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Recent questions tagged cat1997

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CAT 1997 | Question: 143
In the given figure, $EADF$ is a rectangle and $ABC$ is a triangle whose vertices lie on the sides of $EADF$. $AE = 22,BE = 6,CF = l6$ and $BF = 2$. Find the length of the line joining the midpoints of the sides $AB$ and $BC$. $4\sqrt{2}$ $5$ $3.5$ None of these
In the given figure, $EADF$ is a rectangle and $ABC$ is a triangle whose vertices lie on the sides of $EADF$. $AE = 22,BE = 6,CF = l6$ and $BF = 2$. Find the length of th...
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CAT 1997 | Question: 142
In the adjoining figure, points $A, B, C$ and $D$ lie on the circle. $AD = 24$ and $BC =12$. What is the ratio of the area of the triangle $CBE$ to that of the triangle $ADE$? $1:4$ $1:2$ $1:3$ Insufficient data
In the adjoining figure, points $A, B, C$ and $D$ lie on the circle. $AD = 24$ and $BC =12$. What is the ratio of the area of the triangle $CBE$ to that of the triangle $...
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CAT 1997 | Question: 136
In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the shorter to the longer side? $3:2$ $1:3$ $2:5$ $3:4$
In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the shorter to the longe...
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CAT 1997 | Question: 135
In a triangle $ABC$, points $P, Q$ and $R$ are the mid-points of the sides $AB, BC$ and $CA$ respectively. If the area of the triangle $ABC$ is $20$ sq units, find the area of the triangle $PQR$ $10$ sq. units $15$ sq. units $5$ sq. units None of these
In a triangle $ABC$, points $P, Q$ and $R$ are the mid-points of the sides $AB, BC$ and $CA$ respectively. If the area of the triangle $ABC$ is $20$ sq units, find the ar...
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CAT 1997 | Question: 131
$ABC$ is a three-digit number in which $A>O$. The value of $ABC$ is equal to the sum of the factorials of its three digits. What is the value of $B$? $9$ $7$ $4$ $2$
$ABC$ is a three-digit number in which $A>O$. The value of $ABC$ is equal to the sum of the factorials of its three digits. What is the value of $B$?$9$$7$ $4$ $2$
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CAT 1997 | Question: 129
For these questions, the following functions have been defined: $la(x,y,z) = min(x+y, y+z)$ $le (x,y,z) = max(x–y, y–z)$ $ma(x,y,z)=(1/2) [le(x,y,z)+la(x,y,z)]$ What is the value of $ma(10, 4, le(la(10, 5, 3), 5,3))$ $7.0$ $6.5$ $8.0$ $7.5$
For these questions, the following functions have been defined:$la(x,y,z) = min(x+y, y+z)$$le (x,y,z) = max(x–y, y–z)$$ma(x,y,z)=(1/2) [le(x,y,z)+la(x,y,z)]$What is t...
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CAT 1997 | Question: 127
P, Q and R are three consecutive odd numbers in ascending order. If the value of three times P is three less than two times R, find the value of R. $5$ $7$ $9$ $11$
P, Q and R are three consecutive odd numbers in ascending order. If the value of three times P is three less than two times R, find the value of R.$5$$7$$9$$11$
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CAT 1997 | Question: 126
AB is the diameter of the given circle, while points C and D lie on the circumference as shown. If AB is $15$ cm, AC is $12$ cm and BD is $9$ cm, find the area of the quadrilateral ACBD. $54 \pi$ $216\pi$ $162\pi$ None of these
AB is the diameter of the given circle, while points C and D lie on the circumference as shown. If AB is $15$ cm, AC is $12$ cm and BD is $9$ cm, find the area of the qua...
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CAT 1997 | Question: 125
A man earns $x$% on the first $2000$ rupees and $y$% on the rest of his income. If he earns Rs $700$ from Rs $4000$ and Rs $900$ from Rs $5000$ of income, find $x$. $20$ $15$ $35$ None of these
A man earns $x$% on the first $2000$ rupees and $y$% on the rest of his income. If he earns Rs $700$ from Rs $4000$ and Rs $900$ from Rs $5000$ of income, find $x$.$20$$1...
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CAT 1997 | Question: 121
Which of the following is true? $_{7}^{3^{2}} = (7^{3})^{2}$ $_{7}^{3^{2}} > (7^{3})^{2}$ $_{7}^{3^{2}} < (7^{3})^{2}$ None of these
Which of the following is true?$_{7}^{3^{2}} = (7^{3})^{2}$$_{7}^{3^{2}} (7^{3})^{2}$$_{7}^{3^{2}} < (7^{3})^{2}$None of these
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CAT 1997 | Question: 120
If $m$ and $n$ are integers divisible by $5$, which of the following is not necessarily true? $m–n$ is divisible $5$. $m^{2}-n^{2}$ is divisible by $25$. $m+n$ is divisible by $10$ None of the above.
