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CAT 2020 Set-2 | Question: 39
The humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students $\text{- A, B, C, D, E, F, G}$ and $\text{H}.$ ...
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CAT 2020 Set-2 | Question: 40
The humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students $\text{- A, B, C, D, E, F, G}$ and $\text{H}.$ ...
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CAT 2020 Set-2 | Question: 41
The humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students $ – \text{A, B, C, D, E, F, G}$ and $\text{H}.$...
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CAT 2020 Set-2 | Question: 43
The Humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students $ – \text{A, B, C, D, E, F, G}$ and $\text{H}.$...
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CAT 2020 Set-2 | Question: 44
The humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students $ – \text{A, B, C, D, E, F, G}$ and $\text{H}.$...
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CAT 2020 Set-2 | Question: 46
In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who polled the highest number of votes, the first r...
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CAT 2020 Set-2 | Question: 47
In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who polled the highest number of votes, the first r...
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CAT 2020 Set-2 | Question: 48
In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who polled the highest number of votes, the first r...
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CAT 2020 Set-2 | Question: 49
In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who polled the highest number of votes, the first r...
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CAT 2020 Set-2 | Question: 50
In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who polled the highest number of votes, the first r...
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CAT 2020 Set-2 | Question: 51
​​​​​​​​​​​​​​​​​​​​​​​​​​​​The sum of the perimeters of an equilateral triangle and a rectangle is $90 \; \text{cm}.$ The area, $\text{T},$ of the triangle and the area,...
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CAT 2020 Set-2 | Question: 52
In May, John bought the same amount of rice and the same amount of wheat as he had bought in April, but spent ₹$150$ more due to price increase of rice and wheat by $20\%...
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CAT 2020 Set-2 | Question: 53
In a car race, car $\text{A}$ beats car $\text{B}$ by $45 \; \text{km},$ car $\text{B}$ beats car $\text{C}$ by $50 \; \text{km},$ and car $\text{A}$ beats car $\text{C}$...
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CAT 2020 Set-2 | Question: 54
John takes twice as much time as Jack to finish a job. Jack and Jim together take one-thirds of the time to finish the job than John takes working alone. Moreover, in ord...
2 2 votes
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CAT 2020 Set-2 | Question: 55
Let the $\text{m-th}$ and $\text{n-th}$ terms of a geometric progression be $\dfrac{3}{4}$ and $12,$ respectively, where $\text{m < n}.$ If the common ratio of the progr...
2 2 votes
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CAT 2020 Set-2 | Question: 56
If $\textsf{x}$ and $\textsf{y}$ are positive real numbers satisfying $\textsf{x+y = 102},$ then the minimum possible value of $\textsf{2601} \left( 1 + \frac{1}{\textsf{...
3 3 votes
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CAT 2020 Set-2 | Question: 57
The value of $\log_{a} \left( \frac {a}{b} \right) + \log_{b} \left( \frac{b}{a} \right),$ for $ 1 < a \leq b$ cannot be equal to $ – 0.5$$1$$0$$ – 1$
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CAT 2020 Set-2 | Question: 58
In how many ways can a pair of integers $\textsf{(x , a)}$ be chosen such that $x^{2} – 2 |x| + |a-2| = 0 ?$$4$ $5$$6$$7$
4 4 votes
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CAT 2020 Set-2 | Question: 59
Students in a college have to choose at least two subjects from chemistry, mathematics, and physics. The number of students choosing all three subjects is $18,$ choosing ...
2 2 votes
1 1 answer
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CAT 2020 Set-2 | Question: 60
For real $\textsf{x}$ , the maximum possible value of $ \frac{x}{\sqrt{1+x^{4}}}$ is $ \frac{1}{\sqrt{3}}$$1$$\frac{1}{\sqrt{2}}$$\frac{1}{2}$
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CAT 2020 Set-2 | Question: 61
Aron bought some pencils and sharpeners. Spending the same amount of money as Aron, Aditya bought twice as many pencils and $10$ less sharpeners. If the cost of one sharp...
