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1481
CAT 2003 | Question: 2-69
The infinite sum $1 + \frac{4}{7} + \frac{9}{7^2} + \frac{16}{7^3} + \frac{25}{7^4} + \dots$ equals $\frac{27}{14}$ $\frac{21}{13}$ $\frac{49}{27}$ $\frac{256}{147}$
The infinite sum $1 + \frac{4}{7} + \frac{9}{7^2} + \frac{16}{7^3} + \frac{25}{7^4} + \dots$ equals$\frac{27}{14}$$\frac{21}{13}$$\frac{49}{27}$$\frac{256}{147}$
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1486
CAT 2003 | Question: 2-62
If $|b| \geq 1$ and $x =\; – |a| b$, then which one of the following is necessarily true? $a – xb < 0$ $a – xb \geq 0$ $a – xb > 0$ $a – xb \leq 0$
If $|b| \geq 1$ and $x =\; – |a| b$, then which one of the following is necessarily true?$a – xb < 0$$a – xb \geq 0$$a – xb 0$$a – xb \leq 0$
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1488
CAT 2003 | Question: 2-60
If $13x + 1 < 2$ and $z,$ and $z + 3 = 5y^2$, then $x$ is necessarily less than $y$ $x$ is necessarily greater than $y$ $x$ is necessarily equal to $y$ None of the above is necessarily true.
If $13x + 1 < 2$ and $z,$ and $z + 3 = 5y^2$, then$x$ is necessarily less than $y$$x$ is necessarily greater than $y$$x$ is necessarily equal to $y$None of the above is n...
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1489
CAT 2003 | Question: 2-59
If n is such that $36 \leq n \leq 72$ then $x = \frac{n^2 + 2 \sqrt{n}(n+4) +16}{n+4\sqrt{n}+4}$ satisfies $20 < x < 54$ $23 < x < 58$ $25 < x < 64$ $28 < x < 60$
If n is such that $36 \leq n \leq 72$ then $x = \frac{n^2 + 2 \sqrt{n}(n+4) +16}{n+4\sqrt{n}+4}$ satisfies$20 < x < 54$$23 < x < 58$$25 < x < 64$$28 < x < 60$
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1491
CAT 2003 | Question: 2-57
Let $x$ and $y$ be positive integers such that $x$ is prime and $y$ is composite. Then, $y – x$ cannot be an even integer $xy$ cannot be an even integer. $\frac{x+y}{x}$ cannot be an even integer None of these.
Let $x$ and $y$ be positive integers such that $x$ is prime and $y$ is composite. Then,$y – x$ cannot be an even integer$xy$ cannot be an even integer.$\frac{x+y}{x}$ c...
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1494
CAT 2003 | Question: 2-54
If $a, a + 2$ and $a + 4$ are prime numbers, then the number of possible solutions for $a$ is: one two three more than three
If $a, a + 2$ and $a + 4$ are prime numbers, then the number of possible solutions for $a$ is:onetwothreemore than three
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1517
CAT 2002 | Question: 90
The $n$th element of a series is represented as $X_n = (-1)^n x_{n-1}$ If $X_0 =x$ and $x>0$, then which of the following is always true? $X_n$ is positive if $n$ is even $X_n$ is positive if $n$ is odd $X_n$ is negative if $n$ is even None of these
The $n$th element of a series is represented as$X_n = (-1)^n x_{n-1}$If $X_0 =x$ and $x>0$, then which of the following is always true?$X_n$ is positive if $n$ is even$X_...
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1520
CAT 2000 | Question: 76
Answer the following question based on the information given below. For real numbers $x, y,$ ... $x$ and $y$ are less than $-1$ Both $x$ and $y$ are positive Both $x$ and $y$ are negative $y > x$
Answer the following question based on the information given below.For real numbers $x, y,$ let$f(x, y) = \left\{\begin{matrix} \text{Positive square-root of}\; (x + y),\...
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