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49
CAT 2012 | Question: 12
If $x$ is a real number, $[x]$ is greatest integer less than or equal to $x$, then $3[x]+2-[x]= 0$. Will the above equation have any real root? Yes No Will have real roots for $x< 0$ Will have real roots for $x> 0$
If $x$ is a real number, $[x]$ is greatest integer less than or equal to $x$, then $3[x]+2-[x]= 0$. Will the above equation have any real root?YesNoWill have real roots f...
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51
CAT 2012 | Question: 10
A certain number written in a certain base is $144$. Which of the following is always true? Square root of the number written in the same base is $12$. If base is increased by $2$, the number becomes $100$. Only I Only II Neither I nor II Both I and II
A certain number written in a certain base is $144$. Which of the following is always true?Square root of the number written in the same base is $12$.If base is increased...
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52
CAT 2012 | Question: 9
$p$ is a prime and $m$ is a positive integer. How many solutions exist for the equation $p^{6}-p= (m^{2}+m+6)(p-1)$? $0$ $1$ $2$ $\text{Infinite}$
$p$ is a prime and $m$ is a positive integer. How many solutions exist for the equation $p^{6}-p= (m^{2}+m+6)(p-1)$?$0$$1$$2$$\text{Infinite}$
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54
CAT 2012 | Question: 7
In the figure below, $\angle \text{MON} = \angle \text{MPO} = \angle \text{NQO} = 90^{\circ}$ and $\text{OQ}$ is the bisector of $\angle \text{MON}$ and $\text{QN} = 10, \text{OR} = 40/7$. Find $\text{OP}$. $4.8$ $4.5$ $4$ $5$
In the figure below, $\angle \text{MON} = \angle \text{MPO} = \angle \text{NQO} = 90^{\circ}$ and $\text{OQ}$ is the bisector of $\angle \text{MON}$ and $\text{QN} = 10,...
1 votes
1 answer
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CAT 2012 | Question: 6
Find the remainder of $2^{1040}$ divided by $131$. $1$ $3$ $5$ $7$
Find the remainder of $2^{1040}$ divided by $131$.$1$$3$$5$$7$
1 votes
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CAT 2012 | Question: 5
If the roots of the equation $(a^{2}+b^{2})x^{2}+2(b^{2}+c^{2})x+(b^{2}+c^{2})= 0$ are real, which of the following must hold true? $c^{2}\geq a^{2}$ $c^{4}\geq a^{2}(b^{2}+c^{2})$ $b^{2}\geq a^{2}$ $a^{4}\leq b^{2}(a^{2}+c^{2})$
If the roots of the equation $(a^{2}+b^{2})x^{2}+2(b^{2}+c^{2})x+(b^{2}+c^{2})= 0$ are real, which of the following must hold true?$c^{2}\geq a^{2}$$c^{4}\geq a^{2}(b^{2}...
1 votes
1 answer
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CAT 2012 | Question: 4
Which of the terms $2^{\frac{1}{3}},3^{\frac{1}{4}},4^{\frac{1}{6}},6^{\frac{1}{8}}$ and $10^{\frac{1}{12}}$ is the largest? $2^{\frac{1}{3}} \\$ $3^{\frac{1}{4}} \\$ $4^{\frac{1}{6}} \\$ $10^{\frac{1}{12}}$
Which of the terms $2^{\frac{1}{3}},3^{\frac{1}{4}},4^{\frac{1}{6}},6^{\frac{1}{8}}$ and $10^{\frac{1}{12}}$ is the largest?$2^{\frac{1}{3}} \\$$3^{\frac{1}{4}} \\$$4^{\f...
1 votes
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CAT 2012 | Question: 3
What is the sum of all the $2$-digit numbers which leave a remainder of $6$ when divided by $8$? $612$ $594$ $324$ $872$
What is the sum of all the $2$-digit numbers which leave a remainder of $6$ when divided by $8$?$612$$594$$324$$872$
1 votes
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CAT 2012 | Question: 2
Let $\text{P} = \{2,3,4,\ldots 100\}$ and $\text{Q}= \{101,102,103,\ldots 200\}.$ How many elements of $\text{Q}$ are there such that they do not have any element of $\text{P}$ as a factor? $20$ $24$ $23$ $21$
Let $\text{P} = \{2,3,4,\ldots 100\}$ and $\text{Q}= \{101,102,103,\ldots 200\}.$ How many elements of $\text{Q}$ are there such that they do not have any element of $\te...
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60
CAT 2012 | Question: 1
Consider a sequence $\text{S}$ whose $n$th term $T_{n}$ is defined as $1+\frac{3}{n}$, where $n=1,2, \dots$. Find the product of all the consecutive terms of $\text{S}$ starting from the $4$th term to the $60$th term. $1980.50$ $1985.55$ $1990.55$ $1975.55$
Consider a sequence $\text{S}$ whose $n$th term $T_{n}$ is defined as $1+\frac{3}{n}$, where $n=1,2, \dots$. Find the product of all the consecutive terms of $\text{S}$ s...
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