MAH MBA CET 2026 April 7 Shift 1 Question Paper: Download Answer Key with Solutions

Step 1: Understanding the Concept:

This problem uses the Fundamental Principle of Counting, specifically the Product Rule. When one event can occur in \(m\) ways and a second event can occur in \(n\) ways, the number of ways the two events can occur together is \(m \times n\).


Step 2: Key Formula or Approach:

Total ways = (Number of Shirt options) \(\times\) (Number of Trouser options)


Step 3: Detailed Explanation:

1. Ram must choose one shirt AND one trouser to complete an outfit.
2. Number of ways to choose a shirt = 4.
3. Number of ways to choose a trouser = 5.
4. Total combinations = \(4 \times 5 = 20\).


Step 4: Final Answer:

Ram can choose his outfit in 20 ways. Quick Tip: Use the "AND" rule: If you have to do one thing {AND} another thing, you {Multiply} the number of options.

Step 1: Understanding the Concept:

This problem uses the Addition Rule of counting. When an event can occur in \(m\) ways or \(n\) ways, and these two ways cannot happen at the same time (mutually exclusive), the total ways is \(m + n\).


Step 2: Detailed Explanation:

1. Babita chooses to wear either a Saree OR a dress. She cannot wear both as a single outfit choice here.
2. Number of ways to choose a Saree = 5.
3. Number of ways to choose a dress = 6.
4. Total options = \(5 + 6 = 11\).


Step 3: Final Answer:

Babita can choose her outfit in 11 ways. Quick Tip: Use the "OR" rule: If you have to choose between one category {OR} another category, you {Add} the number of options.

Step 1: Understanding the Concept:

This involves two sequential events where the second event is dependent on the choice of the first event because a "different" bus must be used for the return journey.


Step 2: Key Formula or Approach:

Total ways = (Ways to go) \(\times\) (Ways to return)


Step 3: Detailed Explanation:

1. Going to school: There are 23 buses available. So, Dinu has 23 ways to go to school.
2. Returning home: He must use a {different bus than the one he took to school.
3. Therefore, available buses for return = \(23 - 1 = 22\) buses.
4. Total ways = \(23 \times 22\). \[ 23 \times 22 = 23 \times (20 + 2) = 460 + 46 = 506. \]


Step 4: Final Answer:

There are 506 possible ways for Dinu to complete his journey. Quick Tip: Always subtract the "already used" option from the total if the question specifies that items or routes cannot be repeated (different buses, no repetition, etc.).

Step 1: Understanding the Concept:

A handshake occurs between two people. Since the order in which two people shake hands does not matter (A shaking hands with B is the same as B shaking hands with A), this is a problem of combinations.


Step 2: Key Formula or Approach:

The number of ways to choose 2 people out of \(n\) is given by the combination formula: \[ ^nC_2 = \frac{n(n-1)}{2} \]


Step 3: Detailed Explanation:

1. Here, the number of students \(n = 30\).
2. To form one handshake, we need to select any 2 students out of 30.
3. Total Handshakes = \(^{30}C_2\). \[ \frac{30 \times (30 - 1)}{2} = \frac{30 \times 29}{2} \]
4. Simplify the calculation: \[ 15 \times 29 = 435. \]


Step 4: Final Answer:

The total number of handshakes is 435. Quick Tip: For any "handshake" or "matching" problem where order doesn't matter, just use the formula {\( \frac{n(n-1)}{2} \)}.

Step 1: Understanding the Concept:

Unlike a handshake (where one action involves two people), exchanging cards means if Friend A gives a card to Friend B, Friend B also gives a card to Friend A. This is a problem of permutations or simple multiplication.


Step 2: Key Formula or Approach:

Total exchanges = \(n \times (n - 1)\)


Step 3: Detailed Explanation:

1. Total number of friends \(n = 12\).
2. Each friend will give a card to every other friend except themselves.
3. So, each person gives \((12 - 1) = 11\) cards.
4. Total cards = \(12 friends \times 11 cards per friend = 132\).


Step 4: Final Answer:

They exchanged 132 cards altogether. Quick Tip: Remember: {Handshakes} are shared (divide by 2), but {Gifts/Cards} are one-way (do not divide by 2). The formula is just {\( n(n-1) \)}.

