List of top Questions asked in CAT

Archaeologists believe that the pieces of red – ware pottery excavated recently near Bhavnagar and _______ shed light on a hitherto dark 600-year period in the Harappan history of Gujarat.
Identify the incorrect sentence or sentences from the given options.
A. It was a tough situation and Manasi was taking pains to make it better.
B. Slowly her efforts gave fruit and things started improving.
C. Everyone complemented her for her good work.
D. She was very happy and thanked everyone.
Identify the incorrect sentence or sentences from the given options.
A. Harish told Raj to plead guilty.
B. Raj pleaded guilty of stealing money from the shop.
C. The court found Raj guilty of all the crimes he was charged with.
D. He was sentenced for three years in jail.
Identify the incorrect sentence or sentences from the given options.
A. Last Sunday, Archana had nothing to do.
B. After waking up, she lay on the bed thinking of what to do.
C. At 11 o’ clock she took shower and got ready.
D. She spent most of the day shopping.
In this question, the word at the top of the table is used in four different ways, numbered 1 to 4. Choose the options in which the usage of the word is INCORRECT or INAPPROPRIATE.
BOLT
Many people suggest _______ and still other would like to convince people not to buy pirated cassettes.
The ancient Egyptians believed ______ so that when these objects were magically reanimated through the correct rituals, they would be able to function effectively.

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

The remainder, when \( 15^{23} + 23^{23} \) is divided by 19, 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 so that no two adjacent stripes have the same colour is

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

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?

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

On a semicircle with diameter AD, chord BC is parallel to the diameter. Further, each of the chords AB and CD has length 2, while AD has length 8. What is the length of BC?

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?

A sprinter starts running on a circular path of radius \(r\) metres. Her average speed (in metres/minute) is \( \pi \) during the first 30 seconds, \( \frac{\pi}{2} \) during next one minute, \( \frac{\pi}{4} \) during next 2 minutes, \( \frac{\pi}{8} \) 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?
Consider the sequence of numbers \(a_1, a_2, a_3, \dots \) to infinity where \(a_1 = 81.33\) and \(a_2 = -19\) and \(a_j = a_{j-1} - a_{j-2}\) for \(j \geq 3\). What is the sum of the first 6002 terms of this sequence?
Let C be a circle with center P, and AB be a diameter of C. Suppose P1 is the midpoint of the line segment PB, P2 is the midpoint of the line segment P1B, and so on. Let C1, C2, C3, C4, ... be circles with diameters P1P2, P2P3, P3P4, ... respectively. Suppose the circles C1, C2, C3, ... 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 integer pairs \( (x, y) \) satisfying the equation \( x + y = xy \) 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 the son standing from his father?
In NutsAndBolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5 minutes after production of every 1000 nuts. Another machine produces only bolts at the rate of 75 bolts per minute and needs to be cleaned for 10 minutes after production of every 1500 bolts. If both the machines start production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts?
Each family in a locality has at most two adults, and no family has fewer than 3 children. Considering all the families together, there are more adults than boys, more boys than girls, and more girls than families. Then the minimum possible number of families in the locality is
Let \( f(x) = ax^2 - b |x| \), where \(a\) and \(b\) are constants. Then at \(x = 0\), \(f(x)\) is
If \( \frac{a}{b+c} = \frac{b}{c+a} = \frac{c}{a+b} = r \), then \( r \) cannot take any value except.
Karan and Arjun run a 100-meter race, where Karan beats Arjun 10 meters. To do a favour to Arjun, Karan starts 10 meters behind the starting line in a second 100 meter race. They both run at their earlier speeds. Which of the following is true in connection with the second race?