List of top Questions asked in CAT- 2012

What is the value of $2^{100} \mod 5$? 
 

Let \( P = \{2, 3, 4, \ldots, 100\} \) and \( Q = \{101, 102, 103, \ldots, 200\} \). How many elements of \( Q \) are there such that they do not have any element of \( P \) as a factor?

In how many ways can 5 identical balls be distributed into 3 distinct boxes? 
 

If $3x + 4y = 12$ and $x - y = 1$, what is the value of $x + y$? 
 

When asked for his taxi number, the driver replied, “If you divide the number of my taxi by 2, 3, 4, 5, 6 each time you will find a remainder of one. But if you divide it by 11, the remainder is zero.” What is the taxi number?

A car travels at 60 km/h for half the distance and 80 km/h for the other half. What is the average speed for the entire journey? 
 

What is the number of solutions to $|x - 2| = |x - 4|$? 
 

The ratio of ages of A and B is 3:4. After 6 years, their ages will be in the ratio 4:5. What is A's current age? 
 

If \[ x = \frac{x}{y+z}, \quad y = \frac{y}{z+x}, \quad z = \frac{z}{x+y} \] then which of the following statements is/are true?
A solid sphere of radius 12 inches is melted and cast into a right circular cone whose base diameter is \( \sqrt{2} \) times its slant height. If the radius of the sphere and the cone are the same, how many such cones can be made and how much material is left out?
If \( (a^2 + b^2), (b^2 + c^2) \) and \( (a^2 + c^2) \) are in geometric progression, which of the following holds true?

A number when divided by 7 leaves a remainder of 4. What is the remainder when its square is divided by 7? 
 

A circle is inscribed in an equilateral triangle with side length 12 cm. What is the radius of the circle? 
 

In the figure below, \( \angle MON = \angle MPO = \angle NQO = 90^\circ \), \( OQ \) is the bisector of \( \angle MON \), and \( QN = 10 \), \( OR = 40/\sqrt{7} \). Find \( OP \).

What is the value of $\sqrt{50 + \sqrt{50 + \sqrt{50 + \ldots}}}$? 
 

The roots of the quadratic equation $x^2 - 6x + k = 0$ are real and distinct. How many integer values of $k$ are possible if $k$ is positive? 
 

In the figure, \( OABC \) is a parallelogram. The area of the parallelogram is 21. Coordinates are: \( O = (0,0) \), \( A = (7,0) \), and point \( C \) lies on line \( x = 3 \). Find coordinates of \( B \).

What is the remainder when $7^{100}$ is divided by 8? 
 

It is unfortunate that the lure of visiting foreign countries still draws a very large number of our people, who \underline{do not seem to be realizing what their own country is and how much can be seen and learnt from it.}
Feminism is not simply a movement to ensure that women will have equal rights with men \underline{but that a commitment for eradicating the ideology of domination} that permeates Indian culture at various levels.

The sum of the first $n$ natural numbers is 55. What is $n$? 
 

A, B, C, D sit around a circular table. A is opposite B. How many arrangements are possible?
A pie chart shows expenses: Salaries (50%), Rent (30%), Utilities (20%). If Salaries are Rs. 25,000, what is the total expense?
A table shows production (in units): Factory A (200, 250, 300), Factory B (150, 200, 250). What is Factory A's average production?
A table shows sales (in lakhs): Q1 (20), Q2 (25), Q3 (30), Q4 (35). What is the percentage increase from Q1 to Q4?