial coefficient C(8, 2) — the coefficient of x^2 in (1 + x)^8.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  10. 10.
    Quantitative Aptitude

    Find the HCF and LCM of 7 and 17.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  11. 11.
    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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  12. 12.
    Mathematics

    Evaluate log base 2 of 4.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  13. 13.
    Mathematics

    Find the sum of the first 6 terms of a GP with first term 4 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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  14. 14.
    Quantitative Aptitude

    Find the average of these 6 numbers: 21, 51, 90, 77, 76, 55.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  15. 15.
    Mathematics

    Evaluate log base 5 of 625.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  16. 16.
    Quantitative Aptitude

    Find the HCF and LCM of 34 and 11.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  17. 17.
    Mathematics

    Find the binomial coefficient C(10, 4) — the coefficient of x^4 in (1 + x)^10.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  18. 18.
    Quantitative Aptitude

    Pipe A fills a tank in 8 hours and pipe B in 11 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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  19. 19.
    Mathematics

    Find the sum of the first 17 terms of an AP with first term 15 and common difference 5.

    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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  20. 20.
    Mathematics

    For the quadratic 3x² − 7x + 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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