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CAT · Practice Sheet 41

Sheet code: CAT-S41 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Quantitative Aptitude

    An item is bought for ₹500 and sold for ₹750. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  2. 2.
    Mathematics

    Find the binomial coefficient C(6, 3) — the coefficient of x^3 in (1 + x)^6.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  3. 3.
    Quantitative Aptitude

    What is 50% of 980?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  4. 4.
    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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  5. 5.
    Quantitative Aptitude

    A can finish a job in 7 days and B in 15 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  6. 6.
    Quantitative Aptitude

    A value changes from 900 to 1,260. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  7. 7.
    Mathematics

    Find term number 5 of a geometric progression with first term 2 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  8. 8.
    Mathematics

    Evaluate log base 10 of 1,000.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  9. 9.
    Quantitative Aptitude

    A can finish a job in 7 days and B in 16 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  10. 10.
    Quantitative Aptitude

    Pipe A fills a tank in 10 hours and pipe B in 12 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.
    Mathematics

    Find the distance between the points (0, 1) and (-8, -3).

    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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  12. 12.
    Quantitative Aptitude

    A value changes from 200 to 260. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  13. 13.
    Quantitative Aptitude

    What is 15% of 260?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  14. 14.
    Quantitative Aptitude

    Find the simple interest on ₹50,000 at 10% per annum for 4 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  15. 15.
    Mathematics

    For the quadratic 1x² + 5x + 6 = 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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  16. 16.
    Mathematics

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

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  17. 17.
    Quantitative Aptitude

    Find the simple interest on ₹10,000 at 12% per annum for 4 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  18. 18.
    Mathematics

    Evaluate log base 5 of 3,125.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  19. 19.
    Mathematics

    Find the sum of the first 17 terms of an AP with first term 14 and common difference 10.

    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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  20. 20.
    Mathematics

    Find the sum of the first 4 terms of a GP with first term 6 and common ratio 2.

    Formula:GP Sum of n Terms
    Sn=a rn−1r−1S_n = a\,\dfrac{r^{n}-1}{r-1}
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