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42
CAT 2022 Set-2 | Quantitative Aptitude | Question: 16
For some natural number $n$, assume that $(15,000) !$ is divisible by $(n !) !$. The largest possible value of $n$ is $5$ $4$ $6$ $7$
For some natural number $n$, assume that $(15,000) !$ is divisible by $(n !) !$. The largest possible value of $n$ is$5$$4$$6$$7$
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43
CAT 2022 Set-2 | Quantitative Aptitude | Question: 17
Suppose for all integers $x$, there are two functions $f$ and $g$ such that $f(x)+$ $f(x-1)-1=0$ and $g(x)=x^{2}$. If $f\left(x^{2}-x\right)=5$, then the value of the sum $f(g(5))+g(f(5))$ is
Suppose for all integers $x$, there are two functions $f$ and $g$ such that $f(x)+$ $f(x-1)-1=0$ and $g(x)=x^{2}$. If $f\left(x^{2}-x\right)=5$, then the value of the sum...
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45
CAT 2022 Set-2 | Quantitative Aptitude | Question: 19
The number of integer solutions of the equation $\left(x^{2}-10\right)^{\left(x^{2}-3 x-10\right)}=1$ is
The number of integer solutions of the equation $\left(x^{2}-10\right)^{\left(x^{2}-3 x-10\right)}=1$ is
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46
CAT 2022 Set-2 | Quantitative Aptitude | Question: 20
Let $r$ and $c$ be real numbers. If $r$ and $-r$ are roots of $5 x^{3}+c x^{2}-10 x+9=0$, then $c$ equals $4$ $-4$ $-\frac{9}{2}$ $\frac{9}{2}$
Let $r$ and $c$ be real numbers. If $r$ and $-r$ are roots of $5 x^{3}+c x^{2}-10 x+9=0$, then $c$ equals$4$$-4$$-\frac{9}{2}$$\frac{9}{2}$
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47
CAT 2022 Set-2 | Quantitative Aptitude | Question: 21
Consider the arithmetic progression $3,7,11, \ldots$ and let $A_{n}$ denote the sum of the first $\mathrm{n}$ terms of this progression. Then the value of $1^{25}, A$ is $442$ $404$ $455$ $415$
Consider the arithmetic progression $3,7,11, \ldots$ and let $A_{n}$ denote the sum of the first $\mathrm{n}$ terms of this progression. Then the value of $1^{25}, A$ is$...
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50
CAT 2022 Set-1 | Quantitative Aptitude | Question: 2
The largest real value of $a$ for which the equation $|x+a|+|x-1|=2$ has an infinite number of solutions for $x$ is $2$ $-1$ $0$ $1$
The largest real value of $a$ for which the equation $|x+a|+|x-1|=2$ has an infinite number of solutions for $x$ is$2$$-1$$0$$1$
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51
CAT 2022 Set-1 | Quantitative Aptitude | Question: 3
The average of three integers is $13$. When a natural number $n$ is included, the average of these four integers remains an odd integer. The minimum possible value of $n$ is $5$ $1$ $3$ $4$
The average of three integers is $13$. When a natural number $n$ is included, the average of these four integers remains an odd integer. The minimum possible value of $n$...
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54
CAT 2022 Set-1 | Quantitative Aptitude | Question: 6
Let $\text{A B C D}$ be a parallelogram such that the coordinates of its three vertices $\text{A, B, C}$ are $(1,1),(3,4)$ and $(-2,8)$, respectively. Then, the coordinates of the vertex $\text{D}$ are $(-4,5)$ $(-3,4)$ $(0,11)$ $(4,5)$
Let $\text{A B C D}$ be a parallelogram such that the coordinates of its three vertices $\text{A, B, C}$ are $(1,1),(3,4)$ and $(-2,8)$, respectively. Then, the coordinat...
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57
CAT 2022 Set-1 | Quantitative Aptitude | Question: 9
A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio $1: 3$, then the ratio of lemon juice and sugar syrup in the new mixture is Ans $1: 7$ $1: 6$ $1: 5$ $1: 4$
A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio $1: 3$, then the ratio...
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60
CAT 2022 Set-1 | Quantitative Aptitude | Question: 12
All the vertices of a rectangle lie on a circle of radius $R$. If the perimeter of the rectangle is $P$, then the area of the rectangle is $\frac{P^{2}}{16}-R^{2}$ $\frac{P^{2}}{8}-2 R^{2} $ $\frac{P^{2}}{2}-2 P R $ $\frac{P^{2}}{8}-\frac{R^{2}}{2}$
All the vertices of a rectangle lie on a circle of radius $R$. If the perimeter of the rectangle is $P$, then the area of the rectangle is$\frac{P^{2}}{16}-R^{2}$$\frac{P...
