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CAT · Practice Sheet 26

Sheet code: CAT-S26 · 20 questions

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

    Two varieties costing ₹36 and ₹67 per kg are mixed to give a mixture worth ₹44 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.
    Quantitative Aptitude

    Find the average of these 6 numbers: 47, 21, 78, 60, 21, 62.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  3. 3.
    Quantitative Aptitude

    Divide ₹871 between two people in the ratio 6:7. 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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  4. 4.
    Mathematics

    Find the binomial coefficient C(10, 3) — the coefficient of x^3 in (1 + x)^10.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  5. 5.
    Quantitative Aptitude

    A invests ₹3,000 and B invests ₹8,000 for the same period. If the total profit is ₹28,000, 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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  6. 6.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 7?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  7. 7.
    Quantitative Aptitude

    Pipe A fills a tank in 7 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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  8. 8.
    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 3.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  9. 9.
    Mathematics

    Find term number 3 of a geometric progression with first term 5 and common ratio 3.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  10. 10.
    Quantitative Aptitude

    Two varieties costing ₹10 and ₹80 per kg are mixed to give a mixture worth ₹67 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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  11. 11.
    Quantitative Aptitude

    A vehicle covers 440 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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  12. 12.
    Quantitative Aptitude

    Find the simple interest on ₹32,000 at 4% per annum for 6 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  13. 13.
    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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  14. 14.
    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 3.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  15. 15.
    Quantitative Aptitude

    Find the average of these 10 numbers: 23, 61, 36, 28, 33, 45, 31, 78, 37, 90.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  16. 16.
    Mathematics

    Find the sum of the first 6 terms of an AP with first term 19 and common difference 3.

    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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  17. 17.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 4?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  18. 18.
    Quantitative Aptitude

    Find the compound interest on ₹20,000 at 20% per annum compounded annually for 2 years.

    Formula:Compound Interest
    A=P(1+R100)TA = P\left(1+\dfrac{R}{100}\right)^{T}
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  19. 19.
    Quantitative Aptitude

    Divide ₹792 between two people in the ratio 2:6. 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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  20. 20.
    Quantitative Aptitude

    Two varieties costing ₹31 and ₹88 per kg are mixed to give a mixture worth ₹62 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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