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CAT · Practice Sheet 44

Sheet code: CAT-S44 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    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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  2. 2.
    Quantitative Aptitude

    Find the simple interest on ₹26,000 at 12% per annum for 1 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  3. 3.
    Mathematics

    Find the binomial coefficient C(10, 4) — the coefficient of x^4 in (1 + x)^10.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  4. 4.
    Quantitative Aptitude

    What is 15% of 220?

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

    The marked price of an item is ₹600. After a 20% 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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  6. 6.
    Quantitative Aptitude

    Find the compound interest on ₹6,000 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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  7. 7.
    Mathematics

    Evaluate log base 2 of 64.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  8. 8.
    Mathematics

    Find the binomial coefficient C(6, 4) — the coefficient of x^4 in (1 + x)^6.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  9. 9.
    Mathematics

    Find the distance between the points (-7, 8) and (-6, -2).

    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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  10. 10.
    Quantitative Aptitude

    A vehicle covers 413 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

    In how many ways can 3 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 3.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  12. 12.
    Mathematics

    Find the sum of the first 5 terms of a GP with first term 6 and common ratio 3.

    Formula:GP Sum of n Terms
    Sn=a rn−1r−1S_n = a\,\dfrac{r^{n}-1}{r-1}
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  13. 13.
    Quantitative Aptitude

    A can finish a job in 4 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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  14. 14.
    Mathematics

    Find the sum of the first 8 terms of an AP with first term 11 and common difference 6.

    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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  15. 15.
    Quantitative Aptitude

    A vehicle covers 204 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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  16. 16.
    Mathematics

    Evaluate log base 3 of 27.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  17. 17.
    Mathematics

    Find the sum of the first 25 terms of an AP with first term 11 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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  18. 18.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 5?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  19. 19.
    Quantitative Aptitude

    An item is bought for ₹600 and sold for ₹780. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  20. 20.
    Mathematics

    For the quadratic 3x² − 3x + 5 = 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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