List of top Questions asked in CAT- 1997

A, B and C are defined as follows: $A = \frac{2.000004}{\sqrt{(2.000004)^2 + (4.000008)^2}}$
$B = \frac{3.000003}{\sqrt{(3.000003)^2 + (9.000009)^2}}$
$C = \frac{4.000002}{\sqrt{(4.000002)^2 + (8.000004)^2}}$
Which of the following is true about the values of the above three expressions?
After allowing a discount of 11.11%, a trader still makes a gain of 14.28%. At how many percentage above the cost price does he mark his goods?
Raja starts working on February 25, 1996, and finishes the job on March 2, 1996. How much time would T and J take to finish the same job if both start on the same day as Raja?
If his journey, including stoppage, is covered at an average speed of 180 mph, what is the distance between Frankfurt and India?
An express train travelling at 80 km/hr overtakes a goods train, twice as long and going at 40 km/hr on a parallel track, in 54 s. How long will the express train take to cross a platform of 400 m long?
What is X's average speed for the entire journey (to and fro)?
If X had started the return journey from India at 2.55 a.m. on the same day that he reached there, after how much time would he reach Frankfurt?
Starting on February 25, 1996, if Raja had finished his job on April 2, 1996, when would T and S together likely to have completed the job, had they started on the same day as Raja?

The adjoining figure shows a set of concentric squares. If the diagonal of the innermost square is 2 units, and if the distance between corresponding corners of any two successive squares is 1 unit, find the difference between the areas of the eighth and seventh squares, counting from the innermost square. 

What is the value of $a^3 + b^3$?
I. $a^2 + b^2 = 22$
II. $ab = 3$
Three friends P, Q, R wear hats either black or white. Each sees the other two hats. What is the colour of P's hat?
I. P says he can see one black hat and one white hat.
II. Q says that he can see one white hat and one black hat.
What is the value of $x$ and $y$?
I. $3x + 2y = 45$
II. $10.5x + 7y = 157.5$
What is the area bounded by the two lines and the coordinate axes in the first quadrant?
I. The lines intersect at a point which also lies on $3x - 4y = 1$ and $7x - 8y = 5$.
II. The lines are perpendicular, and one of them intersects the Y-axis at an intercept of 4.

AB is the diameter of the given circle, while points C and D lie on the circumference as shown. If AB is 15 cm, AC is 12 cm and BD is 9 cm, find the area of the quadrilateral ACBD. 

In $\triangle ABC$, points P, Q and R are the mid-points of sides AB, BC and CA respectively. If area of $\triangle ABC$ is 20 sq. units, find the area of $\triangle PQR$.
What is the speed of the car? I. The speed of a car is 10 km/hr more than that of a motorcycle.
II. The motorcycle takes 2 hr more than the car to cover 100 km.
After what time will Tez and Gati meet while moving around the circular track? Both start at the same point and at the same time.
I. Tez moves at 5 m/s constant speed; Gati starts at 2 m/s and increases speed by 0.5 m/s every second thereafter.
II. Gati can complete one entire lap in exactly 10 s.

In the adjoining figure, points A, B, C and D lie on the circle. $AD = 24$ and $BC = 12$. What is the ratio of the area of $\triangle CBE$ to that of $\triangle ADE$?

In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the shorter to the longer side?
The sum of the areas of two circles, which touch each other externally, is $153\pi$. If the sum of their radii is 15, find the ratio of the larger to the smaller radius.
What is the ratio of the volume of the given right circular cone to the one obtained from it?
I. The smaller cone is obtained by passing a plane parallel to the base and dividing the original height in the ratio 1:2.
II. The height and base of the new cone are one-third those of the original cone.
Is the number completely divisible by 99?
I. The number is divisible by 9 and 11 simultaneously.
II. If the digits of the number are reversed, the number is divisible by 9 and 11.
What is the cost price of the chair?
I. The chair and the table are sold at profits of 15% and 20% respectively.
II. If the cost price of the chair is increased by 10% and that of the table by 20%, the profit reduces by Rs.\ 20.
A person is walking from Mali to Pali, which lies to its north-east. What is the distance between Mali and Pali?
I. When the person has covered $\frac{1}{3}$ the distance, he is 3 km east and 1 km north of Mali.
II. When the person has covered $\frac{2}{3}$ the distance, he is 6 km east and 2 km north of Mali.
ABC is a three-digit number in which A $>$ 0. The value of ABC is equal to the sum of the factorials of its three digits. What is the value of B?