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CAT · Practice Sheet 17

Sheet code: CAT-S17 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Evaluate log base 2 of 16.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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2.
Mathematics
For the quadratic 2x² − 4x + 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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3.
Quantitative Aptitude
A invests ₹3,000 and B invests ₹7,000 for the same period. If the total profit is ₹14,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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4.
Mathematics
Find the sum of the first 23 terms of an AP with first term 8 and common difference 4.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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5.
Quantitative Aptitude
A invests ₹3,000 and B invests ₹9,000 for the same period. If the total profit is ₹34,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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6.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 9?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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7.
Quantitative Aptitude
Find the compound interest on ₹1,000 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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8.
Quantitative Aptitude
What is 75% of 820?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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9.
Mathematics
For the quadratic 5x² − 5x − 9 = 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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10.
Mathematics
In an arithmetic progression with first term 8 and common difference 8, find term number 17.
Formula:AP nth Term
$a_n = a + (n-1)d$
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11.
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
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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12.
Quantitative Aptitude
A can finish a job in 5 days and B in 8 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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13.
Quantitative Aptitude
The marked price of an item is ₹900. After a 40% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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14.
Quantitative Aptitude
In how many ways can 4 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 4.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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15.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 7?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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16.
Quantitative Aptitude
The marked price of an item is ₹300. After a 40% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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17.
Mathematics
For the quadratic 4x² − 2x + 0 = 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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18.
Quantitative Aptitude
Find the average of these 5 numbers: 37, 67, 39, 66, 24.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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19.
Quantitative Aptitude
What is 60% of 980?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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20.
Mathematics
Find the binomial coefficient C(6, 3) — the coefficient of x^3 in (1 + x)^6.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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