GRE · Practice Sheet 17

1. 1.

   Quantitative Aptitude

   In how many ways can 3 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 3.)

   Formula:Combinations

   $^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$

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2. 2.

   Mathematics

   Find the distance between the points (3, -7) and (-6, -8).

   Formula:Distance Between Two Points

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

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3. 3.

   Quantitative Aptitude

   The sum of the ages of two people is 84 years, and one is 16 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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4. 4.

   Mathematics

   Evaluate ∫ from 0 to 5 of 1x^1 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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5. 5.

   Mathematics

   Find the distance between the points (-1, -4) and (-2, 3).

   Formula:Distance Between Two Points

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

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6. 6.

   Mathematics

   Evaluate log base 5 of 25.

   Formula:Logarithm Evaluation

   $\log_{b}(b^{k}) = k$

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7. 7.

   Quantitative Aptitude

   In how many ways can 3 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 3.)

   Formula:Combinations

   $^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$

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8. 8.

   Quantitative Aptitude

   Find the simple interest on $39,000 at 12% per annum for 4 year(s).

   Formula:Simple Interest

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

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9. 9.

   Quantitative Aptitude

   Find the HCF and LCM of 37 and 29.

   Formula:LCM & HCF

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

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10. 10.

    Mathematics

    Find the sum of the first 21 terms of an AP with first term 18 and common difference 10.

    Formula:AP Sum of n Terms

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

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11. 11.

    Mathematics

    Evaluate log base 5 of 15,625.

    Formula:Logarithm Evaluation

    $\log_{b}(b^{k}) = k$

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12. 12.

    Quantitative Aptitude

    Find the HCF and LCM of 27 and 31.

    Formula:LCM & HCF

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

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13. 13.

    Mathematics

    Find the slope of the line through (-2, 2) and (5, 3).

    Formula:Slope of a Line

    $m = \dfrac{y_2-y_1}{x_2-x_1}$

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14. 14.

    Quantitative Aptitude

    Find the HCF and LCM of 25 and 20.

    Formula:LCM & HCF

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

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15. 15.

    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 2.)

    Formula:Permutations

    $^{n}P_{r} = \dfrac{n!}{(n-r)!}$

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16. 16.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 6?

    Formula:Probability (two dice)

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

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17. 17.

    Quantitative Aptitude

    Pipe A fills a tank in 9 hours and pipe B in 7 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

    $T = \dfrac{xy}{x+y}$

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18. 18.

    Mathematics

    In an arithmetic progression with first term 12 and common difference 2, find term number 8.

    Formula:AP nth Term

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

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19. 19.

    Mathematics

    Evaluate ∫ from 2 to 4 of 2x^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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20. 20.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 9?

    Formula:Probability (two dice)

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

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