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1 answer
1441
CAT 1999 | Question: 64
If $|r − 6| = 11$ and $|2q − 12| = 8$, what is the minimum possible value of $\frac{q}{r}$? $- \frac{2}{5}$ $\frac{2}{17}$ $\frac{10}{17}$ None of these
If $|r − 6| = 11$ and $|2q − 12| = 8$, what is the minimum possible value of $\frac{q}{r}$?$- \frac{2}{5}$$\frac{2}{17}$$\frac{10}{17}$None of these
0 votes
2 answers
1445
CAT 1999 | Question: 60
For a scholarship, at the most n candidates out of 2n + 1 can be selected. If the number of different ways of selection of at least one candidate is 63, the maximum number of candidates that can be selected for the scholarship is 3 4 6 5
For a scholarship, at the most n candidates out of 2n + 1 can be selected. If the number of different ways of selection of at least one candidate is 63, the maximum numbe...
0 votes
1 answer
1446
CAT 1999 | Question: 59
Ten points are marked on a straight-line and 11 points are marked on another straight-line. How many triangles can be constructed with vertices from among the above points? 495 550 1045 2475
Ten points are marked on a straight-line and 11 points are marked on another straight-line. How many triangles can be constructed with vertices from among the above point...
0 votes
1 answer
1447
CAT 1999 | Question: 58
The remainder when 7$^{84}$ is divided by 342 is 0 1 49 341
The remainder when 7$^{84}$ is divided by 342 is0149341
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2 answers
1448
CAT 1999 | Question: 57
Let a, b, c be distinct digits. Consider a two-digit number ‘ab’ and a three-digit number ‘ccb’, both defined under the usual decimal number system, if $(ab)^2= ccb > 300$ then the value of b is 1 0 5 6
Let a, b, c be distinct digits. Consider a two-digit number ‘ab’ and a three-digit number ‘ccb’, both defined under the usual decimal number system, if $(ab)^2= c...
0 votes
1 answer
1449
CAT 1999 | Question: 56
The number of positive integer valued pairs (x, y) satisfying $4x – 17y = 1$ and $x \leq 1000$ is 59 57 55 58
The number of positive integer valued pairs (x, y) satisfying $4x – 17y = 1$ and $x \leq 1000$ is59575558
1 votes
1 answer
1450
CAT 2003 | Question: 2-105
$70\%$ of the employees in a multinational corporation have VCD players, $75$ percent have microwave ovens, $80$ percent have ACs and $85$ percent have washing machines. At least what percentage of employees has all four gadgets? $15\%$ $5\%$ $10\%$ Cannot be determined
$70\%$ of the employees in a multinational corporation have VCD players, $75$ percent have microwave ovens, $80$ percent have ACs and $85$ percent have washing machines. ...
1 votes
1 answer
1456
CAT 2003 | Question: 2-94
What is the sum of all two-digit numbers that give a remainder of $3$ when they are divided by $7?$ $666$ $676$ $683$ $777$
What is the sum of all two-digit numbers that give a remainder of $3$ when they are divided by $7?$$666$$676$$683$$777$
1 votes
1 answer
1457
CAT 2003 | Question: 2-93
If $\log_{10} x - \log_{10} \sqrt{x} = 2 \log_x 10$ then a possible value of $x$ is given by $10$ $\frac{1}{100}$ $\frac{1}{1000}$ None of these
If $\log_{10} x - \log_{10} \sqrt{x} = 2 \log_x 10$ then a possible value of $x$ is given by$10$$\frac{1}{100}$$\frac{1}{1000}$None of these
0 votes
1 answer
1461
CAT 2003 | Question: 2-89
If three positive real numbers $x, y, z$ satisfy $y – x = z – y$ and $x y z = 4,$ then what is the minimum possible value of $y?$ $2^{\frac{1}{3}}$ $2^{\frac{2}{3}}$ $2^{\frac{1}{4}}$ $2^{\frac{3}{4}}$
If three positive real numbers $x, y, z$ satisfy $y – x = z – y$ and $x y z = 4,$ then what is the minimum possible value of $y?$$2^{\frac{1}{3}}$$2^{\frac{2}{3}}$$2^...
0 votes
1 answer
1462
CAT 2003 | Question: 2-88
If both $a$ and $b$ belong to the set $\{1, 2, 3, 4\}$, then the number of equations of the form $ax^2 + bx + 1 = 0$ having real roots is $10$ $7$ $6$ $12$
If both $a$ and $b$ belong to the set $\{1, 2, 3, 4\}$, then the number of equations of the form $ax^2 + bx + 1 = 0$ having real roots is$10$$7$$6$$12$
0 votes
0 answers
1463
CAT 2003 | Question: 2-87
In the figure (not drawn to scale) given below, if $\text{AD = CD = BC},$ and $\measuredangle \text{BCE} = 96^{\circ}$, how much is $\measuredangle \text{DBC}?$ $32^{\circ}$ $84^{\circ}$ $64^{\circ}$ Cannot be determined
In the figure (not drawn to scale) given below, if $\text{AD = CD = BC},$ and $\measuredangle \text{BCE} = 96^{\circ}$, how much is $\measuredangle \text{DBC}?$$32^{\cir...
