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CAT · Practice Sheet 37

Sheet code: CAT-S37 · 20 questions

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

    Two varieties costing ₹20 and ₹70 per kg are mixed to give a mixture worth ₹63 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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  2. 2.
    Mathematics

    Find the sum of the first 19 terms of an AP with first term 16 and common difference 7.

    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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  3. 3.
    Quantitative Aptitude

    A value changes from 600 to 360. Find the percentage decrease.

    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 vehicle covers 405 km in 5 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  5. 5.
    Mathematics

    Evaluate log base 10 of 100.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  6. 6.
    Mathematics

    Find the binomial coefficient C(7, 4) — the coefficient of x^4 in (1 + x)^7.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  7. 7.
    Quantitative Aptitude

    An item is bought for ₹600 and sold for ₹690. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  8. 8.
    Quantitative Aptitude

    Find the simple interest on ₹30,000 at 4% per annum for 2 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  9. 9.
    Quantitative Aptitude

    The marked price of an item is ₹200. After a 30% 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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  10. 10.
    Quantitative Aptitude

    A vehicle covers 210 km in 7 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  11. 11.
    Quantitative Aptitude

    What is 40% of 720?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  12. 12.
    Quantitative Aptitude

    The marked price of an item is ₹1,900. After a 15% 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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  13. 13.
    Quantitative Aptitude

    What is 25% of 1,160?

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

    A invests ₹3,000 and B invests ₹3,000 for the same period. If the total profit is ₹24,000, 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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  15. 15.
    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 4.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(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 10?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  17. 17.
    Mathematics

    Evaluate log base 10 of 10,000.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  18. 18.
    Mathematics

    Find the binomial coefficient C(5, 2) — the coefficient of x^2 in (1 + x)^5.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  19. 19.
    Mathematics

    In an arithmetic progression with first term 4 and common difference 10, find term number 7.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  20. 20.
    Mathematics

    Find the sum of the first 9 terms of an AP with first term 2 and common difference 9.

    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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