Step 1: Understanding the Concept:

A "standard dice" (also known as a regular or fair dice) has a specific mathematical property regarding its opposite faces.


Step 2: Key Formula or Approach:

In a standard dice, the sum of the numbers on any two opposite faces is always equal to 7.


Step 3: Detailed Explanation:

1. We are asked to find the face opposite to 1.
2. Using the standard dice rule: Opposite Face + 1 = 7.
3. Opposite Face = \(7 - 1 = 6\).
4. Similarly, 2 is opposite to 5, and 3 is opposite to 4.


Step 4: Final Answer:

The number opposite to 1 is 6. Quick Tip: Always check if the word {"Standard"} is used. If it is, you don't even need to look at the image; the sum of opposites is always 7. If it's a {"General"} dice, the rule doesn't apply!

Step 1: Understanding the Concept:

In dice problems, if the type of dice (Standard or General) is not specified and only one position is shown, we cannot definitively determine the opposite face unless it is a standard dice.


Step 3: Detailed Explanation:

1. If the dice is not "Standard," any of the hidden faces could be opposite to 6.
2. In a single view of a dice, we see three faces (e.g., 1, 2, and 6). These are adjacent faces.
3. The faces that are not visible (3, 4, and 5) are the candidates for being opposite to the visible faces.
4. Without further information or multiple positions, 6 could be opposite to either 3, 4, or 5.


Step 4: Final Answer:

The opposite of 6 is 3/4/5. Quick Tip: If only one position of a dice is given and it is not mentioned as a "Standard" dice, the opposite of any visible face is any one of the three invisible faces.

Step 1: Understanding the Concept:

An "ordinary dice" is synonymous with a "standard dice." In such a dice, the sum of opposite faces is always 7.


Step 2: Key Formula or Approach:

1. Opposite face = \(7 - Current face\).

2. Result = \((Opposite face)^4\).


Step 3: Detailed Explanation:

1. Arnav gets a '3'.
2. The number on the opposite face is \(7 - 3 = 4\).
3. We need to multiply this number (4) by itself four times: \[ 4 \times 4 \times 4 \times 4 = 4^4 \] \[ 4^1 = 4 \] \[ 4^2 = 16 \] \[ 4^3 = 64 \] \[ 4^4 = 256 \]


Step 4: Final Answer:

The resulting number is 256. Quick Tip: "Ordinary," "Standard," and "Fair" dice all follow the rule that the sum of opposite faces is 7. Memorize powers of 4 for speed: \(4^1=4, 4^2=16, 4^3=64, 4^4=256\).

Step 1: Understanding the Concept:

Similar to question 7, if we only have one view of a general dice, the faces adjacent to 3 are visible, and the faces opposite to 3 are hidden.


Step 3: Detailed Explanation:

1. Let's assume the visible faces are 1, 2, and 3.
2. Since 1 and 2 are adjacent to 3, they cannot be opposite to it.
3. The remaining numbers on a dice are 4, 5, and 6.
4. In the absence of "Standard dice" rules or a second position, 3 could be opposite to 4, 5, or 6.


Step 4: Final Answer:

The opposite of 3 is 4/5/6. Quick Tip: Unless specified as standard, a single dice view only tells you what is {not} opposite (the adjacent faces). Everything else remains a possibility.

Step 1: Understanding the Concept:

When two positions of the same dice are given with one common face, we can find all opposite pairs by rotating the numbers clockwise starting from the common face.


Step 2: Key Formula or Approach:

1. Identify the common face in both positions.

2. Write the numbers in clockwise order for both positions.

3. The numbers appearing in the same relative positions are opposite to each other.


Step 3: Detailed Explanation:

{(Assuming Position 1 shows 1, 2, 5 and Position 2 shows 1, 6, 4)

1. The common number is 1.
2. Clockwise from 1 in Position 1: \(1 \to 2 \to 5\).
3. Clockwise from 1 in Position 2: \(1 \to 6 \to 4\).
4. Comparing the sequences:
- 2 is opposite to 6.
- 5 is opposite to 4.
- The remaining number (3) must be opposite to the common number (1).
{(Note: If the common number was 5 and the rotation led to 6 being opposite 3, then 3 is the answer.)


Step 4: Final Answer:

The number opposite to 6 is 3. Quick Tip: The "Clockwise Rule" is the most reliable method for dice problems with one common face. Always start your list with the common number.