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Recent questions tagged cat2003-1

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81
CAT 2003 | Question: 1-139
If the product of $n$ positive real numbers is unity, then their sum is necessarily a multiple of $n$ equal to $n+\left(\frac{1}{n}\right)$ never less than $n$ a positive integer
If the product of $n$ positive real numbers is unity, then their sum is necessarily a multiple of $n$equal to $n+\left(\frac{1}{n}\right)$never less than $n$a positive in...
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82
CAT 2003 | Question: 1-138
There are $8436$ steel balls, each with a radius of $1$ centimeter, stacked in a pile, with $1$ ball on top, $3$ balls in second layer, $6$ in the third layer, $10$ in the fourth, and so on. The number of horizontal layers in the pile is $34$ $38$ $36$ $32$
There are $8436$ steel balls, each with a radius of $1$ centimeter, stacked in a pile, with $1$ ball on top, $3$ balls in second layer, $6$ in the third layer, $10$ in th...
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85
CAT 2003 | Question: 1-137
In the diagram given below, $\measuredangle \text{ABD} = \measuredangle \text{CDB} = \measuredangle \text{PQD} = 90^{\circ}$. If $\text{AB : CD} = 3:1,$ the ratio of $\text{CD : PQ}$ is $1:0.69$ $1:0.75$ $1:0.72$ None of these
In the diagram given below, $\measuredangle \text{ABD} = \measuredangle \text{CDB} = \measuredangle \text{PQD} = 90^{\circ}$. If $\text{AB : CD} = 3:1,$ the ratio of $\t...
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86
CAT 2003 | Question: 1-134
How many three digit positive integers, with digits $x, y$ and $z$ in the hundred's, ten's and unit's place respectively, exist such that $x < y, z < y$ and $x \neq 0?$ $245$ $285$ $240$ $320$
How many three digit positive integers, with digits $x, y$ and $z$ in the hundred's, ten's and unit's place respectively, exist such that $x < y, z < y$ and $x \neq 0?$$2...
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91
CAT 2003 | Question: 1-129
Let $p$ and $q$ be the roots of the quadratic equation $x^2 - (a-2) x-a -1 =0.$ What is the minimum possible value of $p^2 + q^2?$ $0$ $3$ $4$ $5$
Let $p$ and $q$ be the roots of the quadratic equation $x^2 - (a-2) x-a -1 =0.$ What is the minimum possible value of $p^2 + q^2?$$0$$3$$4$$5$
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CAT 2003 | Question: 1-128
The $288$-th term of the series $a,b,b,c,c,c,d,d,d,d,e,e,e,e,e,f,f,f,f,f,f, \dots$ is $u$ $v$ $w$ $x$
The $288$-th term of the series $a,b,b,c,c,c,d,d,d,d,e,e,e,e,e,f,f,f,f,f,f, \dots$ is$u$$v$$w$$x$
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98
CAT 2003 | Question: 1-118
How many even integers $n,$ where $100 \leq n \leq 200$, are divisible neither by $7$ nor by $9?$ $40$ $37$ $39$ $38$
How many even integers $n,$ where $100 \leq n \leq 200$, are divisible neither by $7$ nor by $9?$$40$$37$$39$$38$
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99
CAT 2003 | Question: 1-117
The function $f(x) = |x-2| + |2.5-x| + |3.6-x|$, where $x$ is a real number, attains a minimum at $x=2.3$ $x=2.5$ $x=2.7$ None of these
The function $f(x) = |x-2| + |2.5-x| + |3.6-x|$, where $x$ is a real number, attains a minimum at$x=2.3$$x=2.5$$x=2.7$None of these
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100
CAT 2003 | Question: 1-116
Let $g(x) = \max(5-x, \: x+2)$. The smallest possible value of $g(x)$ is $4.0$ $4.5$ $1.5$ None of these
Let $g(x) = \max(5-x, \: x+2)$. The smallest possible value of $g(x)$ is$4.0$$4.5$$1.5$None of these
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104
CAT 2003 | Question: 1-110
The sum of $3$-rd and $15$-th elements of an arithmetic progression is equal to the sum of $6$-th, $11$-th and $13$-th elements of the same progression. Then which element of the series should necessarily be equal to zero? $1$-st $9$-th $12$-th None of these
The sum of $3$-rd and $15$-th elements of an arithmetic progression is equal to the sum of $6$-th, $11$-th and $13$-th elements of the same progression. Then which elemen...
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108
CAT 2003 | Question: 1-106
When the curves, $y=\log_{10} x$ and $y=x^{-1}$ are drawn in the $x-y$ plane, how many times do they intersect for values $x \geq 1?$ Never Once Twice More than twice
When the curves, $y=\log_{10} x$ and $y=x^{-1}$ are drawn in the $x-y$ plane, how many times do they intersect for values $x \geq 1?$NeverOnceTwiceMore than twice
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109
CAT 2003 | Question: 1-105
The number of non-negative real roots of $2^x - x - 1 =0$ equals _______ $0$ $1$ $2$ $3$
The number of non-negative real roots of $2^x - x - 1 =0$ equals _______$0$$1$$2$$3$
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