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Recent questions tagged quantitative-aptitude

1 votes
1 answer
122
CAT 2021 Set-1 | Quantitative Aptitude | Question: 12
Suppose the length of each side of a regular hexagon $\text{ABCDEF}$ is $2 \; \text{cm}.$ It $\text{T}$ is the mid point of $\text{CD},$ then the length of $\text{AT, in cm},$ is $\sqrt{15}$ $\sqrt{13}$ $\sqrt{12}$ $\sqrt{14}$
Suppose the length of each side of a regular hexagon $\text{ABCDEF}$ is $2 \; \text{cm}.$ It $\text{T}$ is the mid point of $\text{CD},$ then the length of $\text{AT, in ...
1 votes
1 answer
123
CAT 2021 Set-1 | Quantitative Aptitude | Question: 13
If $r$ is a constant such that $|x^{2} – 4x -13| = r$ has exactly three distinct real roots, then the value of $r$ is $15$ $18$ $17$ $21$
If $r$ is a constant such that $|x^{2} – 4x -13| = r$ has exactly three distinct real roots, then the value of $r$ is$15$$18$$17$$21$
1 votes
1 answer
124
CAT 2021 Set-1 | Quantitative Aptitude | Question: 14
If $x_{0} = 1, x_{1} = 2$ and $x_{n+2} = \dfrac{1 + x_{n+1}}{x_{n}}, n = 0, 1, 2, 3, \dots ,$ then $x_{2021}$ is equal to $1$ $3$ $4$ $2$
If $x_{0} = 1, x_{1} = 2$ and $x_{n+2} = \dfrac{1 + x_{n+1}}{x_{n}}, n = 0, 1, 2, 3, \dots ,$ then $x_{2021}$ is equal to$1$$3$$4$$2$
1 votes
1 answer
125
CAT 2021 Set-1 | Quantitative Aptitude | Question: 15
If $5 – \log_{10} \sqrt{1+x} + 4 \log_{10} \sqrt{1-x} = \log_{10} \frac{1}{\sqrt{1-x^{2}}},$ then $100x$ equals
If $5 – \log_{10} \sqrt{1+x} + 4 \log_{10} \sqrt{1-x} = \log_{10} \frac{1}{\sqrt{1-x^{2}}},$ then $100x$ equals
0 votes
0 answers
127
CAT 2021 Set-1 | Quantitative Aptitude | Question: 17
The number of integers $n$ that satisfy the inequalities $ |n – 60| < |n – 100| < |n – 20|$ is $18$ $19$ $21$ $20$
The number of integers $n$ that satisfy the inequalities $ |n – 60| < |n – 100| < |n – 20|$ is$18$$19$$21$$20$
2 votes
1 answer
133
CAT 2020 Set-3 | Question: 51
If $\log_{a} 30 = \text{A}, \log_{a} (5/3) = – \text{B} $ and $\log_{2} a = 1/3,$ then $\log_{3}a $ equals $ \dfrac{2}{\text{A + B}} \;– 3 $ $ \dfrac{\text{A + B} - 3}{2} $ $ \dfrac{2}{\text{A + B} – 3} $ $ \dfrac{\text{A + B}}{2}\; – 3 $
If $\log_{a} 30 = \text{A}, \log_{a} (5/3) = – \text{B} $ and $\log_{2} a = 1/3,$ then $\log_{3}a $ equals$ \dfrac{2}{\text{A + B}} \;– 3 $ $ \dfrac{\text{A + B} - 3}...
3 votes
2 answers
134
CAT 2020 Set-3 | Question: 52
Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick’s age is $1$ year less than the average age of all three, then Harry’s age, in years, is
Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick’s age is $1$ year less than the average age of all three, then Harry’s age, in years, is
1 votes
1 answer
136
CAT 2020 Set-3 | Question: 54
Let $k$ be a constant. The equations $kx + y= 3$ and $4x + ky= 4$ have a unique solution if and only if $|k| \neq 2$ $|k| = 2$ $k \neq 2$ $k= 2$
Let $k$ be a constant. The equations $kx + y= 3$ and $4x + ky= 4$ have a unique solution if and only if $|k| \neq 2$$|k| = 2$$k \neq 2$$k= 2$
1 votes
1 answer
137
CAT 2020 Set-3 | Question: 55
If $x_{1} = \;– 1$ and $x_{m} = x_{m+1} + (m + 1)$ for every positive integer $m, $ then $x_{100}$ equals $ – 5151 $ $ – 5150 $ $ – 5051 $ $ – 5050 $
If $x_{1} = \;– 1$ and $x_{m} = x_{m+1} + (m + 1)$ for every positive integer $m, $ then $x_{100}$ equals $ – 5151 $$ – 5150 $$ – 5051 $$ – 5050 $
1 votes
1 answer
140
CAT 2020 Set-3 | Question: 58
If $ f(x+y) = f(x) f(y) $ and $ f(5) = 4,$ then $ f(10) – f(-10) $ is equal to $0$ $15.9375$ $3$ $14.0625$
If $ f(x+y) = f(x) f(y) $ and $ f(5) = 4,$ then $ f(10) – f(-10) $ is equal to $0$$15.9375$$3$$14.0625$
1 votes
1 answer
141
CAT 2020 Set-3 | Question: 59
If $\text{a,b,c}$ are non-zero and $14^{a} = 36^{b} = 84^{c},$ then $6b \left( \frac{1}{c} \;– \frac{1}{a} \right)$ is equal to
If $\text{a,b,c}$ are non-zero and $14^{a} = 36^{b} = 84^{c},$ then $6b \left( \frac{1}{c} \;– \frac{1}{a} \right)$ is equal to
1 votes
1 answer
143
CAT 2020 Set-3 | Question: 61
Let $\text{m}$ and $\text{n}$ be positive integers, If $x^{2} + mx + 2n = 0$ and $x^{2} + 2nx + m = 0$ have real roots, then the smallest possible value of $m + n$ is $7$ $8$ $5$ $6$
Let $\text{m}$ and $\text{n}$ be positive integers, If $x^{2} + mx + 2n = 0$ and $x^{2} + 2nx + m = 0$ have real roots, then the smallest possible value of $m + n$ is $7$...
