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1642
CAT 2002 | Question: 96
If $pqr=1$ then $\frac{1}{1+p+r^{-1}} + \frac{1}{1+q+r^{-1}} + \frac{1}{1+r+p^{-1}} $ is equivalent to $p+q+r$ $\frac{1}{p+q+r}$ $1$ $p^{-1}+q^{-1}+r^{-1}$
If $pqr=1$ then $\frac{1}{1+p+r^{-1}} + \frac{1}{1+q+r^{-1}} + \frac{1}{1+r+p^{-1}} $ is equivalent to$p+q+r$$\frac{1}{p+q+r}$$1$$p^{-1}+q^{-1}+r^{-1}$
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1649
CAT 2002 | Question: 86
In how many ways, we can choose a black and a white square on a chess board such that the two are not in the same row or column? $32$ $96$ $24$ None of these
In how many ways, we can choose a black and a white square on a chess board such that the two are not in the same row or column?$32$$96$$24$None of these
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1650
CAT 2002 | Question: 85
How many numbers between $0$ and one million can be formed using $0, 7$ and $8?$ $486$ $1086$ $728$ None of these
How many numbers between $0$ and one million can be formed using $0, 7$ and $8?$$486$$1086$$728$None of these
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1652
CAT 2002 | Question: 83
Neeraj has a rectangular field of size $20 \times 40$ sq.mt. He has to mow the field with a moving machine of width $1$ mt. If he mows the field from the extremes to the centre, then the number of rounds taken by him to mow half of the field will be $3.5$ $3.8$ $3$ $4$
Neeraj has a rectangular field of size $20 \times 40$ sq.mt. He has to mow the field with a moving machine of width $1$ mt. If he mows the field from the extremes to the ...
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1654
CAT 2002 | Question: 81
The area of the triangle with the vertices $(a,a), (a+1, a)$ and $(a, a+2)$ is $a^3$ $1$ $0$ None of these
The area of the triangle with the vertices $(a,a), (a+1, a)$ and $(a, a+2)$ is$a^3$$1$$0$None of these
1 votes
1 answer
1656
CAT 2002 | Question: 79
Three friends went for a picnic. First brought five apples and the second brought three. The third friend however brought only Rs. $8$. What is the share of the first friend? $8$ $7$ $1$ None of these
Three friends went for a picnic. First brought five apples and the second brought three. The third friend however brought only Rs. $8$. What is the share of the first fri...
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1 answer
1657
CAT 2002 | Question: 78
A thief was stealing diamonds from a jewellery store. On his way out, he encountered three guards, each was given half of the existing diamonds and two, to cover it by the thief. In the end, he was left with one diamond. How many did the thief steal? $40$ $36$ $42$ $38$
A thief was stealing diamonds from a jewellery store. On his way out, he encountered three guards, each was given half of the existing diamonds and two, to cover it by th...
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1658
CAT 2002 | Question: 77
A student finds the sum $1 + 2 + 3 + \dots $ as his patience runs out. He found the sum as $575.$ When the teacher declared the result wrong, the student realized that he missed a number. What was the number the student missed? $16$ $18$ $14$ $20$
A student finds the sum $1 + 2 + 3 + \dots $ as his patience runs out. He found the sum as $575.$ When the teacher declared the result wrong, the student realized that he...
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1661
CAT 2002 | Question: 74
There is a common chord of $2$ circles with radius $15$ and $20.$ The distance between the two centres is $25.$ The length of the chord is $48$ $24$ $36$ $28$
There is a common chord of $2$ circles with radius $15$ and $20.$ The distance between the two centres is $25.$ The length of the chord is$48$$24$$36$$28$
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1662
CAT 2002 | Question: 73
Let $S=2x + 5x^2 + 9x^3 + 14x^4 + 20x^5 \dots \dots $ infinity. The coefficient of $n$-th term is$\frac{n(n+3)}{2}$. Then the sum $S$ is $\frac{x(2-x)}{(1-x)^3}$ $\frac{(2-x)}{(1-x)^3}$ $\frac{x(2-x)}{(1-x)^2}$ None of these
Let $S=2x + 5x^2 + 9x^3 + 14x^4 + 20x^5 \dots \dots $ infinity. The coefficient of $n$-th term is$\frac{n(n+3)}{2}$. Then the sum $S$ is$\frac{x(2-x)}{(1-x)^3}$$\frac{(2-...
