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CAT · Practice Sheet 15

Sheet code: CAT-S15 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    For the quadratic 5x² − 7x + 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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  2. 2.
    Mathematics

    Find the binomial coefficient C(8, 2) — the coefficient of x^2 in (1 + x)^8.

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

    Find the simple interest on ₹8,000 at 4% per annum for 1 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  4. 4.
    Quantitative Aptitude

    Divide ₹3,724 between two people in the ratio 7:7. 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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  5. 5.
    Mathematics

    Find the binomial coefficient C(5, 4) — the coefficient of x^4 in (1 + x)^5.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  6. 6.
    Quantitative Aptitude

    An item is bought for ₹700 and sold for ₹980. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  7. 7.
    Quantitative Aptitude

    The marked price of an item is ₹1,500. After a 25% 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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  8. 8.
    Mathematics

    Find the distance between the points (-2, 8) and (-2, -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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  9. 9.
    Mathematics

    Evaluate log base 10 of 1,000.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  10. 10.
    Quantitative Aptitude

    A value changes from 600 to 630. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  11. 11.
    Mathematics

    Find the sum of the first 13 terms of an AP with first term 6 and common difference 2.

    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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  12. 12.
    Mathematics

    Find term number 5 of a geometric progression with first term 6 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  13. 13.
    Quantitative Aptitude

    A invests ₹6,000 and B invests ₹9,000 for the same period. If the total profit is ₹17,000, 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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  14. 14.
    Mathematics

    Find term number 5 of a geometric progression with first term 6 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  15. 15.
    Quantitative Aptitude

    Two varieties costing ₹28 and ₹67 per kg are mixed to give a mixture worth ₹52 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 the binomial coefficient C(8, 3) — the coefficient of x^3 in (1 + x)^8.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  17. 17.
    Quantitative Aptitude

    Find the average of these 10 numbers: 50, 29, 33, 86, 58, 33, 48, 69, 78, 22.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  18. 18.
    Quantitative Aptitude

    Two varieties costing ₹24 and ₹61 per kg are mixed to give a mixture worth ₹56 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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  19. 19.
    Quantitative Aptitude

    A value changes from 700 to 525. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  20. 20.
    Quantitative Aptitude

    Find the average of these 10 numbers: 77, 53, 34, 52, 64, 51, 73, 53, 24, 72.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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