0 votes
0 answers
146
CAT 2020 Set-3 | Question: 64
The area, in $\text{sq. units},$ enclosed by the lines $x = 2, y = |x – 2| + 4,$ the X-axis and the Y-axis is equal to $8$ $12$ $10$ $6$
The area, in $\text{sq. units},$ enclosed by the lines $x = 2, y = |x – 2| + 4,$ the X-axis and the Y-axis is equal to $8$$12$$10$$6$
0 votes
0 answers
147
CAT 2020 Set-3 | Question: 65
The vertices of a triangle are $(0,0), (4,0)$ and $(3,9).$ The area of the circle passing through these three points is $\frac{14 \pi}{3}$ $\frac{12 \pi}{5}$ $\frac{123 \pi}{7}$ $\frac{205 \pi}{9}$
The vertices of a triangle are $(0,0), (4,0)$ and $(3,9).$ The area of the circle passing through these three points is $\frac{14 \pi}{3}$$\frac{12 \pi}{5}$$\frac{123 \pi...
0 votes
0 answers
148
CAT 2020 Set-3 | Question: 66
How many integers in the set $\{ 100, 101, 102, \dots, 999\}$ have at least one digit repeated $?$
How many integers in the set $\{ 100, 101, 102, \dots, 999\}$ have at least one digit repeated $?$
0 votes
0 answers
149
CAT 2020 Set-3 | Question: 67
Let $\text{N}, x$ and $y$ be positive integers such that $N = x + y, 2 < x < 10$ and $14 < y < 23.$ If $\text{N} > 25,$ then how many distinct values are possible for $\text{N} ?$
Let $\text{N}, x$ and $y$ be positive integers such that $N = x + y, 2 < x < 10$ and $14 < y < 23.$ If $\text{N} 25,$ then how many distinct values are possible for $\...
0 votes
0 answers
150
CAT 2020 Set-3 | Question: 68
The points $(2,1)$ and $( – 3, – 4)$ are opposite vertices of a parallelogram. If the other two vertices lie on the line $x + 9y + c = 0,$ then $\text{c}$ is $12$ $14$ $13$ $15$
The points $(2,1)$ and $( – 3, – 4)$ are opposite vertices of a parallelogram. If the other two vertices lie on the line $x + 9y + c = 0,$ then $\text{c}$ is $12$$14$...
0 votes
0 answers
151
CAT 2020 Set-3 | Question: 69
How many pairs $(a,b)$ of positive integers are there such that $a \leq b$ and $ab = 4^{2017} \; ?$ $2017$ $2019$ $2020$ $2018$
How many pairs $(a,b)$ of positive integers are there such that $a \leq b$ and $ab = 4^{2017} \; ?$$2017$$2019$$2020$$2018$
2 votes
1 answer
153
CAT 2020 Set-3 | Question: 71
How many of the integers $1,2, \dots, 120,$ are divisible by none of $2,5$ and $7 ?$ $40$ $42$ $43$ $41$
How many of the integers $1,2, \dots, 120,$ are divisible by none of $2,5$ and $7 ?$$40$$42$$43$$41$
2 votes
1 answer
155
CAT 2020 Set-3 | Question: 73
$\dfrac{2 \times 4 \times 8 \times 16} {(\log_{2} 4)^{2} (\log_{4} 8)^{3} (\log_{8} 16)^{4}}$ equals
$\dfrac{2 \times 4 \times 8 \times 16} {(\log_{2} 4)^{2} (\log_{4} 8)^{3} (\log_{8} 16)^{4}}$ equals
0 votes
0 answers
158
CAT 2020 Set-3 | Question: 76
Let $\text{m}$ and $\text{n}$ be natural numbers such that $\text{n}$ is even and $0.2 < \frac{m}{20}, \frac{n}{m}, \frac{n}{11} < 0 \cdot 5.$ Then $m – 2n$ equals $3$ $4$ $1$ $2$
Let $\text{m}$ and $\text{n}$ be natural numbers such that $\text{n}$ is even and $0.2 < \frac{m}{20}, \frac{n}{m}, \frac{n}{11} < 0 \cdot 5.$ Then $m – 2n$ equals $3$$...
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