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Recent questions tagged cat2019-1

1 votes
1 answer
81
CAT 2019 Set-1 | Question: 76
In a circle of radius $11$ cm, CD is a diameter and AB is a chord of length $20.5$ cm. If AB and CD intersect at a point E inside the circle and CE has length $7$ cm, then the difference of the lengths of BE and AE, in cm, is $2.5$ $3.5$ $0.5$ $1.5$
In a circle of radius $11$ cm, CD is a diameter and AB is a chord of length $20.5$ cm. If AB and CD intersect at a point E inside the circle and CE has length $7$ cm, the...
1 votes
1 answer
83
CAT 2019 Set-1 | Question: 87
For any positive integer $n$, let $f(n)=n(n+1)$ if n is even, and $f(n)=n+3$ if n is odd. if $m$ is a positive integer such that $8f(m+1)-f(m)=2$, then $m$ equals _______
For any positive integer $n$, let $f(n)=n(n+1)$ if n is even, and $f(n)=n+3$ if n is odd. if $m$ is a positive integer such that $8f(m+1)-f(m)=2$, then $m$ equals ______...
2 votes
1 answer
86
CAT 2019 Set-1 | Question: 83
If $(5.55)^{x}=(0.555)^{y}=1000$, then the value of $\frac{1}{x}-\frac{1}{y}$ is $3$ $1$ $\frac{1}{3}$ $\frac{2}{3}$
If $(5.55)^{x}=(0.555)^{y}=1000$, then the value of $\frac{1}{x}-\frac{1}{y}$ is$3$$1$$\frac{1}{3}$$\frac{2}{3}$
2 votes
1 answer
88
CAT 2019 Set-1 | Question: 84
The product of the distinct roots of $|x^{2}-x-6|=x+2$ is $-8$ $-24$ $-4$ $-16$
The product of the distinct roots of $|x^{2}-x-6|=x+2$ is$-8$$-24$$-4$$-16$
2 votes
1 answer
92
CAT 2019 Set-1 | Question: 94
If the rectangular faces of a brick have their diagonals in the ratio $3:2\sqrt{3}:\sqrt{15}$, then the ratio of the length of the shortest edge of the brick to that of its longest edge is $\sqrt{3}:2$ $2:\sqrt{5}$ $1:\sqrt{3}$ $\sqrt{2}:\sqrt{3}$
If the rectangular faces of a brick have their diagonals in the ratio $3:2\sqrt{3}:\sqrt{15}$, then the ratio of the length of the shortest edge of the brick to that of i...
1 votes
1 answer
93
CAT 2019 Set-1 | Question: 92
Let $x$ and $y$ be positive real numbers such that $\log _{5}(x+y)+\log _{5}(x-y)=3$, and $\log _{2}y-\log _{2}x=1-\log_{2}3$. Then $xy$ equals $250$ $25$ $100$ $150$
Let $x$ and $y$ be positive real numbers such that $\log _{5}(x+y)+\log _{5}(x-y)=3$, and $\log _{2}y-\log _{2}x=1-\log_{2}3$. Then $xy$ equals$250$$25$$100$$150$
2 votes
1 answer
94
CAT 2019 Set-1 | Question: 91
The number of the real roots of the equation $2\cos (x(x+1))=2^{x}+2^{-x}$ is $2$ $1$ infinite $0$
The number of the real roots of the equation $2\cos (x(x+1))=2^{x}+2^{-x}$ is$2$$1$infinite$0$
1 votes
1 answer
95
CAT 2019 Set-1 | Question: 90
Consider a function $f$ satisfying $f(x+y)=f(x)f(y)$ where $x,y$ are positive integers, and $f(1)=2$. If $f(a+1)+f(a+2)+\ldots +f(a+n)=16(2^{n}-1)$ then $a$ is equal to ______
Consider a function $f$ satisfying $f(x+y)=f(x)f(y)$ where $x,y$ are positive integers, and $f(1)=2$. If $f(a+1)+f(a+2)+\ldots +f(a+n)=16(2^{n}-1)$ then $a$ is equal to _...
2 votes
1 answer
96
CAT 2019 Set-1 | Question: 89
If $a_{1}+a_{2}+a_{3}+\dots+a_{n}=3(2^{n+1}-2)$, for every $n\geq 1$, then $a_{11}$ equals ______
If $a_{1}+a_{2}+a_{3}+\dots+a_{n}=3(2^{n+1}-2)$, for every $n\geq 1$, then $a_{11}$ equals ______
2 votes
1 answer
98
CAT 2019 Set-1 | Question: 98
In a race of three horses, the first beat the second by $11$ metres and the third by $90$ metres. If the second beat the third by $80$ metres, what was the length, in metres,of the racecourse _________
In a race of three horses, the first beat the second by $11$ metres and the third by $90$ metres. If the second beat the third by $80$ metres, what was the length, in met...
1 votes
1 answer
99
CAT 2019 Set-1 | Question: 99
The number of solutions to the equation $|x|(6x^{2}+1)=5x^{2}$ is _________
The number of solutions to the equation $|x|(6x^{2}+1)=5x^{2}$ is _________
2 votes
1 answer
100
CAT 2019 Set-1 | Question: 100
The product of two positive numbers is $616$. If the ratio of the difference of their cubes to the cube of their difference is $157:3$, then the sum of the two numbers is $58$ $50$ $95$ $85$
The product of two positive numbers is $616$. If the ratio of the difference of their cubes to the cube of their difference is $157:3$, then the sum of the two numbers i...
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