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CAT · Practice Sheet 50

Sheet code: CAT-S50 · 20 questions

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

    A vehicle covers 352 km in 4 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  2. 2.
    Mathematics

    In an arithmetic progression with first term 18 and common difference 3, find term number 28.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  3. 3.
    Quantitative Aptitude

    An item is bought for ₹300 and sold for ₹360. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  4. 4.
    Quantitative Aptitude

    A vehicle covers 222 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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  5. 5.
    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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  6. 6.
    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 3.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  7. 7.
    Mathematics

    Find the sum of the first 21 terms of an AP with first term 11 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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  8. 8.
    Mathematics

    Find term number 3 of a geometric progression with first term 1 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  9. 9.
    Quantitative Aptitude

    What is 60% of 260?

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

    A value changes from 400 to 200. Find the percentage decrease.

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

    An item is bought for ₹900 and sold for ₹1,035. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  12. 12.
    Mathematics

    Find the sum of the first 21 terms of an AP with first term 8 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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  13. 13.
    Mathematics

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

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  14. 14.
    Mathematics

    In an arithmetic progression with first term 6 and common difference 8, find term number 26.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  15. 15.
    Quantitative Aptitude

    Divide ₹1,750 between two people in the ratio 3:4. 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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  16. 16.
    Quantitative Aptitude

    What is 20% of 920?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  17. 17.
    Quantitative Aptitude

    A vehicle covers 518 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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  18. 18.
    Mathematics

    In an arithmetic progression with first term 5 and common difference 2, find term number 23.

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

    A invests ₹7,000 and B invests ₹7,000 for the same period. If the total profit is ₹32,000, 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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  20. 20.
    Mathematics

    Find the sum of the first 8 terms of an AP with first term 12 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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