Explanation

E: This is the leftmost node in the in-order sequence. It becomes the root in the preorder traversal.

A: The next node after E is its left child. So, A is the left child of E.

C: Moving further, C is the right child of A.

K: K is the right child of C.

F: F is the right child of K.

H: H is the right child of F.

D: D is the left child of F.

B: B is the left child of A.

G: Finally, G is the right child of B.

Putting it all together, we get the preorder traversal: FAEKCDHGB.

Explanation

• Tomorrow is one day ahead.
• The day after tomorrow is two days ahead.
• The day after the day after tomorrow is three days ahead.

• Thursday (3 days ahead) -> Wednesday (2 days ahead) -> Tuesday (1 day ahead) -> Monday (today).

Explanation

Let's break it down step by step:

1. Four to the left of G:

The alphabet sequence is A B C D E F G.

Four positions to the left of G would be C (G -> F -> E -> D -> C).

2. Immediately to the left of C:

The letter immediately to the left of C is B.

3. Three to the right of B:

Starting from B and moving three positions to the right: B -> C -> D -> E.

So, the letter three positions to the right of B is E.

Explanation

To find the total number of handshakes, we use the combination formula since each member shakes hands with every other member exactly once before and after the meeting.

Number of members = 12

Handshakes before the meeting = 12C2 = (12 × 11) / 2 = 66

Handshakes after the meeting = 66

Total handshakes = 66 + 66 = 132

Explanation

To convert 3 4/5 to a decimal:

3 + 4/5 = 3 + 0.8 = 3.8

Explanation

To find the fraction of work left undone, calculate the total work completed:

Day 1: 3/8

Day 2: 1/4 = 2/8 (common denominator)

Total work completed = 3/8 + 2/8 = 5/8

Work left undone = 1 - 5/8 = 3/8

Explanation

To find the original price of the shirt, let's denote the original price as x. Since the price increased by 20%, the new price is 120% of the original price, or 1.2x.

Given that the new price is Rs. 480, we can set up the equation:

1.2x = 480

To solve for x, divide both sides by 1.2:

x = 480 / 1.2

x = 400

So, the original price of the shirt is 400.

Explanation

The equation is x² - 4 = 0.

x² = 4

x = ±2

There are two solutions: x = 2 and x = -2.

Explanation

Given the average of 10, k, and 30 is 21:

(10 + k + 30) / 3 = 21

Multiply both sides by 3:

10 + k + 30 = 63

Combine constants:

40 + k = 63

Subtract 40 from both sides:

k = 23

Explanation

A subset is a set whose elements are all contained within another set.

Given the set {b, c, d}, both {b} and {} (the empty set) are subsets of {b, c, d}.