View solutions
FormulaWon

CAT · Practice Sheet 33

Sheet code: CAT-S33 · 20 questions

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

    In how many ways can 2 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 2.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
    View formula →
  2. 2.
    Quantitative Aptitude

    What is 15% of 280?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
    View formula →
  3. 3.
    Quantitative Aptitude

    A vehicle covers 352 km in 4 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
    View formula →
  4. 4.
    Mathematics

    Evaluate log base 3 of 729.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
    View formula →
  5. 5.
    Quantitative Aptitude

    Find the average of these 5 numbers: 87, 62, 39, 34, 67.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
    View formula →
  6. 6.
    Mathematics

    Find the binomial coefficient C(9, 4) — the coefficient of x^4 in (1 + x)^9.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
    View formula →
  7. 7.
    Mathematics

    Find the distance between the points (2, -6) and (4, -2).

    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 →
  8. 8.
    Mathematics

    For the quadratic 5x² + 2x + 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 →
  9. 9.
    Quantitative Aptitude

    A can finish a job in 17 days and B in 12 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
    View formula →
  10. 10.
    Quantitative Aptitude

    An item is bought for ₹300 and sold for ₹360. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
    View formula →
  11. 11.
    Mathematics

    Evaluate log base 3 of 9.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
    View formula →
  12. 12.
    Mathematics

    Find the sum of the first 7 terms of an AP with first term 5 and common difference 4.

    Formula:AP Sum of n Terms
    Sn=n2 [2a+(n−1)d]S_n = \dfrac{n}{2}\,[2a+(n-1)d]
    View formula →
  13. 13.
    Quantitative Aptitude

    Two varieties costing ₹33 and ₹68 per kg are mixed to give a mixture worth ₹39 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 →
  14. 14.
    Quantitative Aptitude

    A value changes from 600 to 750. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
    View formula →
  15. 15.
    Mathematics

    Evaluate log base 10 of 100,000.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
    View formula →
  16. 16.
    Quantitative Aptitude

    An item is bought for ₹600 and sold for ₹690. Find the profit percentage.

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

    Find the sum of the first 19 terms of an AP with first term 14 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]
    View formula →
  18. 18.
    Quantitative Aptitude

    A invests ₹2,000 and B invests ₹9,000 for the same period. If the total profit is ₹7,000, find A's share.

    Formula:Partnership (profit share)
    ShareA=Profit×AA+B\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}
    View formula →
  19. 19.
    Quantitative Aptitude

    Two varieties costing ₹12 and ₹63 per kg are mixed to give a mixture worth ₹41 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 →
  20. 20.
    Mathematics

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

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
    View formula →

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

Go to full solutions for this sheet