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62
CAT 2022 Set-1 | Quantitative Aptitude | Question: 14
Let $a$ and $b$ be natural numbers. If $a^{2}+a b+a=14$ and $b^{2}+a b+b=28$, then $(2 a+b)$ equals $8$ $9$ $7$ $10$
Let $a$ and $b$ be natural numbers. If $a^{2}+a b+a=14$ and $b^{2}+a b+b=28$, then $(2 a+b)$ equals$8$$9$$7$$10$
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66
CAT 2022 Set-1 | Quantitative Aptitude | Question: 18
For natural numbers $x, y$, and $z$, if $x y+y z=19$ and $y z+x z=51$, then the minimum possible value of $x y z$ is
For natural numbers $x, y$, and $z$, if $x y+y z=19$ and $y z+x z=51$, then the minimum possible value of $x y z$ is
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67
CAT 2022 Set-1 | Quantitative Aptitude | Question: 19
Let $0 \leq a \leq x \leq 100$ and $f(x)=|x-a|+|x-100|+|x-a-50|$. Then the maximum value of $f(x)$ becomes $100$ when $a$ is equal to $0$ $25$ $100$ $50$
Let $0 \leq a \leq x \leq 100$ and $f(x)=|x-a|+|x-100|+|x-a-50|$. Then the maximum value of $f(x)$ becomes $100$ when $a$ is equal to$0$$25$$100$$50$
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68
CAT 2022 Set-1 | Quantitative Aptitude | Question: 20
For any real number $x$, let $[x]$ be the largest integer less than or equal to $x$. If $\sum_{n=1}^{N}\left[\frac{1}{5}+\frac{n}{25}\right]=25$ then $N$ is
For any real number $x$, let $[x]$ be the largest integer less than or equal to $x$. If $\sum_{n=1}^{N}\left[\frac{1}{5}+\frac{n}{25}\right]=25$ then $N$ is
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69
CAT 2022 Set-1 | Quantitative Aptitude | Question: 21
For any natural number $n$, suppose the sum of the first $n$ terms of an arithmetic progression is $\left(n+2 n^{2}\right)$. If the $n^{\text {th }}$ term of the progression is divisible by $9$ , then the smallest possible value of $n$ is $8$ $7$ $4$ $9$
For any natural number $n$, suppose the sum of the first $n$ terms of an arithmetic progression is $\left(n+2 n^{2}\right)$. If the $n^{\text {th }}$ term of the progress...
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70
CAT 2022 Set-1 | Quantitative Aptitude | Question: 22
The number of ways of distributing $20$ identical balloons among $4$ children such that each child gets some balloons but no child gets an odd number of balloons, is
The number of ways of distributing $20$ identical balloons among $4$ children such that each child gets some balloons but no child gets an odd number of balloons, is
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72
NIELIT 2022 Feb Scientist D - Section D: 1
If $4.25 – \left[ 4.25 + \left\{ 4.25 – \left( 8.5 – \overline{\rm 4.25+x} \right) \right\} \right]$ the value of $x$ is : $0$ $4.25$ $8.5$ $12.75$
If $4.25 – \left[ 4.25 + \left\{ 4.25 – \left( 8.5 – \overline{\rm 4.25+x} \right) \right\} \right]$ the value of $x$ is :$0$$4.25$$8.5$$12.75$
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73
NIELIT 2022 Feb Scientist D - Section D: 2
The effective annual rate of interest corresponding to a nominal rate of $8 \%$ per annum payable half yearly is : $4 \%$ $7.84 \%$ $8.08 \%$ $8.16 \%$
The effective annual rate of interest corresponding to a nominal rate of $8 \%$ per annum payable half yearly is :$4 \%$$7.84 \%$$8.08 \%$$8.16 \%$
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75
NIELIT 2022 Feb Scientist D - Section D: 4
If $x + \dfrac{1}{x} = 99,$ then the value of $\dfrac{100x}{2x^{2} + 102x + 2}$ is : $1/3$ $1/99$ $99/100$ $3$
If $x + \dfrac{1}{x} = 99,$ then the value of $\dfrac{100x}{2x^{2} + 102x + 2}$ is :$1/3$$1/99$$99/100$$3$
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76
NIELIT 2022 Feb Scientist D - Section D: 5
If we multiply a fraction by itself and divide the product by its reciprocal, the fraction thus obtained is $15 \frac{5}{8}.$ The original fraction is : $2 \frac{1}{2}$ $3 \frac{1}{2}$ $\frac{8}{125}$ $\frac{125}{8}$
If we multiply a fraction by itself and divide the product by its reciprocal, the fraction thus obtained is $15 \frac{5}{8}.$ The original fraction is :$2 \frac{1}{2}$$3 ...
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77
NIELIT 2022 Feb Scientist D - Section D: 6
Income of $\text{A}$ and $\text{B}$ are in the ratio $4:7$ and their spending is in the ratio $6:11.$ If $\text{A}$ saves one third of his income, then the ratio of their savings will be : $12:19$ $11:19$ $3:5$ $10:19$
Income of $\text{A}$ and $\text{B}$ are in the ratio $4:7$ and their spending is in the ratio $6:11.$ If $\text{A}$ saves one third of his income, then the ratio of their...
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79
NIELIT 2022 Feb Scientist D - Section D: 8
If $\{ (2 \sin \theta – \cos \theta) / (\cos \theta + \sin \theta) \} = 1,$ then the value of $\tan \theta$ is : $\frac{1}{3}$ $\frac{1}{2}$ $2$ $3$
If $\{ (2 \sin \theta – \cos \theta) / (\cos \theta + \sin \theta) \} = 1,$ then the value of $\tan \theta$ is :$\frac{1}{3}$$\frac{1}{2}$$2$$3$
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80
NIELIT 2022 Feb Scientist D - Section D: 9
If $x = 5/12, y = – 3/4, z = 1/3,$ the value of $x^{3} + y^{3} + z^{3}$ is : $-15/16$ $-3/4$ $-9/4$ $-5/16$
If $x = 5/12, y = – 3/4, z = 1/3,$ the value of $x^{3} + y^{3} + z^{3}$ is :$-15/16$$-3/4$$-9/4$$-5/16$
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