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CAT · Practice Sheet 13

Sheet code: CAT-S13 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    In an arithmetic progression with first term 10 and common difference 7, find term number 30.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  2. 2.
    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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  3. 3.
    Quantitative Aptitude

    The marked price of an item is ₹1,300. After a 10% 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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  4. 4.
    Quantitative Aptitude

    A vehicle covers 702 km in 9 hours. Find its average speed.

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

    Find the average of these 10 numbers: 62, 35, 76, 32, 67, 63, 69, 55, 72, 58.

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

    An item is bought for ₹500 and sold for ₹550. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  7. 7.
    Quantitative Aptitude

    Find the compound interest on ₹19,000 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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  8. 8.
    Mathematics

    Find the sum of the first 21 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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  9. 9.
    Quantitative Aptitude

    A value changes from 300 to 360. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  10. 10.
    Quantitative Aptitude

    Find the average of these 8 numbers: 74, 89, 60, 58, 40, 90, 50, 81.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  11. 11.
    Mathematics

    Find the distance between the points (0, -2) and (5, -8).

    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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  12. 12.
    Quantitative Aptitude

    The marked price of an item is ₹1,000. After a 15% discount, find the selling price.

    Formula:Discount & Selling Price
    SP=MP(1−d100)SP = MP\left(1-\dfrac{d}{100}\right)
    View formula →
  13. 13.
    Quantitative Aptitude

    A invests ₹3,000 and B invests ₹8,000 for the same period. If the total profit is ₹16,000, 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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  14. 14.
    Quantitative Aptitude

    Pipe A fills a tank in 3 hours and pipe B in 8 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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  15. 15.
    Mathematics

    Find the binomial coefficient C(6, 3) — the coefficient of x^3 in (1 + x)^6.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  16. 16.
    Quantitative Aptitude

    An item is bought for ₹900 and sold for ₹990. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  17. 17.
    Mathematics

    For the quadratic 2x² + 3x − 2 = 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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  18. 18.
    Mathematics

    In an arithmetic progression with first term 3 and common difference 9, find term number 18.

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

    Find term number 7 of a geometric progression with first term 4 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  20. 20.
    Mathematics

    Find the sum of the first 18 terms of an AP with first term 17 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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