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Recent questions tagged cat2019-2

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48
CAT 2019 Set-2 | Question: 54
Three doctors, Dr. Ben, Dr. Kane and Dr. Wayne visit a particular clinic Monday to Saturday to see patients. Dr. Ben sees each patient for $10$ minutes and charges Rs. $100/-$. Dr. Kane sees each patient for $15$ minutes and charges Rs. $200/-$, ... $15$ $30$ $10$ $0$
Three doctors, Dr. Ben, Dr. Kane and Dr. Wayne visit a particular clinic Monday to Saturday to see patients. Dr. Ben sees each patient for $10$ minutes and charges Rs. $1...
1 votes
1 answer
57
CAT 2019 Set-2 | Question: 70
How many pairs $(m,n)$ of positive integers satisfy the equation $m^{2}+105=n^{2}$ _______
How many pairs $(m,n)$ of positive integers satisfy the equation $m^{2}+105=n^{2}$ _______
1 votes
1 answer
60
CAT 2019 Set-2 | Question: 68
If x is a real number, then $\sqrt{\log _{e}\frac{4x-x^{2}}{3}}$ is a real number if and only if $1\leq x\leq 2$ $-3\leq x\leq 3$ $1\leq x\leq 3$ $-1\leq x\leq 3$
If x is a real number, then $\sqrt{\log _{e}\frac{4x-x^{2}}{3}}$ is a real number if and only if$1\leq x\leq 2$$-3\leq x\leq 3$$1\leq x\leq 3$$-1\leq x\leq 3$
1 votes
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65
CAT 2019 Set-2 | Question: 75
The average of $30$ integers is $5$. Among these $30$ integers, there are exactly $20$ which do not exceed $5$. What is the highest possible value of the average of these $20$ integers? $4$ $3.5$ $4.5$ $5$
The average of $30$ integers is $5$. Among these $30$ integers, there are exactly $20$ which do not exceed $5$. What is the highest possible value of the average of these...
1 votes
1 answer
66
CAT 2019 Set-2 | Question: 72
Two circles, each of radius $4$ cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, is $\sqrt{2}$ $\frac{\pi }{3}$ $\frac{1}{\sqrt{2}}$ $1$
Two circles, each of radius $4$ cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, the...
1 votes
1 answer
68
CAT 2019 Set-2 | Question: 82
In a triangle $\text{ABC}$, medians $\text{AD}$ and $\text{BE}$ are perpendicular to each other, and have lengths $12$ cm and $9$ cm, respectively. Then, the area of triangle $\text{ABC}$, in sq cm. is $68$ $72$ $78$ $80$
In a triangle $\text{ABC}$, medians $\text{AD}$ and $\text{BE}$ are perpendicular to each other, and have lengths $12$ cm and $9$ cm, respectively. Then, the area of tria...
1 votes
1 answer
69
CAT 2019 Set-2 | Question: 80
Let $a_{1},a_{2}\dots$ be integers such that $a_{1}-a_{2}+a_{3}-a_{4}+\dots+(-1)^{n-1}a_{n}=n$, for all $n\geq 1$ Then $a_{51}+a_{52}+\dots+a_{1023}$ equals $-1$ $10$ $0$ $1$
Let $a_{1},a_{2}\dots$ be integers such that $a_{1}-a_{2}+a_{3}-a_{4}+\dots+(-1)^{n-1}a_{n}=n$, for all $n\geq 1$ Then $a_{51}+a_{52}+\dots+a_{1023}$ equals$-1$$10$$0$$1$...
1 votes
1 answer
70
CAT 2019 Set-2 | Question: 79
The real root of the equation $2^{6x}+2^{3x+2}-21=0$ is $\frac{\log_{2}7}{3}$ $\log_{2}9$ $\frac{\log_{2}3}{3}$ $\log_{2}27$
The real root of the equation $2^{6x}+2^{3x+2}-21=0$ is$\frac{\log_{2}7}{3}$$\log_{2}9$$\frac{\log_{2}3}{3}$$\log_{2}27$
1 votes
1 answer
71
CAT 2019 Set-2 | Question: 78
The quadratic equation $x^{2}+bx+c=0$ has two roots $4a$ and $3a$, where a is an integer. Which of the following is a possible value of $b^{2}+c$? $3721$ $549$ $427$ $361$
The quadratic equation $x^{2}+bx+c=0$ has two roots $4a$ and $3a$, where a is an integer. Which of the following is a possible value of $b^{2}+c$?$3721$$549$$427$$361$
4 votes
1 answer
75
CAT 2019 Set-2 | Question: 85
How many factors $2^{4}\times3^{5}\times10^{4}$ are perfect squares which are greater than $1$ _______
How many factors $2^{4}\times3^{5}\times10^{4}$ are perfect squares which are greater than $1$ _______
1 votes
1 answer
76
CAT 2019 Set-2 | Question: 87
Let $a,b,x,y$ be real numbers such that $a^{2}+b^{2}=25,x^{2}+y^{2}=169$, and $ax+by=65$. If $k=ay-bx$, then $k=0$ $0< k\leq \frac{5}{13}$ $k=\frac{5}{13}$ $k> \frac{5}{13}$
Let $a,b,x,y$ be real numbers such that $a^{2}+b^{2}=25,x^{2}+y^{2}=169$, and $ax+by=65$. If $k=ay-bx$, then$k=0$$0< k\leq \frac{5}{13}$$k=\frac{5}{13}$$k \frac{5}{13}$
1 votes
1 answer
77
CAT 2019 Set-2 | Question: 86
What is the largest positive integer $n$ such that $\frac{n^{2}+7n+12}{n^{2}-n-12}$ is also a positive integer? $8$ $12$ $16$ $6$
What is the largest positive integer $n$ such that $\frac{n^{2}+7n+12}{n^{2}-n-12}$ is also a positive integer?$8$$12$$16$$6$
1 votes
1 answer
79
CAT 2019 Set-2 | Question: 91
John gets Rs $57$ per hour of regular work and Rs $114$ per hour of overtime work. He works altogether $172$ hours and his income from overtime hours is $15\%$ of his income from regular hours. Then, for how many hours did he work overtime _________
John gets Rs $57$ per hour of regular work and Rs $114$ per hour of overtime work. He works altogether $172$ hours and his income from overtime hours is $15\%$ of his inc...
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