List of top Quantitative Aptitude Questions asked in CAT

$P, Q, S, R$ are points on a circle of radius $r$, such that $PQR$ is an equilateral triangle and $PS$ is a diameter. What is the perimeter of quadrilateral $PQSR$?

Two identical circles intersect so that their centers and intersection points form a square of side 1 cm. The area in sq. cm of the portion common to both circles is:

A new flag is to be designed with six vertical stripes using some or all of the colours yellow, green, blue and red. Then, the number of ways this can be done such that no two adjacent stripes have the same colour is

In the adjoining figure, chord ED is parallel to the diameter AC of the circle. If angle CBE = 65°, then what is the value of angle DEC?

A circle with radius 2 is placed against a right angle. Another smaller circle is also placed as shown in the adjoining figure. What is the radius of the smaller circle?

On a semicircle with diameter AD, chord BC is parallel to the diameter. Further; AD and BC are separated by 2cm, while AD has length 8. What is the length of BC?

In the adjoining figure, the lines represent one-way roads allowing travel only northwards or only westwards. Along how many distinct routes can a car reach point B from point A?

If the lengths of diagonals DF, AG and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the circle circumscribing that triangle will be?

Let \( u = (\log_2 x)^2 - 6\log_2 x + 12 \) where x is a real number. Then the equation \( x^u = 256 \), has

A sprinter starts running on a circular path of radius \( r \) metres. Her average speed (in metres/minute) is \( \pi r \) during the first 30 seconds, \( \pi r/2 \) during next one minute, \( \pi r/4 \) during next 2 minutes, \( \pi r/8 \) during next 4 minutes, and so on. What is the ratio of the time taken for the nth round to that for the previous round?

Let \( C \) be a circle with centre \( P_0 \) and \( AB \) be a diameter of \( C \). Suppose \( P_1 \) is the mid point of the line segment \( P_0B \), \( P_2 \) is the mid point of the line segment \( P_1B \) and so on. Let \( C_1, C_2, C_3, \ldots \) be circles with diameters \( P_0P_1, P_1P_2, P_2P_3, \ldots \) respectively. Suppose the circles \( C_1, C_2, C_3, \ldots \) are all shaded. The ratio of the area of the unshaded portion of \( C \) to that of the original circle is

The total number of integers pairs \( (x, y) \) satisfying the equation \( x + y = xy \) is

Let \( f(x) = ax^2 - b|x| \), where a and b are constants. Then at x = 0, f(x) is

A father and his son are waiting at a bus stop in the evening. There is a lamp post behind them. The lamp post, the father and his son stand on the same straight line. The father observes that the shadows of his head and his son's head are incident at the same point on the ground. If the heights of the lamp post, the father and his son are 6 metres, 1.8 metres and 0.9 metres respectively, and the father is standing 2.1 metres away from the post then how far (in metres) is son standing form his father?

N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two-minute song one pair after the other. If the total time taken for singing is 28 minutes, what is N?

Karan and Arjun run a 100-metre race, where Karan beats Arjun by 10 metres. To do a favour to Arjun, Karan starts 10 metres behind the starting line in a second 100 metre race. They both run at their earlier speeds. Which of the following is true in connection with the second race?

Let \( y = \dfrac{1}{2+\dfrac{1}{3+\dfrac{1}{2+\dfrac{1}{3+\cdots}}}} \). Then \( y \) equals?

If \(\frac{a}{b+c}=\frac{b}{a+c}=\frac{c}{b+a}=r\), then r cannot take any value except

A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he had sold. What is the current proportion of water to milk?

Suppose n is an integer such that the sum of digits on n is 2, and \(10^{10} < n < 10^{11}\). The number of different values of n is

If \(f(x)=x^3-4x+p\), and f(0) and f(1) are of opposite signs, then which of the following is necessarily true

On January 1, 2004 two new societies S1 and S2 are formed, each n numbers. On the first day of each subsequent month, S1 adds b members while S2 multiples its current numbers by a constant factor r. Both the societies have the same number of members on July 2, 2004. If b = 10.5n, what is the value of r?

If the sum of the first 11 terms of an arithmetic progression equals that of the first 19 terms, then what is the sum of the first 30 terms?

A rectangular sheet of paper, when halved by folding it at the mid point of its longer side, results in a rectangle, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle?