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Recent questions tagged cat2018-2

2 votes
1 answer
2
CAT 2018 Set-2 | Question: 69
The smallest integer $n$ such that $n^{3} - 11n^{2} + 32n - 28 >0$ is
The smallest integer $n$ such that $n^{3} - 11n^{2} + 32n - 28 >0$ is
3 votes
1 answer
3
CAT 2018 Set-2 | Question: 67
The value of the sum $7 \times 11 + 11 \times 15 + 15 \times 19 + \dots$ + $95 \times 99$ is $80707$ $80773$ $80730$ $80751$
The value of the sum $7 \times 11 + 11 \times 15 + 15 \times 19 + \dots$ + $95 \times 99$ is$80707$$80773$$80730$$80751$
3 votes
1 answer
4
CAT 2018 Set-2 | Question: 68
How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits? $5$ $6$ $8$ $7$
How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits?...
3 votes
1 answer
6
CAT 2018 Set-2 | Question: 73
A chord of length $5$ cm subtends an angle of $60^\circ$ at the centre of a circle. The length, in cm, of a chord that subtends an angle of $120^\circ$ at the centre of the same circle is $8$ $6\sqrt2$ $5\sqrt3$ $2\pi$
A chord of length $5$ cm subtends an angle of $60^\circ$ at the centre of a circle. The length, in cm, of a chord that subtends an angle of $120^\circ$ at the centre of t...
2 votes
1 answer
9
CAT 2018 Set-2 | Question: 74
Let $f\left (x \right ) = \max\left \{5x, 52 – 2x^{2}\right \}$ , where $x$ is any positive real numbers. Then the minimum possible value of $f(x)$ is ________
Let $f\left (x \right ) = \max\left \{5x, 52 – 2x^{2}\right \}$ , where $x$ is any positive real numbers. Then the minimum possible value of $f(x)$ is ________
2 votes
1 answer
12
CAT 2018 Set-2 | Question: 77
If $a$ and $b$ are integers such that $2x^{2}- ax + 2 > 0$ and $x^{2}-bx+8 \geq 0$ for all real numbers $x$, then the largest possible value of $2a-6b$ is _________
If $a$ and $b$ are integers such that $2x^{2}- ax + 2 0$ and $x^{2}-bx+8 \geq 0$ for all real numbers $x$, then the largest possible value of $2a-6b$ is _________
4 votes
2 answers
14
CAT 2018 Set-2 | Question: 83
A jar contains a mixture of $175$ ml water and $700$ ml alcohol. Gopal takes out $10\%$ of the mixture and substitutes it by water of the same amount. The process is repeated once again. The percentage of water in the mixture is now $35.2$ $30.3$ $20.5$ $25.4$
A jar contains a mixture of $175$ ml water and $700$ ml alcohol. Gopal takes out $10\%$ of the mixture and substitutes it by water of the same amount. The process is repe...
3 votes
1 answer
17
CAT 2018 Set-2 | Question: 81
If $p^{3}=q^{4}=r^{5}=s^{6}$, then the value of $\log_{s}\left ( pqr \right )$ is equal to $16/5$ $1$ $24/5$ $47/10$
If $p^{3}=q^{4}=r^{5}=s^{6}$, then the value of $\log_{s}\left ( pqr \right )$ is equal to $16/5$$1$$24/5$$47/10$
2 votes
1 answer
18
CAT 2018 Set-2 | Question: 80
Let $t_{1}, t_{2},\dots$ be a real numbers such that $t_{1}+t_{2}+\dots+t_{n}=2n^{2}+9n+13$, for every positive integers $n\geq2$.If $t_{k}=103$ , then $k$ equals
Let $t_{1}, t_{2},\dots$ be a real numbers such that $t_{1}+t_{2}+\dots+t_{n}=2n^{2}+9n+13$, for every positive integers $n\geq2$.If $t_{k}=103$ , then $k$ equals
2 votes
1 answer
19
CAT 2018 Set-2 | Question: 79
If $\text{N}$ and $x$ are positive integers such that $\text{N}^{\text{N}}=2^{160}$ and $\text{N}^{2} + 2^{\text{N}}$ is an integral multiple of $2^{x}$, then the largest possible $x$ is _______
If $\text{N}$ and $x$ are positive integers such that $\text{N}^{\text{N}}=2^{160}$ and $\text{N}^{2} + 2^{\text{N}}$ is an integral multiple of $2^{x}$, then the largest...
