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CAT 2015 | Question: 72
$\text{PQRS}$ is a square. $\text{SR}$ is a tangent (at point $\text{S})$ to the circle with centre $\text{O}$ and $\text{TR = OS}$. Then the ratio of area of the circle to the area of the square is $\pi /3$ $11/7$ $3 /\pi$ $7/11$
$\text{PQRS}$ is a square. $\text{SR}$ is a tangent (at point $\text{S})$ to the circle with centre $\text{O}$ and $\text{TR = OS}$. Then the ratio of area of the circle ...
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CAT 2015 | Question: 73
From a circular sheet of paper with a radius $20$ cm, four circles of radius $5$ each are cut out. What is the ratio of the uncut to the cut portion? $1: 3$ $4: 1$ $3: 1$ $4: 3$
From a circular sheet of paper with a radius $20$ cm, four circles of radius $5$ each are cut out. What is the ratio of the uncut to the cut portion?$1: 3$$4: 1$$3: 1$$4:...
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CAT 2015 | Question: 70
For the product $n\left ( n+1 \right )\left ( 2n+1 \right ),n \in \mathbf{N}$, which one of the following is not necessarily true? It is even Divisible by $3$ Divisible by the sum of the square of first $n$ natural numbers Never divisible by $237$
For the product $n\left ( n+1 \right )\left ( 2n+1 \right ),n \in \mathbf{N}$, which one of the following is not necessarily true? It is evenDivisible by $3$Divisible by ...
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CAT 2015 | Question: 67
A person who has a certain amount with him goes to market. He can buy $50$ oranges or $40$ mangoes. He retains $10\%$ of the amount for taxi fares and buys $20$ mangoes and of the balance he purchases oranges. Number of oranges he can purchase is $36$ $40$ $15$ $20$
A person who has a certain amount with him goes to market. He can buy $50$ oranges or $40$ mangoes. He retains $10\%$ of the amount for taxi fares and buys $20$ mangoes a...
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CAT 2015 | Question: 81
The set of all positive integers is the union of two disjoint subsets$:\left \{ f\left ( 1 \right ),f\left ( 2 \right ), \dots, f\left ( n \right ), \dots \right \}$ ... $n \geq 1$. What is the value of $g\left ( 1 \right )?$ $0$ $2$ $1$ Cannot be determined
The set of all positive integers is the union of two disjoint subsets$:\left \{ f\left ( 1 \right ),f\left ( 2 \right ), \dots, f\left ( n \right ), \dots \right \}$ and ...
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CAT 2015 | Question: 79
If $x^{2}+y^{2}= 0.1$ and $\left | x-y \right |=0.2$, then $\left | x \right |+\left | y \right |$ is equal to $0.3$ $0.4$ $0.2$ $0.6$
If $x^{2}+y^{2}= 0.1$ and $\left | x-y \right |=0.2$, then $\left | x \right |+\left | y \right |$ is equal to$0.3$$0.4$$0.2$$0.6$
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CAT 2015 | Question: 83
In the figure above, $\text{AB = BC = CD = DE = EF = FG = GA}$. Then $\angle \text{DAE}$ is approximately $15^{\circ}$ $20^{\circ}$ $30^{\circ}$ $25^{\circ}$
In the figure above, $\text{AB = BC = CD = DE = EF = FG = GA}$. Then $\angle \text{DAE}$ is approximately $15^{\circ}$$20^{\circ}$$30^{\circ}$$25^{\circ}$
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CAT 2015 | Question: 89
Let $u_{n+1}=2u_{n}+1 \;(n=0,1,2,\dots)$ and $u_{n}=0$. Then $u_{10}$ nearest to ________
Let $u_{n+1}=2u_{n}+1 \;(n=0,1,2,\dots)$ and $u_{n}=0$. Then $u_{10}$ nearest to ________
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CAT 2015 | Question: 82
For all non-negative integers $x$ and $y$, $f(x,y)$ is defined as below. $f( 0,y) = y+1$ $f(x+1,0) = f( x, 1)$ $f( x+1, y+1) = f\left( x,f( x+1,y) \right)$ Then what is the value of $f(1,2)$ ________
For all non-negative integers $x$ and $y$, $f(x,y)$ is defined as below.$f( 0,y) = y+1$$f(x+1,0) = f( x, 1)$$f( x+1, y+1) = f\left( x,f( x+1,y) \right)$Then what is the v...
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CAT 2015 | Question: 86
Fourth term of an arithmetic progression is $8$. What is the sum of the first $7$ terms of the arithmetic progression? $7$ $64$ $56$ Cannot be determined
Fourth term of an arithmetic progression is $8$. What is the sum of the first $7$ terms of the arithmetic progression?$7$$64$$56$Cannot be determined
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CAT 2015 | Question: 95
The number of solutions of the equation $2x+y=40$ where both $x$ and $y$ are positive integers and $x\leq y$ is __________
The number of solutions of the equation $2x+y=40$ where both $x$ and $y$ are positive integers and $x\leq y$ is __________
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CAT 2015 | Question: 96
If $\log_{y}x=\left ( a \cdot \log_{z} y\right ) = \left ( b \cdot \log_{x}z \right )=ab,$ then which of the following pairs of values for $(a,b)$ is not possible? $(-2, 1/2)$ $(1, 1)$ $(\pi , 1/\pi )$ $(2 ,2)$
If $\log_{y}x=\left ( a \cdot \log_{z} y\right ) = \left ( b \cdot \log_{x}z \right )=ab,$ then which of the following pairs of values for $(a,b)$ is not possible?$(-2, 1...
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CAT 2015 | Question: 94
Consider the set $\text{S} = \left \{ 1, 2, 3, \dots,1000 \right \}$. How many arithmetic progressions can be formed from the elements of $\text{S}$ that start with $1$ and end with $1000$ and have at least $3$ elements? $3$ $4$ $6$ $7$
Consider the set $\text{S} = \left \{ 1, 2, 3, \dots,1000 \right \}$. How many arithmetic progressions can be formed from the elements of $\text{S}$ that start with $1$ a...
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CAT 2015 | Question: 92
Let $x<0,\:0<y<1,\:z>1$. Which of the following may be false? $\left (x ^{2} -z^{2}\right )$ has to be positive. $yz$ can be less than one. $xy$ can never be zero. $\left (y ^{2} -z^{2}\right )$ is always negative.
Let $x<0,\:0<y<1,\:z>1$. Which of the following may be false?$\left (x ^{2} -z^{2}\right )$ has to be positive.$yz$ can be less than one.$xy$ can never be zero.$\left (y ...
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CAT 2015 | Question: 91
The maximum possible value of $y = \min\left ( 1/2-3x^{2}/4,5x^{2}/4 \right )$ for the range $0<x<1$ is $1/3$ $1/2$ $5/27$ $5/16$
The maximum possible value of $y = \min\left ( 1/2-3x^{2}/4,5x^{2}/4 \right )$ for the range $0<x<1$ is$1/3$$1/2$$5/27$$5/16$
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CAT 2015 | Question: 90
Let $x<0.50,\:0<y<1, \:z>1.$. Given a set of numbers, the middle number, when they are arranged in ascending order, is called the median. So the median of the numbers $x,y,$ and $z$ would be less than one between $0$ and $1$ greater than $1$ cannot say
Let $x<0.50,\:0<y<1, \:z>1.$. Given a set of numbers, the middle number, when they are arranged in ascending order, is called the median. So the median of the numbers $x,...
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