0 votes
1 answer
1472
CAT 2003 | Question: 2-78
If $x$ and $y$ are integers then the equation $5x + 19y = 64$ has no solution for $x < 300$ and $y < 0$ no solution for $x > 250$ and $y > – 100$ a solution for $250 < x < 300$ a solution for $– 59 < y < – 56$
If $x$ and $y$ are integers then the equation $5x + 19y = 64$ hasno solution for $x < 300$ and $y < 0$no solution for $x 250$ and $y – 100$a solution for $250 < x < 3...
0 votes
1 answer
1473
CAT 2003 | Question: 2-77
What is the remainder when $4^{96}$ is divided by $6?$ $0$ $2$ $3$ $4$
What is the remainder when $4^{96}$ is divided by $6?$ $0$$2$$3$$4$
0 votes
0 answers
1474
CAT 2003 | Question: 2-76
The length of the circumference of a circle equals the perimeter of a triangle of equal sides, and also the perimeter of a square. The areas covered by the circle, triangle, and square are $c, t,$ and $s,$ respectively. Then, $s > t > c$ $c > t > s$ $c > s > t$ $s > c > t$
The length of the circumference of a circle equals the perimeter of a triangle of equal sides, and also the perimeter of a square. The areas covered by the circle, triang...
0 votes
1 answer
1475
CAT 2003 | Question: 2-75
Using only $2, 5, 10, 25$ and $50$ paise coins, what will be the minimum number of coins required to pay exactly $78$ paise, $69$ paise and Rs $1.01$ to three different persons? $19$ $20$ $17$ $18$
Using only $2, 5, 10, 25$ and $50$ paise coins, what will be the minimum number of coins required to pay exactly $78$ paise, $69$ paise and Rs $1.01$ to three different ...
0 votes
1 answer
1476
CAT 2003 | Question: 2-74
If $\frac{1}{3} \log_3 \text{M} + 3 \log_3 \text{N} =1 + \log_{0.008} 5$, then $\text{M}^9 = \frac{9}{\text{N}}$ $\text{N}^9 = \frac{9}{\text{M}}$ $\text{M}^3 = \frac{3}{\text{N}}$ $\text{N}^9 = \frac{3}{\text{M}}$
If $\frac{1}{3} \log_3 \text{M} + 3 \log_3 \text{N} =1 + \log_{0.008} 5$, then$\text{M}^9 = \frac{9}{\text{N}}$$\text{N}^9 = \frac{9}{\text{M}}$$\text{M}^3 = \frac{3}{\te...
0 votes
1 answer
1477
CAT 2003 | Question: 2-73
A real number $x$ satisfying $1- \frac{1}{n} < x \leq 3 + \frac{1}{n}$ for every positive integer $n,$ is best described by $1 < x < 4$ $0 < x \leq 4$ $0 < x \geq 4$ $1 \leq x \leq 3$
A real number $x$ satisfying $1- \frac{1}{n} < x \leq 3 + \frac{1}{n}$ for every positive integer $n,$ is best described by$1 < x < 4$$0 < x \leq 4$$0 < x \geq 4$$1 \leq ...
0 votes
1 answer
1478
CAT 2003 | Question: 2-72
The number of roots common between $x^3 + 3 x^2 + 4x + 5 = 0$ and $x^3 + 2 x^2 + 7x +3 =0$ is $0$ $1$ $2$ $3$
The number of roots common between $x^3 + 3 x^2 + 4x + 5 = 0$ and $x^3 + 2 x^2 + 7x +3 =0$ is$0$$1$$2$$3$
0 votes
0 answers
1479
CAT 2003 | Question: 2-71
Let $\text{ABCDEF}$ be a regular hexagon. What is the ratio of the area of the triangle $\text{ACE}$ to that of the hexagon $\text{ABCDEF}?$ $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$ $\frac{5}{6}$
Let $\text{ABCDEF}$ be a regular hexagon. What is the ratio of the area of the triangle $\text{ACE}$ to that of the hexagon $\text{ABCDEF}?$$\frac{1}{3}$$\frac{1}{2}$$\fr...
0 votes
0 answers
1480
CAT 2003 | Question: 2-70
Consider the sets $T_n = \{n, n + 1, n + 2, n + 3, n + 4\}$, where $n = 1, 2, 3,\dots, 96.$ How many of these sets contain $6$ or any integral multiple thereof (i.e., any one of the numbers $6, 12, 18, \dots)?$ $80$ $81$ $82$ $83$
Consider the sets $T_n = \{n, n + 1, n + 2, n + 3, n + 4\}$, where $n = 1, 2, 3,\dots, 96.$ How many of these sets contain $6$ or any integral multiple thereof (i.e., any...
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