2 2 votes
1 1 answer
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CAT 2020 Set-2 | Question: 62
A sum of money is split among Amal, Sunil and Mita so that the ratio of the shares of Amal and Sunil is $3:2,$ while the ratio of the shares of Sunil and Mita is $4:5.$ I...
1 1 vote
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CAT 2020 Set-2 | Question: 63
Anil buys $12$ toys and labels each with the same selling price. He sells $8$ toys initially at $20\%$ discount on the labeled price. Then he sells the remaining $4$ toys...
2 2 votes
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CAT 2020 Set-2 | Question: 64
Two circular tracks $\text{T}1$ and $\text{T}2$ of radii $100 \; \text{m}$ and $20 \; \text{m},$ respectively touch at a point $\text{A}.$ Starting from $\text{A}$ at the...
2 2 votes
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CAT 2020 Set-2 | Question: 65
How many $4$-digit numbers, each greater than $1000$ and each having all four digits distinct, are there with $7$ coming before $3.$
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CAT 2020 Set-2 | Question: 66
The number of pairs of integers $(x,y)$ satisfying $ x \geq y \geq – 20 $ and $ 2x + 5y = 99 $ is
2 2 votes
1 1 answer
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CAT 2020 Set-2 | Question: 67
If $\textsf{x}$ and $\textsf{y}$ are non-negative integers such that $\textsf{x+9=z, y+1=z}$ and $\textsf{x+y<z+5},$ then the maximum possible value of $\textsf{2x+y}$ eq...
2 2 votes
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CAT 2020 Set-2 | Question: 68
$\text{A}$ and $\text{B}$ are two points on a straight line. Ram runs from $\text{A}$ to $\text{B}$ while Rahim runs from $\text{B}$ to $\text{A}.$ After crossing each ot...
2 2 votes
1 1 answer
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CAT 2020 Set-2 | Question: 69
The distance from $\text{B}$ to $\text{C}$ is thrice that from $\text{A}$ to $\text{B}.$ Two trains travel from $\text{A}$ to $\text{C}$ via $\text{B}.$ The speed of trai...
2 2 votes
1 1 answer
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CAT 2020 Set-2 | Question: 70
Let $\text{C}$ be a circle of radius $5 \; \text{meters}$ having center at $\text{O}.$ Let $\text{PQ}$ be a chord of $\text{C}$ that passes through points $\text{A}$ and ...
3 3 votes
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CAT 2020 Set-2 | Question: 71
The number of integers that satisfy the equality $\left( x^{2} – 5x + 7 \right)^{x+1} = 1$ is $2$$3$$5$$4$
2 2 votes
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CAT 2020 Set-2 | Question: 72
Let $f(x) = x^{2} + ax + b $ and $g(x) = f(x+1) – f(x-1).$ If $ f(x) \geq 0 $ for all real $x,$ and $ g(20) = 72,$ then the smallest possible value of $b$ is $1$$16$$0$$4...
2 2 votes
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CAT 2020 Set-2 | Question: 73
Let $\text{C}1$ and $\text{C}2$ be concentric circles such that the diameter of $\text{C}1$ is $2 \; \text{cm}$ longer than that of $\text{C}2.$ If a chord of $\text{C}1$...
1 1 vote
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CAT 2020 Set-2 | Question: 74
From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is $s.$ Then the area o...
1 1 vote
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CAT 2020 Set-2 | Question: 75
For the same principal amount, the compound interest for two years at $5\%$ per annum exceeds the simple interest for three years at $3\%$ per annum by $\text{Rs } 1125.$...
2 2 votes
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CAT 2020 Set-2 | Question: 76
In a group of $10$ students, the mean of the lowest $9$ scores is $42$ while the mean of the highest $9$ scores is $47.$ For the entire group of $10$ students, the maximu...
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