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CAT · Practice Sheet 9

Sheet code: CAT-S09 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    Find the sum of the first 10 terms of an AP with first term 14 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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  2. 2.
    Quantitative Aptitude

    A vehicle covers 120 km in 3 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  3. 3.
    Mathematics

    In an arithmetic progression with first term 9 and common difference 1, find term number 30.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  4. 4.
    Mathematics

    Find the sum of the first 7 terms of a GP with first term 1 and common ratio 2.

    Formula:GP Sum of n Terms
    Sn=a rn−1r−1S_n = a\,\dfrac{r^{n}-1}{r-1}
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  5. 5.
    Mathematics

    Find the distance between the points (7, -5) 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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  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

    An item is bought for ₹300 and sold for ₹450. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  8. 8.
    Quantitative Aptitude

    A invests ₹10,000 and B invests ₹4,000 for the same period. If the total profit is ₹5,000, 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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  9. 9.
    Quantitative Aptitude

    An item is bought for ₹600 and sold for ₹660. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  10. 10.
    Mathematics

    For the quadratic 5x² + 1x − 7 = 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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  11. 11.
    Mathematics

    In an arithmetic progression with first term 18 and common difference 3, find term number 29.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  12. 12.
    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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  13. 13.
    Quantitative Aptitude

    The marked price of an item is ₹800. After a 50% 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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  14. 14.
    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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  15. 15.
    Mathematics

    For the quadratic 5x² − 6x + 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}
    View formula →
  16. 16.
    Quantitative Aptitude

    An item is bought for ₹600 and sold for ₹900. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
    View formula →
  17. 17.
    Quantitative Aptitude

    The marked price of an item is ₹1,900. After a 25% discount, find the selling price.

    Formula:Discount & Selling Price
    SP=MP(1−d100)SP = MP\left(1-\dfrac{d}{100}\right)
    View formula →
  18. 18.
    Mathematics

    Find the sum of the first 3 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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  19. 19.
    Mathematics

    For the quadratic 3x² + 4x + 4 = 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}
    View formula →
  20. 20.
    Quantitative Aptitude

    Pipe A fills a tank in 14 hours and pipe B in 13 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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