List of top Questions asked in CAT- 2000

The number of triangles with integral sides that can be made which have perimeter of 14, are:

There are seven consecutive integers. The average of the first five is $n$. What is the average of all seven?

If a function $f(x)$ satisfies the equation \[ f\left(x + \frac{1}{x}\right) = x^2 + \frac{1}{x^2}, \quad x \neq 0 \] then $f(x)$ equals:

$x$ is number of numbers between 100 and 200 such that $x$ is odd and $x$ is divisible by 3 but not by 7. What is $x$?

A farmer planned fence-posts at $6$ metre intervals along a straight side, posts at both ends. He bought posts but found he had $5$ less than needed for $6$ m spacing. However, with $8$ m spacing, he had exactly enough. What is the length of the side and how many posts did he buy?

Two full tanks: cylindrical holds $500$ L more than conical. After $200$ L removed from each, cylindrical has twice conical’s amount. How much did the cylindrical hold when full?

A truck travelling at 70 km/h consumes 30% more fuel than another travelling at 50 km/h. If the truck at 50 km/h has a fuel efficiency of 19.5 km/litre, how many km can the 70 km/h truck travel on 10 litres of fuel?

The three sides of a triangle have lengths $a, b, c$. If $a^2 + b^2 + c^2 = ab + bc + ca$, then the triangle is:

Let $x, y$ and $z$ be distinct integers, that are odd and positive. Which one of the following statements cannot be true?

$N = 1421 \times 1423 \times 1425$. What is the remainder when $N$ is divided by $12$?

The number 1982 in the decimal system when written in the base 12 is:

1 red, 3 white, 2 blue flags in a line, no adjacent same colour, ends different. How many arrangements?

The expression $N = 55^3 + 17^3 - 72^3$ is exactly divisible by:

Sam has forgotten his friend’s seven-digit telephone number. He remembers the following: the first three digits are either 635 or 674, the number is odd, and the number nine appears once. If Sam were to use a trial-and-error process to reach his friend, what is the minimum number of trials he has to make before he can be certain to succeed?

Let $S$ be the set of prime numbers greater than or equal to 2 and less than 100. Multiply all elements of $S$. With how many consecutive zeros will the product end?

The integers 34,041 and 32,506 when divided by a three-digit integer $n$ leave the same remainder. What is $n$?

There are two positive integers – $x$ and $y$. A function of $x$ and $y$ is defined such that:
$f(0,y) = y + 1$,
$f(x + 1, 0) = f(x, 1)$,
$f(x + 1, y + 1) = f(x, f(x + 1, y))$
What is the value of $f(1, 2)$?

$D$ is a recurring decimal of type $0.\ a_1a_2a_1a_2a_1a_2 \dots$ Here $a_1$ and $a_2$ are single digit numbers between $0$ and $9$. This number $D$, when multiplied by which of the following numbers gives a product which is an integer?

The law prohibits a person from felling a sandalwood tree, even if it grows on one’s own land, without prior permission from the government. As poor people can’t deal with the government, this legal provision leads to a rip-roaring business for ____________, who care neither for the ____________, nor for the tree.

Though one eye is kept firmly on the ____________, the company now also promotes ____________ contemporary art.

In these bleak and depressing times of ____________ prices, non-performing governments and ____________ crime rates, Sourav Ganguly has given us, Indians, a lot to cheer about.

It will take some time for many South Koreans to ____________ the conflicting images of North Korea, let alone to ____________ what to make of their northern cousins.

The manners and ____________ of the nouveau riche is a recurrent ____________ in the literature.

Two concentric circles have the same centre O. A chord on the outer circle AE intersects the inner circle in points B and D. C is a point on the segment BD. What is the ratio of AC to CE?
Statement A
A. Ratio of lengths of BC to CD is 1.
Statement B
B. A third circle intersects the inner circle at B and D. C is on the line joining the centres of the third and inner circle.