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CAT · Practice Sheet 2

Sheet code: CAT-S02 · 20 questions

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

    Find the average of these 10 numbers: 57, 20, 90, 51, 40, 86, 49, 37, 49, 39.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  2. 2.
    Quantitative Aptitude

    Find the simple interest on ₹15,000 at 12% per annum for 2 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 distance between the points (-8, 0) and (8, -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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  4. 4.
    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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  5. 5.
    Quantitative Aptitude

    Find the average of these 8 numbers: 28, 28, 59, 65, 52, 23, 20, 24.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  6. 6.
    Quantitative Aptitude

    Find the compound interest on ₹19,000 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.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 8?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  8. 8.
    Quantitative Aptitude

    Find the compound interest on ₹6,000 at 20% per annum compounded annually for 3 years.

    Formula:Compound Interest
    A=P(1+R100)TA = P\left(1+\dfrac{R}{100}\right)^{T}
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  9. 9.
    Quantitative Aptitude

    A vehicle covers 376 km in 8 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  10. 10.
    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}}
    View formula →
  11. 11.
    Quantitative Aptitude

    Find the average of these 10 numbers: 88, 58, 37, 87, 23, 20, 26, 21, 38, 25.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  12. 12.
    Mathematics

    For the quadratic 4x² + 2x − 1 = 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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  13. 13.
    Quantitative Aptitude

    Pipe A fills a tank in 8 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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  14. 14.
    Mathematics

    Find the sum of the first 7 terms of an AP with first term 7 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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  15. 15.
    Mathematics

    Find the distance between the points (8, 8) and (3, 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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  16. 16.
    Mathematics

    Evaluate log base 3 of 729.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  17. 17.
    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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  18. 18.
    Quantitative Aptitude

    A invests ₹4,000 and B invests ₹2,000 for the same period. If the total profit is ₹36,000, 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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  19. 19.
    Quantitative Aptitude

    Pipe A fills a tank in 7 hours and pipe B in 14 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns
    T=xyx+yT = \dfrac{xy}{x+y}
    View formula →
  20. 20.
    Mathematics

    Evaluate log base 5 of 625.

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