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CAT · Practice Sheet 8

Sheet code: CAT-S08 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
For the quadratic 2x² − 4x − 3 = 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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2.
Quantitative Aptitude
What is 30% of 780?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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3.
Mathematics
For the quadratic 3x² + 0x + 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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4.
Mathematics
Evaluate log base 5 of 625.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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5.
Quantitative Aptitude
A can finish a job in 4 days and B in 7 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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6.
Mathematics
Find term number 3 of a geometric progression with first term 2 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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7.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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8.
Quantitative Aptitude
Find the compound interest on ₹9,000 at 20% per annum compounded annually for 3 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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9.
Quantitative Aptitude
A vehicle covers 166 km in 2 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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10.
Quantitative Aptitude
Pipe A fills a tank in 10 hours and pipe B in 7 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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11.
Mathematics
Evaluate log base 3 of 81.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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12.
Mathematics
Find the sum of the first 7 terms of a GP with first term 5 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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13.
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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14.
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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15.
Mathematics
In an arithmetic progression with first term 15 and common difference 6, find term number 7.
Formula:AP nth Term
$a_n = a + (n-1)d$
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16.
Mathematics
Find the sum of the first 20 terms of an AP with first term 10 and common difference 7.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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17.
Quantitative Aptitude
An item is bought for ₹600 and sold for ₹690. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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18.
Quantitative Aptitude
The marked price of an item is ₹900. After a 30% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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19.
Mathematics
Find the sum of the first 21 terms of an AP with first term 2 and common difference 6.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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20.
Mathematics
Find the sum of the first 5 terms of a GP with first term 2 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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