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1663
CAT 2002 | Question: 72
The remainder when $2^{256}$ is divided by $17$ is $7$ $13$ $11$ $1$
The remainder when $2^{256}$ is divided by $17$ is$7$$13$$11$$1$
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1664
CAT 2002 | Question: 71
In the figure given below, find the distance $\text{PQ}.$ $7$ m $4.5$ m $10.5$ m $6$ m
In the figure given below, find the distance $\text{PQ}.$ $7$ m$4.5$ m$10.5$ m$6$ m
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1667
CAT 2002 | Question: 68
If $f(x) = \log(1+x)/(1-x))$, then $f(x)+f(y)=$ $f(x+y)$ $f(1+xy)$ $(x+y) \: f(1+xy)$ $f (\frac{x+y}{1+xy})$
If $f(x) = \log(1+x)/(1-x))$, then $f(x)+f(y)=$$f(x+y)$$f(1+xy)$$(x+y) \: f(1+xy)$$f (\frac{x+y}{1+xy})$
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1668
CAT 2002 | Question: 67
If $\text{U, V, W}$ and $m$ are natural numbers such that $\text{U}^m + \text{V}^m = \text{W}^m$, then which of the following is true? $m < \min\text{(U, V, W)}$ $m > \max\text{(U, V, W)}$ $m < \max\text{(U, V, W)}$ None of these
If $\text{U, V, W}$ and $m$ are natural numbers such that $\text{U}^m + \text{V}^m = \text{W}^m$, then which of the following is true?$m < \min\text{(U, V, W)}$$m \max\t...
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1670
CAT 2002 | Question: 65
The number of roots of $\frac{A^2}{x} + \frac{b^2}{x-1} =1$ is $1$ $2$ $3$ None of these
The number of roots of $\frac{A^2}{x} + \frac{b^2}{x-1} =1$ is $1$$2$$3$None of these
1 votes
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1673
CAT 2002 | Question: 62
For all integers $n>0, \: \: 7^{6n} - 6^{6n}$ is divisible by $13$ $128$ $549$ None of these
For all integers $n>0, \: \: 7^{6n} - 6^{6n}$ is divisible by$13$$128$$549$None of these
1 votes
0 answers
1674
CAT 2002 | Question: 61
A string of length $40$ meters is divided into three parts of different lengths. The first part is three times the second part, and the last part is $23$ meters smaller than the first part. Find the length of the largest part $27$ $4$ $5$ $9$
A string of length $40$ meters is divided into three parts of different lengths. The first part is three times the second part, and the last part is $23$ meters smaller t...
1 votes
1 answer
1676
CAT 2002 | Question: 59
Number $\text{S}$ is equal to the square of the sum of the digits of a $2$ digit number $\text{D}.$ If the difference between $\text{S}$ and $\text{D}$ is $27,$ then $\text{D}$ is $32$ $54$ $64$ $52$
Number $\text{S}$ is equal to the square of the sum of the digits of a $2$ digit number $\text{D}.$ If the difference between $\text{S}$ and $\text{D}$ is $27,$ then $\te...
0 votes
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1677
CAT 2002 | Question: 58
In the following figure, the area of the isosceles right triangle $\text{ABE}$ is $7$ sq.cm. If $\text{EC = 3BE},$ then the area of rectangle $\text{ABCD}$ id (insq.cm.) $64$ $82$ $26$ $56$
In the following figure, the area of the isosceles right triangle $\text{ABE}$ is $7$ sq.cm. If $\text{EC = 3BE},$ then the area of rectangle $\text{ABCD}$ id (insq.cm.)$...
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1678
CAT 2002 | Question: 57
If $x^2 + 5y^2 + z^2 = 2y(2x+z)$, then which of the following statements are necessarily true? $x=2y$ $x=2z$ $2x=z$ Only I Only II Only III Only I and II
If $x^2 + 5y^2 + z^2 = 2y(2x+z)$, then which of the following statements are necessarily true?$x=2y$$x=2z$$2x=z$Only IOnly IIOnly IIIOnly I and II
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