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43
CAT 2023 Set-3 | Quantitative Aptitude | Question: 18
Q. 18) A rectangle with the largest possible area is drawn inside a semicircle of radius $2 \mathrm{~cm}$. Then, the ratio of the lengths of the largest to the smallest side of this rectangle is $1: 1$ $\sqrt{5}: 1$ $\sqrt{2}: 1$ $2: 1$
Q. 18)A rectangle with the largest possible area is drawn inside a semicircle of radius $2 \mathrm{~cm}$. Then, the ratio of the lengths of the largest to the smallest si...
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44
CAT 2023 Set-3 | Quantitative Aptitude | Question: 19
Q. 19) In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is
Q. 19)In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is
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45
CAT 2023 Set-3 | Quantitative Aptitude | Question: 20
Q. 20) Let $a_{n}=46+8 n$ and $b_{n}=98+4 n$ be two sequences for natural numbers $n \leq 100$. Then, the sum of all terms common to both the sequences is 14900 15000 14798 14602
Q. 20)Let $a_{n}=46+8 n$ and $b_{n}=98+4 n$ be two sequences for natural numbers $n \leq 100$. Then, the sum of all terms common to both the sequences is14900150001479814...
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 21
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 22
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 1
Section: Quantitative Aptitude Q. 1) If $x$ is a positive real number such that $x^{8}+\left(\frac{1}{x}\right)^{8}=47$, then the value of $x^{9}+\left(\frac{1}{x}\right)^{9}$ is $34 \sqrt{5}$ $40 \sqrt{5}$ $36 \sqrt{5}$ $30 \sqrt{5}$
Section: Quantitative AptitudeQ. 1)If $x$ is a positive real number such that $x^{8}+\left(\frac{1}{x}\right)^{8}=47$, then the value of $x^{9}+\left(\frac{1}{x}\right)^{...
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49
CAT 2023 Set-3 | Quantitative Aptitude | Question: 2
Q. 2) Let $n$ and $m$ be two positive integers such that there are exactly 41 integers greater than $8^{m}$ and less than $8^{n}$, which can be expressed as powers of 2 . Then, the smallest possible value of $n+m$ is 44 16 42 14
Q. 2)Let $n$ and $m$ be two positive integers such that there are exactly 41 integers greater than $8^{m}$ and less than $8^{n}$, which can be expressed as powers of 2 . ...
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50
CAT 2023 Set-3 | Quantitative Aptitude | Question: 3
Q. 3) For some real numbers $a$ and $b$, the system of equations $x+y=4$ and $(a+5) x+\left(b^{2}-15\right) y=8 b$ has infinitely many solutions for $x$ and $y$. Then, the maximum possible value of $a b$ is 15 55 33 25
Q. 3)For some real numbers $a$ and $b$, the system of equations $x+y=4$ and $(a+5) x+\left(b^{2}-15\right) y=8 b$ has infinitely many solutions for $x$ and $y$. Then, the...
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51
CAT 2023 Set-3 | Quantitative Aptitude | Question: 4
Q. 4) For a real number $x$, if $\frac{1}{2}, \frac{\log _{3}\left(2^{x}-9\right)}{\log _{3} 4}$, and $\frac{\log _{5}\left(2^{x}+\frac{17}{2}\right)}{\log _{5} 4}$ ... $\log _{4}\left(\frac{3}{2}\right)$ $\log _{4} 7$ $\log _{4}\left(\frac{7}{2}\right)$
Q. 4)For a real number $x$, if $\frac{1}{2}, \frac{\log _{3}\left(2^{x}-9\right)}{\log _{3} 4}$, and $\frac{\log _{5}\left(2^{x}+\frac{17}{2}\right)}{\log _{5} 4}$ are in...
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52
CAT 2023 Set-3 | Quantitative Aptitude | Question: 5
Q. 5) A quadratic equation $x^{2}+b x+c=0$ has two real roots. If the difference between the reciprocals of the roots is $\frac{1}{3}$, and the sum of the reciprocals of the squares of the roots is $\frac{5}{9}$, then the largest possible value of $(b+c)$ is
Q. 5)A quadratic equation $x^{2}+b x+c=0$ has two real roots. If the difference between the reciprocals of the roots is $\frac{1}{3}$, and the sum of the reciprocals of t...
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53
CAT 2023 Set-3 | Quantitative Aptitude | Question: 6
Q. 6) The sum of the first two natural numbers, each having 15 factors (including 1 and the number itself), is
Q. 6)The sum of the first two natural numbers, each having 15 factors (including 1 and the number itself), is
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54
CAT 2023 Set-3 | Quantitative Aptitude | Question: 7
Q. 7) Let $n$ be any natural number such that $5^{n-1}
Q. 7)Let $n$ be any natural number such that $5^{n-1}
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65
CAT 2023 Set-3 | Quantitative Aptitude | Question: 18
Q. 18) A rectangle with the largest possible area is drawn inside a semicircle of radius $2 \mathrm{~cm}$. Then, the ratio of the lengths of the largest to the smallest side of this rectangle is $1: 1$ $\sqrt{5}: 1$ $\sqrt{2}: 1$ $2: 1$
Q. 18)A rectangle with the largest possible area is drawn inside a semicircle of radius $2 \mathrm{~cm}$. Then, the ratio of the lengths of the largest to the smallest si...
