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CAT · Practice Sheet 20

Sheet code: CAT-S20 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    Find the sum of the first 5 terms of a GP with first term 5 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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  2. 2.
    Mathematics

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

    A value changes from 500 to 650. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  4. 4.
    Quantitative Aptitude

    A invests ₹2,000 and B invests ₹2,000 for the same period. If the total profit is ₹27,000, 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.
    Quantitative Aptitude

    The marked price of an item is ₹300. After a 20% discount, find the selling price.

    Formula:Discount & Selling Price
    SP=MP(1−d100)SP = MP\left(1-\dfrac{d}{100}\right)
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  6. 6.
    Quantitative Aptitude

    What is 50% of 1,180?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  7. 7.
    Quantitative Aptitude

    A invests ₹9,000 and B invests ₹9,000 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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  8. 8.
    Quantitative Aptitude

    A vehicle covers 330 km in 6 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  9. 9.
    Quantitative Aptitude

    What is 25% of 660?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  10. 10.
    Quantitative Aptitude

    A can finish a job in 4 days and B in 7 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  11. 11.
    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 4.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  12. 12.
    Mathematics

    For the quadratic 2x² − 2x − 3 = 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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  13. 13.
    Mathematics

    Evaluate log base 10 of 100.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  14. 14.
    Mathematics

    Find the distance between the points (7, -2) and (4, 5).

    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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  15. 15.
    Mathematics

    In an arithmetic progression with first term 10 and common difference 7, find term number 16.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  16. 16.
    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 4.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  17. 17.
    Mathematics

    Find the sum of the first 6 terms of a GP with first term 2 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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  18. 18.
    Mathematics

    In an arithmetic progression with first term 4 and common difference 4, find term number 12.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  19. 19.
    Quantitative Aptitude

    A invests ₹9,000 and B invests ₹7,000 for the same period. If the total profit is ₹30,000, find A's share.

    Formula:Partnership (profit share)
    ShareA=Profit×AA+B\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}
    View formula →
  20. 20.
    Mathematics

    Find the sum of the first 5 terms of an AP with first term 12 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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