1.

In a coaching class, some students register online, and some others register offline. No student registers both online and offline; hence the total registration number is the sum of online and offline registrations. The following facts and table pertain to these registration numbers for the five months - January to May of 2023. The table shows the minimum, maximum, median registration numbers of these five months, separately for online, offline and total number of registrations. The following additional facts are known. 
1. In every month, both online and offline registration numbers were multiples of 10 .
2. In January, the number of offline registrations was twice that of online registrations.
3. In April, the number of online registrations was twice that of offline registrations.
4. The number of online registrations in March was the same as the number of offline registrations in February. 
5. The number of online registrations was the largest in May.

	Minimum	Maximum	Median
online	40	100	80
Offline	30	80	50
Total	110	130	120

What was the total number of registrations in April? (This Question was asked as TITA)

• 90 Registration
• 110 Registration
• 120 Registration
• 100 Registration

2.

An air conditioner (AC) company has four dealers - D1, D2, D3 and D4 in a city. It is evaluating sales performances of these dealers. The company sells two variants of ACs Window and Split. Both these variants can be either Inverter type or Non-inverter type. It is known that of the total number of ACs sold in the city, 25% were of Window variant, while the rest were of Split variant. Among the Inverter ACs sold, 20% were of Window variant. 
The following information is also known: 
1. Every dealer sold at least two window ACs. 
2. D1 sold 13 inverter ACs, while D3 sold 5 Non-inverter ACs. 
3. A total of six Window Non-inverter ACs and 36 Split Inverter ACs were sold in the city. 4. The number of Split ACs sold by D1 was twice the number of Window ACs sold by it. 5. D3 and D4 sold an equal number of Window ACs and this number was one-third of the number of similar ACs sold by D2. 
4. D2 and D3 were the only ones who sold Window Non-inverter ACs. The number of these ACs sold by D2 was twice the number of these ACs sold by D3. 
5. D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2
What was the total number of ACs sold by D2 and D4? (This Question was asked as TITA)

• 33 AC's
• 39 AC's
• 42 AC's
• 28 AC's

3.

The equation \(x^3+(2r+1)x^2+(4r-1)x+2=0\) has -2 as one of the roots. If the other two roots are real, then the minimum possible non-negative integer value of \(r\) is

4.

There are nine boxes arranged in a 3×3 array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive.
The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of 
coins in each column is also the same.

Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a * if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by ** if two or more of these conditions are satisfied. 
i) The minimum among the numbers of coins in the three sacks in the box is 1. 
ii) The median of the numbers of coins in the three sacks is 1. 
iii) The maximum among the numbers of coins in the three sacks in the box is 9.
In how many boxes do all three sacks contain different numbers of coins? [This Question was asked as TITA]

• 5 boxes
• 4 boxes
• 3 boxes
• 2 boxes

5.

All of the following can be inferred from the reviewer's discussion of "The Nutmeg's Curse", EXCEPT:

• academic discourses have always served the function of raising awareness about environmental preservation.
• the contemporary dominant perception of nature and the environment was put in place by processes of colonialism.
• environmental preservation policy makers can learn a lot from non-European and/or pre colonial societies.
• the history of climate change is deeply intertwined with the history of colonialism.

6.

There are only three female students - Amala, Koli and Rini - and only three male students - Biman, Mathew and Shyamal - in a course. The course has two evaluation components, a project and a test. The aggregate score in the course is a weighted average of the two components, with the weights being positive and adding to 1 . 
The projects are done in groups of two, with each group consisting of a female and a male student. Both the group members obtain the same score in the project. 
The following additional facts are known about the scores in the project and the test.
1. The minimum, maximum and the average of both project and test scores were identical – 40, 80 and 60 , respectively. 
2. The test scores of the students were all multiples of 10 ; four of them were distinct and the remaining two were equal to the average test scores.
3. Amala's score in the project was double that of Koli in the same, but Koli scored 20 more than Amala in the test. Yet Amala had the highest aggregate score. 
4. Shyamal scored the second highest in the test. He scored two more than Koli, but two less than Amala in the aggregate. 
5. Biman scored the second lowest in the test and the lowest in the aggregate. 
6. Mathew scored more than Rini in the project, but less than her in the test.
What was Rini's score in the project?(This Question was asked as TITA)

• 45 Marks
• 60 Marks
• 70 Marks
• 80 Marks