AP ICET 2026 May 2 Shift 1 Question Paper: Download Answer Key with Solutions

1.

The probability that in 10 throws of a fair die, a score which is a multiple of 3 is obtained in 8 of the throws is:

• \( \frac{160}{3^{10}} \)
  
• \( \frac{140}{3^{10}} \)
  
• \( \frac{180}{3^{10}} \)
  
• \( \frac{100}{3^{10}} \)

2.

The median of the frequency distribution is: \[ \begin{array}{c|cccc} x & 1 & 2 & 3 & 4\\ \hline f & 2 & 4 & 1 & 3 \end{array} \]

• 1
  
• 2
  
• 3
  
• 4

3.

If the mean of a frequency distribution is 100 and the coefficient of variation is 45%, then what is the value of the variance?

• \(2025\)
  
• \(450\)
  
• \(45\)
  
• \(4.5\)

4.

If the mean and median are 28.33 and 28 respectively, then the mode is ____.

• 28.5
  
• 27.33
  
• 28
  
• 28.66

5.

The cumulative frequency table of marks is given. Then, the number of students scoring between 20 and 40 is: \[ \begin{array}{c|ccccc} {Marks} & \le 10 & \le 20 & \le 30 & \le 40 & \le 50 \\ \hline {Frequency} & 5 & 12 & 26 & 37 & 50 \end{array} \]

• 12
  
• 25
  
• 26
  
• 37

6.

The Rise of E-Sports and Gaming Culture: The e-sports industry has experi enced explosive growth, transforming gaming from a niche hobby into a global phenomenon. This surge has had significant social and economic impacts. Socially, e-sports has fostered a vibrant online community, bringing together individuals from diverse backgrounds with a shared passion. It has created new forms of enter tainment, with live tournaments drawing massive online and in-person audiences.Economically, e-sports has generated substantial revenue streams through sponsor ships, advertising, and prize pools. Professional gamers have become celebrities, and the industry has created numerous jobs in areas like event management, broad casting, and content creation. The rise of e-sports has also influenced mainstream culture, with gaming-related content permeating movies, music, and fashion. How ever, challenges remain, including concerns about the potential for addiction, the need for better regulation, and the importance of promoting inclusivity within the gaming community. As e-sports continues to evolve, its social and economic impact will likely expand, further blurring the lines between traditional sports and digital entertainment. 

7.

When two dice are thrown, the probability of getting a prime number on one die and a composite number on the other die is:

• \( \frac{1}{6} \)
  
• \( \frac{1}{3} \)
  
• \( \frac{1}{2} \)
  
• \( \frac{1}{4} \)

8.

The shift towards remote work has irrevocably altered traditional employment paradigms, compelling companies to reassess their operational structures and adapt to a distributed workforce. This has resulted in a re-evaluation of performance metrics, emphasizing measurable output and productivity over mere physical pres ence in a traditional office setting. In the context of remote work, the onus falls upon employers to foster a robust sense of community and cohesion among ge ographically distributed teams, mitigating the potential for professional isolation and fostering a sense of shared purpose. While the benefits of flexibility, improved work-life balance, and reduced commuting are undeniable, the long-term implications for employee cohesion, and the preservation of organisational knowledge remain subjects of ongoing debate. Experts opine that the subject demands a nuanced and adaptable approach. Companies must prioritise clear communication, excellent virtual collaboration tools, and proactive strategies for maintaining team morale, ensuring that remote work fosters both individual productivity and collec tive success. 

9.

Second central moment (Variance) for the first $n$ natural numbers is ____.

• $\frac{n(n+1)}{2}$
  
• $\frac{n(n+1)(2n+1)}{6}$
  
• $\frac{n^2+1}{12}$
  
• $\frac{n^2-1}{12}$

10.

Legal systems can be broadly divided into two main types: common law and civil law. Most countries in the world use one of these systems, although many countries in the Middle East and North Africa have religious law. Some other countries usually in the developing world- have a system of customary law, which is based on patterns of behaviour in a particular social setting or community. There are also mixed systems in operation, but these are not widespread. Common law is defined as a legal system which is based on a tradition of previous judgments, or ’cases’. In this system judges base their judgements on ’like cases’ which are very similar to the one before them. This is why another term, case law, actually means the same as common law. In countries with civil law systems, judgements are made with reference to codes and statutes rather than previous cases. Civil law systems are more structured and rely on comprehensive legal codes that outline all matters that can be brought before a court. In contrast, common law evolves over time through judicial decisions, allowing for greater flexibility in interpretation. 

11.

The triangle whose vertices are $(5,7), (2,7)$ and $(5,2)$ is a _____ triangle.

• Equilateral
  
• Isosceles
  
• Right angle
  
• Scalene

12.

The mean of four numbers is 37. The mean of the smallest three of them is 34. If the range of the data is 15, what is the mean of the largest three?

• 41
  
• 38
  
• 40
  
• 39

13.

Median of the following discrete data is: \[ 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,......,10,10,10,10,10,10,10,10,10,10 \]

• \(6\)
  
• \(7\)
  
• \(8\)
  
• \(9\)

14.

Just before Christmas in 1944, a letter arrived at our house in Philadelphia. The postmark was from Tuskegee, Alabama, so we all knew who it was from. We excitedly gathered around Mother as she opened it at the kitchen table. My Dear Mother, I did not get the leave I expected for Christmas. I will miss all of you. Please leave the Christmas tree up until I make it back. I hope to be home by March. Love from your son, Clifton I was 17 years old at the time. My heart sank. I felt a profound sadness that my favorite brother would not be home for Christmas. He was one of the Tuskegee Airmen and was responsible for main taining the airplanes flying off to fight in World War II. My mother, being the optimist she always was, said, ”Well, it looks like we’ll get to have two Christ mases this year!” After Christmas, my sister and I worked together to make sure we kept that Christmas tree looking as pretty as possible. This was no easy feat. 
By mid-January, the branches drooped so low to the ground that they became a sliding board for the decorations. Each day, ornaments would come crashing to the ground and there were brand new sprinklings of pine needles all over the wooden floor. My sister and I took turns sweeping them up. We repositioned the omaments to the stronger branches on the tree, hoping they would stay on. Each time we freshened that tree up, my sister and I were full of thoughts about Clifton and how happy we would be to see him again. It made us feel that he was close by, even though he was hundreds of miles away. On March 5, the doorbell rang. We ran to the door and gave Clifton a big hug. As he hugged Mother. I could see him peek over her head at the Christmas tree. ”It’s beautiful,” he said. ”Thank you.” Clifton opened his presents and told us all sorts of stories about his work in Tuskegee. That night as we slept, we heard a crash in the living room. We all ran to see what had happened. The tree had toppled onto the sofa and there were needles and broken ornaments everywhere. We all had a good laugh. It was fortuitous Clifton got home when he did!

15.

A box contains 6 red balls and 4 blue balls. If two balls are drawn at random, then the probability that they are of the same colour is:

• \( \frac{7}{15} \)
  
• \( \frac{9}{17} \)
  
• \( \frac{3}{5} \)
  
• \( \frac{4}{15} \)