3 votes
2 answers
20
CAT 2018 Set-2 | Question: 90
If the sum of squares of two numbers is $97$, then which one of the following cannot be their product? $-32$ $48$ $64$ $16$
If the sum of squares of two numbers is $97$, then which one of the following cannot be their product?$-32$$48$$64$$16$
2 votes
1 answer
21
CAT 2018 Set-2 | Question: 89
The arithmetic mean of $x,y$ and $z$ is $80$, and that of $x,y,z,u$ and $v$ is $75$, where $u=\left (x+y \right)/2$ and $v=\left (y+z \right)/2$. If $x\geq z$, then the minimum possible value of $x$ is ____________
The arithmetic mean of $x,y$ and $z$ is $80$, and that of $x,y,z,u$ and $v$ is $75$, where $u=\left (x+y \right)/2$ and $v=\left (y+z \right)/2$. If $x\geq z$, then the m...
3 votes
1 answer
24
CAT 2018 Set-2 | Question: 86
A parallelogram $\text{ABCD}$ has area $48$ sqcm. If the length of $\text{CD}$ is $8$ cm and that of $\text{AD}$ is $s$ cm, then which one of the following is necessarily true? $s\geq6$ $s\neq6$ $s\leq6$ $5\leq s\leq7$
A parallelogram $\text{ABCD}$ has area $48$ sqcm. If the length of $\text{CD}$ is $8$ cm and that of $\text{AD}$ is $s$ cm, then which one of the following is necessarily...
2 votes
1 answer
26
CAT 2018 Set-2 | Question: 96
From a rectangle $\text{ABCD}$ of area $768$ sq cm, a semicircular part with diameter $\text{AB}$ and area $72\pi$ sq cm is removed. The perimeter of the leftover portion, in cm, is $80 + 16\pi$ $86+8\pi$ $82+24\pi$ $88+12\pi$
From a rectangle $\text{ABCD}$ of area $768$ sq cm, a semicircular part with diameter $\text{AB}$ and area $72\pi$ sq cm is removed. The perimeter of the leftover portion...
3 votes
1 answer
28
CAT 2018 Set-2 | Question: 94
The area of a rectangle and the square of its perimeter are in the ratio $1:25$. Then the lengths of the shorter and longer sides of the rectangle are in the ratio $1:4$ $2:9$ $1:3$ $3:8$
The area of a rectangle and the square of its perimeter are in the ratio $1:25$. Then the lengths of the shorter and longer sides of the rectangle are in the ratio$1:4$$2...
2 votes
1 answer
30
CAT 2018 Set-2 | Question: 91
For two sets $\text{A}$ and $\text{B}$, let $\text{A} \triangle \text{B}$ denote the set of elements which belong to $\text{A}$ or $\text{B}$ ... $(\text{P} \triangle \text{Q}) \triangle (\text{R}\triangle \text{S})$ is $9$ $7$ $6$ $8$
For two sets $\text{A}$ and $\text{B}$, let $\text{A} \triangle \text{B}$ denote the set of elements which belong to $\text{A}$ or $\text{B}$ but not both. If $\text{P} =...
2 votes
1 answer
31
CAT 2018 Set-2 | Question: 92
The smallest integer $n$ for which $4^{n}>17^{19}$ holds, is closest to $33$ $37$ $39$ $35$
The smallest integer $n$ for which $4^{n}>17^{19}$ holds, is closest to$33$$37$$39$$35$
2 votes
1 answer
34
CAT 2018 Set-2 | Question: 97
A triangle $\text{ABC}$ has area $32$ sq units and its side $\text{BC}$, of length $8$ units, lies on the line $x =4$. Then the shortest possible distance between $\text{A}$ and the point $(0,0)$ is $4$ units $8$ units $4\sqrt2$ units $ 2\sqrt2$ units
A triangle $\text{ABC}$ has area $32$ sq units and its side $\text{BC}$, of length $8$ units, lies on the line $x =4$. Then the shortest possible distance between $\text{...
3 votes
1 answer
35
CAT 2018 Set-2 | Question: 100
$\frac{1}{\log_{2}100} – \frac{1}{\log_{4}100} + \frac{1}{\log_{5}100} – \frac{1}{\log_{10}100} + \frac{1}{\log_{20}100} – \frac{1}{\log_{25}100} + \frac{1}{\log_{50}100}=?$ $1/2$ $0$ $10$ $-4$
$\frac{1}{\log_{2}100} – \frac{1}{\log_{4}100} + \frac{1}{\log_{5}100} – \frac{1}{\log_{10}100} + \frac{1}{\log_{20}100} – \frac{1}{\log_{25}100} + \frac{1}{\log_{5...
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