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CAT · Practice Sheet 23

Sheet code: CAT-S23 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    Find the distance between the points (-1, -5) and (7, 7).

    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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  2. 2.
    Quantitative Aptitude

    A vehicle covers 322 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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  3. 3.
    Mathematics

    In an arithmetic progression with first term 11 and common difference 10, find term number 28.

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

    Two fair dice are rolled. What is the probability that the sum of the numbers is 6?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  5. 5.
    Quantitative Aptitude

    Two varieties costing ₹21 and ₹73 per kg are mixed to give a mixture worth ₹50 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)
    q1q2=p2−mm−p1\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}
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  6. 6.
    Quantitative Aptitude

    Divide ₹884 between two people in the ratio 2:2. 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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  7. 7.
    Quantitative Aptitude

    A can finish a job in 14 days and B in 6 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  8. 8.
    Quantitative Aptitude

    An item is bought for ₹900 and sold for ₹1,170. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  9. 9.
    Mathematics

    Find the binomial coefficient C(7, 2) — the coefficient of x^2 in (1 + x)^7.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  10. 10.
    Quantitative Aptitude

    A invests ₹7,000 and B invests ₹6,000 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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  11. 11.
    Quantitative Aptitude

    The marked price of an item is ₹1,200. 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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  12. 12.
    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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  13. 13.
    Mathematics

    Find the distance between the points (-5, 0) and (-5, 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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  14. 14.
    Mathematics

    Find term number 7 of a geometric progression with first term 3 and common ratio 3.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  15. 15.
    Mathematics

    Find the sum of the first 4 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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  16. 16.
    Mathematics

    Evaluate log base 10 of 100,000.

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

    Find the distance between the points (8, 5) and (11, 5).

    Formula:Distance Between Two Points
    d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}
    View formula →
  18. 18.
    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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  19. 19.
    Mathematics

    Find term number 4 of a geometric progression with first term 5 and common ratio 3.

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

    In an arithmetic progression with first term 18 and common difference 6, find term number 6.

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