If $m$ and $n$ are integers divisible by $5$, which of the following is not necessarily true?$m–n$ is divisible $5$.$m^{2}-n^{2}$ is divisible by $25$.$m+n$ is divisibl...
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CAT 1997 | Question: 119
The sum of the areas of two circles which touch each other externally is $153\pi$. If the sum of their radii is $15$, find the ratio of the larger to the smaller radius. $4$ $2$ $3$ None of these
The sum of the areas of two circles which touch each other externally is $153\pi$. If the sum of their radii is $15$, find the ratio of the larger to the smaller radius.$...
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CAT 1997 | Question: 118
If the roots, $x_{1}$ and $x_{2}$ of the quadratic equation $x^{2}-2x+c=0$ also satisfy the equation $7x_{2}-4x_{1}=47$, then which of the following is true? $c=-15$ $x_{1}=-5, x_{2}=3$ $x_{1}=4.5, x_{2}=-2.5$ None of these
If the roots, $x_{1}$ and $x_{2}$ of the quadratic equation $x^{2}-2x+c=0$ also satisfy the equation $7x_{2}-4x_{1}=47$, then which of the following is true? $c=-15$$x_{1...
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CAT 1997 | Question: 117
The average marks of a student in ten papers are $80$. If the highest and the lowest scores are not considered, the average is $81$. If his highest score is $92$, find the lowest. $55$ $60$ $62$ Cannot be determined
The average marks of a student in ten papers are $80$. If the highest and the lowest scores are not considered, the average is $81$. If his highest score is $92$, find th...
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CAT 1997 | Question: 116
$P$ and $Q$ are two integers such that $P \times Q = 64$. Which of the following cannot be the value of $P+Q$? $20$ $65$ $16$ $35$
$P$ and $Q$ are two integers such that $P \times Q = 64$. Which of the following cannot be the value of $P+Q$?$20$$65$$16$$35$
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CAT 1997 | Question: 115
A candidate was asked to find $7/8$th of a positive number; he found $7/18$th of the same by mistake. If his answer was $770$ less than the correct one, then the original given number was $1260$ $6160$ $1584$ None of these
A candidate was asked to find $7/8$th of a positive number; he found $7/18$th of the same by mistake. If his answer was $770$ less than the correct one, then the original...
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CAT 1997 | Question: 113
Fresh grapes contain $90$% water by weight while dried grapes contain $20$% water by weight. The weight of dry grapes available from $20$ kg of fresh grapes will be. $2$ kg $2.4$ kg $2.5$ kg None of these
Fresh grapes contain $90$% water by weight while dried grapes contain $20$% water by weight. The weight of dry grapes available from $20$ kg of fresh grapes will be.$2$ k...
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CAT 1997 | Question: 111
How many values of the natural number $n$ are possible so that the expression $(16n^{2}+7n+6)/n$ is also a natural number? Infinitely many $3$ $4$ None of these d & c
How many values of the natural number $n$ are possible so that the expression $(16n^{2}+7n+6)/n$ is also a natural number?Infinitely many$3$$4$None of thesed & c
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CAT 1997 | Question: 110
After a discount of $11.11$%, a trader still makes a gain of $14.28$%. At how many percent above the cost price does he mark his goods? $28.56$% $35$% $22.22$% None of these
After a discount of $11.11$%, a trader still makes a gain of $14.28$%. At how many percent above the cost price does he mark his goods?$28.56$% $35$%$22.22$%None of these...
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CAT 1997 | Question: 109
If $\log_{2}[ \log_{7} (x^{2}-x+37)]=1$ then what could be the value of $x$? $3$ $5$ $4$ None of these $c$
If $\log_{2}[ \log_{7} (x^{2}-x+37)]=1$ then what could be the value of $x$?$3$$5$$4$None of these$c$
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CAT 1997 | Question: 108
In how many ways can the eight directors, the Vice chairman and the Chairman of a firm be seated at around- table, if the Chairman has to sit between the Vice- chairman and a director? $9! \times 2$ $2 \times 8!$ $2 \times 7!$ None of these
In how many ways can the eight directors, the Vice chairman and the Chairman of a firm be seated at around- table, if the Chairman has to sit between the Vice- chairman a...
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CAT 1997 | Question: 107
A student gets an aggregate of 60% marks in five subjects in the ratio $10:9:8:7:6$. If the passing marks are $50$% of the maximum marks and each subjects has the same maximum marks, in how many subjects did he pass the exam? $2$ $3$ $4$ $5$
A student gets an aggregate of 60% marks in five subjects in the ratio $10:9:8:7:6$. If the passing marks are $50$% of the maximum marks and each subjects has the same ma...
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