GRE · Practice Sheet 48

1. 1.

   Mathematics

   If f(x) = 5x³ + 6x² + 7x, find f′(1).

   Formula:Derivative of a Polynomial

   $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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2. 2.

   Quantitative Aptitude

   The marked price of an item is $600. After a 25% discount, find the selling price.

   Formula:Discount & Selling Price

   $SP = MP\left(1-\dfrac{d}{100}\right)$

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3. 3.

   Quantitative Aptitude

   Find the HCF and LCM of 11 and 27.

   Formula:LCM & HCF

   $\text{LCM}\times\text{HCF} = a\times b$

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4. 4.

   Mathematics

   Find the sum of the first 20 terms of an AP with first term 14 and common difference 10.

   Formula:AP Sum of n Terms

   $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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5. 5.

   Mathematics

   For the quadratic 3x² + 7x − 2 = 0, find the sum and product of its roots.

   Formula:Vieta's Formulas (roots)

   $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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6. 6.

   Mathematics

   Find the sum of the first 7 terms of a GP with first term 3 and common ratio 2.

   Formula:GP Sum of n Terms

   $S_n = a\,\dfrac{r^{n}-1}{r-1}$

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7. 7.

   Mathematics

   In an arithmetic progression with first term 6 and common difference 7, find term number 16.

   Formula:AP nth Term

   $a_n = a + (n-1)d$

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8. 8.

   Mathematics

   Evaluate ∫ from 2 to 4 of 4x^3 dx.

   Formula:Definite Integral of a Power

   $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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9. 9.

   Quantitative Aptitude

   What is 25% of 200?

   Formula:Percentage of a Number

   $\text{Value} = \dfrac{P}{100}\times N$

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10. 10.

    Mathematics

    Find the distance between the points (-4, 7) and (-3, -4).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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11. 11.

    Quantitative Aptitude

    What is 25% of 140?

    Formula:Percentage of a Number

    $\text{Value} = \dfrac{P}{100}\times N$

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12. 12.

    Quantitative Aptitude

    An item is bought for $500 and sold for $700. Find the profit percentage.

    Formula:Profit Percentage

    $\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$

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13. 13.

    Quantitative Aptitude

    The sum of the ages of two people is 69 years, and one is 7 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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14. 14.

    Mathematics

    Find the distance between the points (1, -4) and (-5, -2).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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15. 15.

    Quantitative Aptitude

    A vehicle covers 462 km in 7 hours. Find its average speed.

    Formula:Speed, Distance & Time

    $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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16. 16.

    Mathematics

    Find the sum of the first 6 terms of a GP with first term 1 and common ratio 3.

    Formula:GP Sum of n Terms

    $S_n = a\,\dfrac{r^{n}-1}{r-1}$

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17. 17.

    Quantitative Aptitude

    Find the simple interest on $26,000 at 4% per annum for 5 year(s).

    Formula:Simple Interest

    $SI = \dfrac{P\times R\times T}{100}$

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18. 18.

    Quantitative Aptitude

    Find the compound interest on $20,000 at 20% per annum compounded annually for 3 years.

    Formula:Compound Interest

    $A = P\left(1+\dfrac{R}{100}\right)^{T}$

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19. 19.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 7?

    Formula:Probability (two dice)

    $P = \dfrac{\text{favourable}}{\text{total}}$

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20. 20.

    Quantitative Aptitude

    The marked price of an item is $1,500. After a 20% discount, find the selling price.

    Formula:Discount & Selling Price

    $SP = MP\left(1-\dfrac{d}{100}\right)$

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