List of top Questions asked in CAT- 2000

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.

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

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.

$x$ is a real number. Is $|x|<3$?
Statement A
A. $x(x+3)<0$
Statement B
B. $x(x-3)>0$

Two lines are given by the equations $ax + by = c$ and $dx + ey = f$. Do they intersect?
Statement A
A. $a, b, c, d, e, f$ are distinct \& real.
Statement B
B. $c \neq 0$ \& $f \neq 0$.

$a \oplus b = 1$ if $a,b>0$ or $a,b<0$; \quad $a \oplus b = -1$ otherwise.
What is $(2 \oplus 0) \oplus (-5 \oplus -6)$?
Statement A
A. $a \oplus b = 0$ if $a=0$
Statement B
B. $a \oplus b = b \oplus a$

How many people watch program P?
Statement A
A. The number watching Q is $1000$; the number watching both P and Q is $100$.
Statement B
B. The number of people watching either P or Q or both is $1500$.

Harshad bought shares of a certain company on one day and sold them the next day. He paid a brokerage of $1%$. What was Harshad’s profit per rupee?
Statement A
A. His selling price was $1.05$ times his purchase price.
Statement B
B. The number of shares he purchased was $100$.

Ghosh flies to South Africa from Mumbai non-stop. His flight leaves Mumbai at 5 am on 10\textsuperscript{th} December 2000 as per Indian Standard Time. What is the local time in South Africa when Mr. Ghosh reaches there?
Statement A
A. The average speed of the plane during the flight is 700 km/h.
Statement B
B. The flight distance is 10,500 km.

What are the ages of X and Y?
Statement A
A. The difference in their ages is $6$.
Statement B
B. The product of their ages is divisible by $6$.

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.

In a triangle PQR, $\angle PRQ = 90^\circ$. What is $PR + RQ$?
Statement A
A. The diameter of the incircle is $10$.

Statement B
B. The diameter of the circumcircle is $18$.

Evaluate:
$\frac{1}{2^2 - 1} + \frac{1}{4^2 - 1} + \frac{1}{6^2 - 1} + \dots + \frac{1}{20^2 - 1}$

ABCDEFGH is a regular octagon. A and E are opposite vertices. A frog starts at A, may jump to adjacent vertices except E. When it reaches E, it stops. Let $a_n$ = number of distinct paths of exactly $n$ jumps ending at E. Find $a_{2n-1}$.

ABCD is a rhombus with AC and BD intersecting at the origin. The equation of side AD is $x + y = 1$. What is the equation of BC?