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GRE · Practice Sheet 41

Sheet code: GRE-S41 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    Evaluate ∫ from 2 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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  2. 2.
    Mathematics

    If f(x) = 3x³ + 4x² + 3x, find f′(5).

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
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  3. 3.
    Quantitative Aptitude

    What is 15% of 480?

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

    In an arithmetic progression with first term 6 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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  5. 5.
    Mathematics

    Find the sum of the first 12 terms of an AP with first term 5 and common difference 7.

    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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  6. 6.
    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 2.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  7. 7.
    Mathematics

    Find the distance between the points (8, 0) and (5, 1).

    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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  8. 8.
    Mathematics

    Find the sum of the first 4 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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  9. 9.
    Quantitative Aptitude

    A invests $8,000 and B invests $3,000 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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  10. 10.
    Quantitative Aptitude

    An item is bought for $200 and sold for $230. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  11. 11.
    Quantitative Aptitude

    What is 10% of 380?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  12. 12.
    Mathematics

    Find term number 7 of a geometric progression with first term 4 and common ratio 3.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  13. 13.
    Quantitative Aptitude

    A invests $4,000 and B invests $10,000 for the same period. If the total profit is $28,000, 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

    Find term number 7 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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  15. 15.
    Quantitative Aptitude

    Find the average of these 10 numbers: 61, 41, 82, 74, 45, 77, 84, 22, 52, 29.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  16. 16.
    Quantitative Aptitude

    Two varieties costing $19 and $77 per kg are mixed to give a mixture worth $52 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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  17. 17.
    Mathematics

    Evaluate ∫ from 0 to 5 of 1x^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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  18. 18.
    Quantitative Aptitude

    Find the compound interest on $7,000 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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  19. 19.
    Quantitative Aptitude

    A value changes from 200 to 120. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  20. 20.
    Mathematics

    For the quadratic 1x² − 9x − 5 = 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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