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0 answers
66
CAT 2023 Set-3 | Quantitative Aptitude | Question: 19
Q. 19) In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is
Q. 19)In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is
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67
CAT 2023 Set-3 | Quantitative Aptitude | Question: 20
Q. 20) Let $a_{n}=46+8 n$ and $b_{n}=98+4 n$ be two sequences for natural numbers $n \leq 100$. Then, the sum of all terms common to both the sequences is 14900 15000 14798 14602
Q. 20)Let $a_{n}=46+8 n$ and $b_{n}=98+4 n$ be two sequences for natural numbers $n \leq 100$. Then, the sum of all terms common to both the sequences is14900150001479814...
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0 answers
68
CAT 2023 Set-3 | Quantitative Aptitude | Question: 21
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 22
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70
CAT 2023 Set-2 | Quantitative Aptitude | Question: 1
For any natural numbers $\mathrm{m}, \mathrm{n}$, and $\mathrm{k}$, such that $\mathrm{k}$ divides both $m+2 n$ and $3 m+4 n \mathrm{k}$ must be a common divisor of $m$ and $n$ $2 m$ and $3 n$ $2 m$ and $n$ $m$ and $2 n$
For any natural numbers $\mathrm{m}, \mathrm{n}$, and $\mathrm{k}$, such that $\mathrm{k}$ divides both $m+2 n$ and $3 m+4 n \mathrm{k}$ must be a common divisor of$m$ an...
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71
CAT 2023 Set-2 | Quantitative Aptitude | Question: 2
Any non-zero real numbers $\mathrm{x}$, $\mathrm{y}$ such that $y \neq 3$ and $\frac{x}{y}<\frac{x+3}{y-3}$, will satisfy the condition $\frac{x}{y}<\frac{y}{x}$ If $y>10$, then $-x>y$ If $x<0$, then $-x If $y<0$, then $-x
Any non-zero real numbers $\mathrm{x}$, $\mathrm{y}$ such that $y \neq 3$ and $\frac{x}{y}<\frac{x+3}{y-3}$, will satisfy the condition$\frac{x}{y}<\frac{y}{x}$If $y>10$,...
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72
CAT 2023 Set-2 | Quantitative Aptitude | Question: 3
The sum of all possible values of $x$ satisfying the equation $2^{4 x^{2}}-2^{2 x^{2}+x+16}+2^{2 x+30}=0$, is $\frac{5}{2}$ $\frac{1}{2}$ $3$ $\frac{3}{2}$
The sum of all possible values of $x$ satisfying the equation $2^{4 x^{2}}-2^{2 x^{2}+x+16}+2^{2 x+30}=0$, is$\frac{5}{2}$$\frac{1}{2}$$3$$\frac{3}{2}$
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73
CAT 2023 Set-2 | Quantitative Aptitude | Question: 4
Let $\mathrm{a}, \mathrm{b}, \mathrm{m}$ and $\mathrm{n}$ be natural numbers such that $a>1$ and $b>1$. If $a^{m} b^{n}=144^{145}$, then the largest possible value of $n-m$ is $579$ $289$ $580$ $290$
Let $\mathrm{a}, \mathrm{b}, \mathrm{m}$ and $\mathrm{n}$ be natural numbers such that $a>1$ and $b>1$. If $a^{m} b^{n}=144^{145}$, then the largest possible value of $n-...
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74
CAT 2023 Set-2 | Quantitative Aptitude | Question: 5
The number of positive integers less than $50$, having exactly two distinct factors other than $1$ and itself, is
The number of positive integers less than $50$, having exactly two distinct factors other than $1$ and itself, is
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75
CAT 2023 Set-2 | Quantitative Aptitude | Question: 6
Let $k$ be the largest integer such that the equation $(x-1)^{2}+2 k x+11=0$ has no real roots. If $y$ is a positive real number, then the least possible value of $\frac{k}{4 y}+9 y$ is
Let $k$ be the largest integer such that the equation $(x-1)^{2}+2 k x+11=0$ has no real roots. If $y$ is a positive real number, then the least possible value of $\frac{...
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76
CAT 2023 Set-2 | Quantitative Aptitude | Question: 7
For some positive real number $x$, if $\log _{\sqrt{3}}(x)+\frac{\log _{x}(25)}{\log _{x}(0.008)}=\frac{16}{3}$, then the value of $\log _{3}\left(3 x^{2}\right)$ is
For some positive real number $x$, if $\log _{\sqrt{3}}(x)+\frac{\log _{x}(25)}{\log _{x}(0.008)}=\frac{16}{3}$, then the value of $\log _{3}\left(3 x^{2}\right)$ is
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78
CAT 2023 Set-2 | Quantitative Aptitude | Question: 9
Ravi is driving at a speed of $40 \mathrm{~km} / \mathrm{h}$ on a road. Vijay is $54$ ... should drive so that all the three cross each other at the same time, is $67.2$ $64.4$ $61.6$ $58.8$
Ravi is driving at a speed of $40 \mathrm{~km} / \mathrm{h}$ on a road. Vijay is $54$ meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along...
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