List of top Questions asked in CAT

Consider a sequence where the $n$th term $t_n = \frac{n}{n+2}$, $n = 1, 2, \dots$
The value of $t_3 \times t_4 \times t_5 \times \dots \times t_{53}$ equals:
Which among $2^{1/2}$, $3^{1/3}$, $4^{1/4}$, $6^{1/6}$, and $12^{1/12}$ is the largest?
A group of 630 children is arranged in rows for a group photograph. Each row contains three fewer children than the row in front of it. Which number of rows is not possible?
A survey of 100 people was conducted to find out whether they had read recent issues of Golmal magazine in July, August, and September. Data:
  • Only September: 18
  • September but not August: 23
  • September and July: 8
  • September: 28
  • July: 48
  • July and August: 10
  • None: 24
Find the number who read exactly two consecutive issues out of the three months.
What values of $x$ satisfy $\sqrt[3]{x} + x^{1/3} - 2 \leq 0$ ($x$ is a real number)?
The length, breadth, and height of a room are in the ratio $3 : 2 : 1$. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will:
The graph of $y - x$ against $y + x$ is as shown (straight line with slope>0 through origin). Which of the given five graphs shows $y$ against $x$?
A semi-circle is drawn with $AB$ as its diameter. From $C$, a point on $AB$, a line perpendicular to $AB$ is drawn meeting the circumference of the semi-circle at $D$. Given that $AC = 2 \ \text{cm}$ and $CD = 6 \ \text{cm}$, the area of the semi-circle (in sq. cm) will be:
An equilateral triangle $BPC$ is drawn inside a square $ABCD$. What is the value of $\angle APD$ in degrees?
Consider the set $S = \{1, 2, 3, \dots, 1000\}$. How many arithmetic progressions can be formed from the elements of $S$ that start with $1$ and end with $1000$ and have at least $3$ elements?
When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are reversed?
The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?
What are the values of $x$ and $y$ that satisfy both the equations?
$2^{0.7x} \cdot 3^{-1.25y} = \frac{8\sqrt{6}}{27}$
$4^{0.3x} \cdot 9^{0.2y} = 8 \cdot (81)^{\frac{1}{5}}$
The number of employees in Obelix Menhir Co. is a prime number less than 300. The ratio of graduates and above to non-graduates can possibly be:
Arun, Barun, and Kiranmala start from the same place and travel in the same direction at speeds of 30, 40, and 60 km/h respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?
Relations between the factory and the dealer are distant and usually strained as the factory tries to force cars on the dealers to smooth out production. Relations between the dealer and the customer are equally strained because dealers continuously adjust prices — make deals — to adjust demand with supply while maximizing profits. This becomes a system marked by a lack of long-term commitment on either side, which maximizes feelings of mistrust. In order to maximize their bargaining positions, everyone holds back information — the dealer about the product and the consumer about his true desires.
We can usefully think of theoretical models as maps, which help us navigate unfamiliar territory. The most accurate map that it is possible to construct would be of no practical use whatsoever, for it would be an exact replica, on exactly the same scale, of the place where we were. Good maps pull out the most important features and throw away a huge amount of much less valuable information. Of course, maps can be bad as well as good — witness the attempts by medieval Europe to produce a map of the world. In the same way, a bad theory, no matter how impressive it may seem in principle, does little or nothing to help us understand a problem.
I am sometimes attacked for imposing ‘rules’. Nothing could be further from the truth. I hate rules. All I do is report on how consumers react to different stimuli. I may say to a copywriter, “Research shows that commercials with celebrities are below average in persuading people to buy products. Are you sure you want to use a celebrity?” Call that a rule? Or I may say to an art director, “Research suggests that if you set the copy in black type on a white background, more people will read it than if you set it in white type on a black background.”
In the evolving world order, the comparative advantage of the United States lies in its military force. Diplomacy and international law have always been regarded as annoying encumbrances, unless they can be used to advantage against an enemy. Every active player in world affairs professes to seek only peace and to prefer negotiation to violence and coercion.
Age has a curvilinear relationship with the exploitation of opportunity. Initially, age will increase the likelihood that a person will exploit an entrepreneurial opportunity because people gather much of the knowledge necessary to exploit opportunities over the course of their lives, and because age provides credibility in transmitting that information to others. However, as people become older, their willingness to bear risks declines, their opportunity costs rise, and they become less receptive to new information.
There are 6 tasks and 6 persons. Task 1 cannot be assigned to person 1 or 2; Task 2 must be assigned to either person 3 or person 4. Every person is assigned one task. How many ways can this assignment be done?
If $x = -0.5$, then which of the following has the smallest value?
The number of solutions of the equation $2x + y = 40$ where both $x$ and $y$ are positive integers and $x \leq y$ is:

Members: \( K, L, M, N, P, Q, R, S, U, W \) are the only ten members in a department.

There is a proposal to form a team from within the members of the department, subject to the following conditions:

  1. A team must include exactly one among \( P, R, S \).
  2. A team must include either \( M \) or \( Q \), but not both.
  3. If a team includes \( K \), then it must also include \( L \), and vice versa. \[ K \in \text{Team} \iff L \in \text{Team} \]
  4. If a team includes one among \( S, U, W \), then it must also include the other two. \[ (S \in T) \lor (U \in T) \lor (W \in T) \Rightarrow S, U, W \in T \]
  5. \( L \) and \( N \) cannot be members of the same team.
  6. \( L \) and \( U \) cannot be members of the same team.

The size of a team is defined as the number of members in the team.

In a Class X Board examination, ten papers are distributed over five Groups: PCB, Mathematics, Social Science, Vernacular, and English. Each paper is evaluated out of \(100\).

The final score of a student is calculated as follows:

  1. First, the Group Scores are obtained by averaging marks in the papers within the group.
  2. The Final Score is the simple average of the five Group Scores.

The data for the top ten students are given below. (Dipan’s score in English Paper II is missing.)

NamePCB GroupMathsSocial ScienceVernacularEnglishFinal Score
 Phy.Chem.Bio. Hist.Geo.Paper IPaper IIPaper IPaper II 
Ayesha (G)9896979895939496969896.2
Ram (B)9799959795969494969896.1
Dipan (B)989898959695949694??96.0
Saqnik (B)9798999696989497929495.9
Sanjiv (B)9596979897969293959695.6
Shreya (G)96898510097989495969595.5
Joseph (B)90949810094979092949595.5
Agni (B)9699969995968293929394.3
Pritam (B)9898959883959095949493.9
Tirna (G)9698979985949291879693.7

Note: (B) or (G) indicates whether the student is a boy or girl.