View solutions
FormulaWon

CAT · Practice Sheet 27

Sheet code: CAT-S27 · 20 questions

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

    In how many ways can 4 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 4.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
    View formula →
  2. 2.
    Mathematics

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

    Formula:GP Sum of n Terms
    Sn=a rn−1r−1S_n = a\,\dfrac{r^{n}-1}{r-1}
    View formula →
  3. 3.
    Quantitative Aptitude

    A value changes from 700 to 490. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
    View formula →
  4. 4.
    Quantitative Aptitude

    Two varieties costing ₹23 and ₹94 per kg are mixed to give a mixture worth ₹78 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}
    View formula →
  5. 5.
    Quantitative Aptitude

    Find the simple interest on ₹9,000 at 4% per annum for 1 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
    View formula →
  6. 6.
    Quantitative Aptitude

    Find the average of these 10 numbers: 48, 40, 70, 87, 66, 30, 50, 54, 90, 75.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
    View formula →
  7. 7.
    Quantitative Aptitude

    Divide ₹792 between two people in the ratio 5:3. 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}}
    View formula →
  8. 8.
    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 4.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
    View formula →
  9. 9.
    Quantitative Aptitude

    A vehicle covers 168 km in 4 hours. Find its average speed.

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

    Pipe A fills a tank in 14 hours and pipe B in 5 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns
    T=xyx+yT = \dfrac{xy}{x+y}
    View formula →
  11. 11.
    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 4.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
    View formula →
  12. 12.
    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 →
  13. 13.
    Quantitative Aptitude

    Divide ₹1,596 between two people in the ratio 2:5. 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}}
    View formula →
  14. 14.
    Mathematics

    For the quadratic 2x² − 5x − 8 = 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 →
  15. 15.
    Quantitative Aptitude

    Divide ₹340 between two people in the ratio 3:2. 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}}
    View formula →
  16. 16.
    Quantitative Aptitude

    Two varieties costing ₹16 and ₹61 per kg are mixed to give a mixture worth ₹43 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}
    View formula →
  17. 17.
    Mathematics

    Find the binomial coefficient C(6, 2) — the coefficient of x^2 in (1 + x)^6.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
    View formula →
  18. 18.
    Quantitative Aptitude

    What is 40% of 880?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
    View formula →
  19. 19.
    Quantitative Aptitude

    Find the compound interest on ₹8,000 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}
    View formula →
  20. 20.
    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}
    View formula →

© FormulaWon — formulawon.app · Answers & step-by-step working available on the solutions sheet.

Go to full solutions for this sheet