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GRE · Practice Sheet 46

Sheet code: GRE-S46 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    Evaluate ∫ from 2 to 5 of 2x^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

    Find the distance between the points (8, 1) and (5, -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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  3. 3.
    Quantitative Aptitude

    An item is bought for $900 and sold for $1,350. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  4. 4.
    Quantitative Aptitude

    A invests $10,000 and B invests $5,000 for the same period. If the total profit is $8,000, 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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  5. 5.
    Mathematics

    Find term number 3 of a geometric progression with first term 4 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  6. 6.
    Mathematics

    Evaluate ∫ from 2 to 5 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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  7. 7.
    Quantitative Aptitude

    The sum of the ages of two people is 96 years, and one is 20 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

    An item is bought for $900 and sold for $1,125. 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.
    Mathematics

    Find the distance between the points (-8, -6) and (3, 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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  10. 10.
    Quantitative Aptitude

    Pipe A fills a tank in 15 hours and pipe B in 4 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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  11. 11.
    Quantitative Aptitude

    Find the compound interest on $3,000 at 10% per annum compounded annually for 2 years.

    Formula:Compound Interest
    A=P(1+R100)TA = P\left(1+\dfrac{R}{100}\right)^{T}
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  12. 12.
    Mathematics

    If f(x) = 2x³ + 1x² + 1x, 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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  13. 13.
    Quantitative Aptitude

    Find the HCF and LCM of 8 and 7.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  14. 14.
    Mathematics

    For the quadratic 4x² + 0x + 8 = 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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  15. 15.
    Quantitative Aptitude

    Two varieties costing $36 and $70 per kg are mixed to give a mixture worth $42 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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  16. 16.
    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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  17. 17.
    Mathematics

    Evaluate log base 10 of 100,000.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  18. 18.
    Quantitative Aptitude

    The sum of the ages of two people is 49 years, and one is 15 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  19. 19.
    Quantitative Aptitude

    Divide $1,008 between two people in the ratio 5:7. 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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  20. 20.
    Mathematics

    Find the sum of the first 19 terms of an AP with first term 17 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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