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Recent questions tagged cat2017-2

1 votes
1 answer
81
CAT 2017 Set-2 | Question: 83
The points $\left ( 2,5 \right )$ and $\left ( 6,3 \right )$ are two end points of a diagonal of a rectangle. If the other diagonal has the equation $y=3x+c$, then $c$ is $-5$ $-6$ $-7$ $-8$
The points $\left ( 2,5 \right )$ and $\left ( 6,3 \right )$ are two end points of a diagonal of a rectangle. If the other diagonal has the equation $y=3x+c$, then $c$ is...
2 votes
1 answer
83
CAT 2017 Set-2 | Question: 81
Let $\text{ABCDEF}$ be a regular hexagon with each side of length $1$ cm. The area (in sq cm) of a square with $\text{AC}$ as one side is $3\sqrt{2}$ $3$ $4$ $\sqrt{3}$
Let $\text{ABCDEF}$ be a regular hexagon with each side of length $1$ cm. The area (in sq cm) of a square with $\text{AC}$ as one side is $3\sqrt{2}$$3$$4$$\sqrt{3}$
1 votes
1 answer
85
CAT 2017 Set-2 | Question: 89
Let $f\left ( x \right )=x^{2}$ and $g\left ( x \right )=2^{x}$, for all real $x$. Then the value of $ f \left ( f\left ( g\left ( x \right ) \right )+g\left( f\left ( x \right ) \right ) \right)$ at $x=1$ is $16$ $18$ $36$ $40$
Let $f\left ( x \right )=x^{2}$ and $g\left ( x \right )=2^{x}$, for all real $x$. Then the value of $ f \left ( f\left ( g\left ( x \right ) \right )+g\left( f\left ( x...
1 votes
1 answer
86
CAT 2017 Set-2 | Question: 88
If $x$ is a real number such that $\log_{3}5=\log_{5}\left ( 2+x \right )$, then which of the following is true? $0<x<3$ $23<x<30$ $x>30$ $3<x<23$
If $x$ is a real number such that $\log_{3}5=\log_{5}\left ( 2+x \right )$, then which of the following is true?$0<x<3$$23<x<30$$x>30$$3<x<23$
1 votes
1 answer
88
CAT 2017 Set-2 | Question: 87
If the product of three consecutive positive integers is $15600$ then the sum of the squares of these integers is $1777$ $1785$ $1875$ $1877$
If the product of three consecutive positive integers is $15600$ then the sum of the squares of these integers is $1777$$1785$$1875$$1877$
1 votes
1 answer
89
CAT 2017 Set-2 | Question: 85
If three sides of a rectangular park have a total length $400$ ft, then the area of the park is maximum when the length (in ft) of its longer side is $299$ $200$ $201$ $399$
If three sides of a rectangular park have a total length $400$ ft, then the area of the park is maximum when the length (in ft) of its longer side is$299$$200$$201$$399$
1 votes
1 answer
90
CAT 2017 Set-2 | Question: 94
How many different pairs $(a,b)$ of positive integers are there such that $a\leq b$ and $1/a+1/b=1/9$ None of these $2$ $0$ $1$
How many different pairs $(a,b)$ of positive integers are there such that $a\leq b$ and $1/a+1/b=1/9$None of these$2$$0$$1$
1 votes
1 answer
92
CAT 2017 Set-2 | Question: 93
Let $a_{1},a_{2},a_{3},a_{4},a_{5}$ be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with $2a_{3}$. If the sum of the numbers in the new sequence is $450$, then $a_{5}$ is $50$ $51$ $52$ $49$
Let $a_{1},a_{2},a_{3},a_{4},a_{5}$ be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with $2a_{3}$. If the s...
2 votes
2 answers
93
CAT 2017 Set-2 | Question: 91
If $9^{\left ( x-1/2 \right )}-2^{\left ( 2x-2 \right )}=4^{x}-3^{\left (2x-3 \right )}$, then $x$ is $3/2$ $2/5$ $3/4$ $4/9$
If $9^{\left ( x-1/2 \right )}-2^{\left ( 2x-2 \right )}=4^{x}-3^{\left (2x-3 \right )}$, then $x$ is$3/2$$2/5$$3/4$$4/9$
1 votes
1 answer
94
CAT 2017 Set-2 | Question: 90
The minimum possible value of the sum of the squares of the roots of the equation $x^{2}+\left ( a+3 \right )x-\left ( a+5 \right )=0$ is $1$ $2$ $3$ $4$
The minimum possible value of the sum of the squares of the roots of the equation $x^{2}+\left ( a+3 \right )x-\left ( a+5 \right )=0$ is$1$$2$$3$$4$
1 votes
1 answer
96
CAT 2017 Set-2 | Question: 98
Let $f\left ( x \right )=2x-5$ and $g\left ( x \right )=7-2x.$ Then $ \mid f\left ( x \right ) + g\left ( x \right ) \mid=\mid f(x) \mid + \mid g\left ( x \right ) \mid$ if and only if $5/2<x<7/2$ $x\leq 5/2$ or $x\geq 7/2$ $x< 5/2$ or $x\geq 7/2$ $5/2\leq x\leq 7/2$
Let $f\left ( x \right )=2x-5$ and $g\left ( x \right )=7-2x.$ Then $ \mid f\left ( x \right ) + g\left ( x \right ) \mid=\mid f(x) \mid + \mid g\left ( x \right ) \mid$ ...
0 votes
0 answers
97
CAT 2017 Set-2 | Question: 96
How many four digits number, which are divisible by $6$ , can be formed using the digits $0,2,3,4,6$ such that no digit is used more than once and $0$ does not occur in the left-most positions? $49$ $48$ $50$ $52$
How many four digits number, which are divisible by $6$ , can be formed using the digits $0,2,3,4,6$ such that no digit is used more than once and $0$ does not occur in t...
2 votes
1 answer
98
CAT 2017 Set-2 | Question: 95
In how many ways can $8$ identical pens be distributed among Amal, Bimal, Kamal so that Amal gets at least $1$ pen, Bimal gets a least $2$ pens, and Kamal gets a least $3$ pens? $5$ $6$ $7$ $8$
In how many ways can $8$ identical pens be distributed among Amal, Bimal, Kamal so that Amal gets at least $1$ pen, Bimal gets a least $2$ pens, and Kamal gets a least $3...
1 votes
1 answer
99
CAT 2017 Set-2 | Question: 97
If $f\left ( ab \right )=f\left ( a \right )f\left ( b \right )$ for all positive integers $a$ and $b$, then the largest possible value of $f\left (1\right )$ is $1$ $2$ $0$ $3$
If $f\left ( ab \right )=f\left ( a \right )f\left ( b \right )$ for all positive integers $a$ and $b$, then the largest possible value of $f\left (1\right )$ is $1$$2$$0...
1 votes
1 answer
100
CAT 2017 Set-2 | Question: 100
If $a_1=1/\left ( 2^{*}5 \right ),a_2=1/\left ( 5^{*}8 \right ),a_3=1/\left ( 8^{*}11 \right ),\dots\dots,$ then $a_1+a_2+\dots\dots+a_{100}$ is $25/151$ $1/2$ $1/4$ $111/55$
If $a_1=1/\left ( 2^{*}5 \right ),a_2=1/\left ( 5^{*}8 \right ),a_3=1/\left ( 8^{*}11 \right ),\dots\dots,$ then $a_1+a_2+\dots\dots+a_{100}$ is$25/151$$1/2$$1/4$$111/55$...
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