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CAT · Practice Sheet 22

Sheet code: CAT-S22 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Evaluate log base 5 of 25.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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2.
Quantitative Aptitude
A can finish a job in 16 days and B in 15 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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3.
Mathematics
Evaluate log base 10 of 10,000.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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4.
Quantitative Aptitude
What is 20% of 920?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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5.
Quantitative Aptitude
Pipe A fills a tank in 11 hours and pipe B in 6 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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6.
Quantitative Aptitude
Find the compound interest on ₹5,000 at 10% per annum compounded annually for 3 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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7.
Mathematics
For the quadratic 3x² − 6x + 2 = 0, find the sum and product of its roots.
Formula:Vieta's Formulas (roots)
$\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$
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8.
Quantitative Aptitude
Two varieties costing ₹29 and ₹93 per kg are mixed to give a mixture worth ₹71 per kg. Find the mixing ratio.
Formula:Alligation (Mixtures)
$\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$
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9.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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10.
Quantitative Aptitude
Two varieties costing ₹17 and ₹99 per kg are mixed to give a mixture worth ₹84 per kg. Find the mixing ratio.
Formula:Alligation (Mixtures)
$\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$
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11.
Mathematics
In an arithmetic progression with first term 11 and common difference 8, find term number 14.
Formula:AP nth Term
$a_n = a + (n-1)d$
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12.
Mathematics
Find the binomial coefficient C(9, 3) — the coefficient of x^3 in (1 + x)^9.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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13.
Quantitative Aptitude
Pipe A fills a tank in 7 hours and pipe B in 13 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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14.
Mathematics
For the quadratic 2x² + 8x + 6 = 0, find the sum and product of its roots.
Formula:Vieta's Formulas (roots)
$\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$
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15.
Quantitative Aptitude
Find the average of these 6 numbers: 85, 29, 65, 66, 56, 30.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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16.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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17.
Quantitative Aptitude
Find the simple interest on ₹29,000 at 10% per annum for 5 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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18.
Mathematics
Find term number 5 of a geometric progression with first term 4 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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19.
Quantitative Aptitude
Pipe A fills a tank in 13 hours and pipe B in 15 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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20.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 4?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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