Kothari Interview Questions and Answers

To create a uniform distribution from 1 to 200 using an unbiased coin, we can use the rejection sampling method.

• Divide the range into equal parts based on the number of outcomes of the coin toss.

• Toss the coin and select the corresponding part of the range.

• If the selected number is outside the desired range, reject it and repeat the process.

• Repeat until a number within the desired range is obtained.

• Example: If the coin ...read more

Expected number of tosses of a fair coin to get 3 consecutive heads.

• The probability of getting 3 consecutive heads is 1/8

• The expected number of tosses to get 3 consecutive heads is 14

• This can be calculated using the formula E(X) = 2^k + 2^(k-1) + 2^(k-2) + ... + 2^2 + 2^1 + 2^0, where k is the number of consecutive heads required

Go second. The probability of winning is higher when going second.

• The probability of winning when going first is (1/n+1), while the probability of winning when going second is (n/n+1)

• This is because the first player has a chance of drawing the black ball on their turn, while the second player has a chance of drawing the black ball on their turn or the first player's turn

• For example, if there are 10 red balls and 1 blac...read more

What is the most likely value of the last roll in a game where a die is rolled until the sum of all rolls is at least 100?

• The last roll must be at least 4 to reach a sum of 100

• The probability of rolling a 4, 5, or 6 is 1/2

• The most likely value of the last roll is 4 or 5

Algorithm to search for a number in an n x n matrix with sorted rows and columns.

• Start from the top-right corner of the matrix

• If the current element is greater than the target, move left

• If the current element is less than the target, move down

• Repeat until the target is found or the bottom-left corner is reached

Algorithm to find largest common subarray of two arrays of size n

• Create a 2D array to store the lengths of common subarrays

• Traverse both arrays and fill the 2D array with lengths of common subarrays

• Find the maximum length and its corresponding ending index in the 2D array

• Use the ending index to retrieve the largest common subarray from either of the arrays

I am excited to join Goldman Sachs because of its reputation for excellence and the opportunities it offers for professional growth.

• Goldman Sachs is a leader in the financial industry and has a strong reputation for excellence.

• I am impressed by the firm's commitment to innovation and its focus on delivering value to clients.

• I believe that working at Goldman Sachs will provide me with the opportunity to learn from some ...read more

I have experience in marketing and sales, with a focus on digital marketing and lead generation.

• Started career as a marketing intern at XYZ company

• Managed social media accounts and email campaigns for ABC company

• Implemented SEO strategies and increased website traffic by 30%

• Led a team of 5 sales representatives and exceeded quarterly sales goals by 20%

• Currently working as a digital marketing specialist at DEF company

Probability of a randomly dropped rod of length L intersecting a line on a 2D plane with infinite parallel, vertical lines.

• The probability depends on the length of the rod L.

• The probability can be calculated using geometric probability.

• The probability is 1 - (2L - 1) / infinity.

• For example, if L = 1, the probability is 0.5.

• If L = 2, the probability is 0.75.

Find the magic number in a sorted array where value and index are same.

• Iterate through the array and check if the value and index are same

• If found, return the value

• If not found, return -1

Searching an element in a sorted 2D matrix

• Start from the top-right corner or bottom-left corner

• Compare the target element with the current element

• Move left or down if the target is smaller or move right or up if the target is larger

Design a newspaper subscription system

• Create a user registration system

• Allow users to select subscription plan and payment method

• Provide options for delivery frequency and start/end dates

• Send reminders for subscription renewal

• Allow users to modify or cancel subscription

• Track subscription history and payment records

Number of ways to jump n stairs if a person can climb 1 or 2 stairs.

• Use dynamic programming to solve the problem.

• The number of ways to jump n stairs is equal to the sum of ways to jump n-1 stairs and ways to jump n-2 stairs.

• Base cases: if n=0, return 1 and if n=1, return 1.

An LRU cache can be made using a doubly linked list and a hash map.

• Create a doubly linked list to store the cache items.

• Create a hash map to store the key-value pairs.

• When a new item is added, check if the cache is full. If it is, remove the least recently used item from the linked list and hash map.

• When an item is accessed, move it to the front of the linked list.

• When an item is removed, remove it from both the linked

Probability of winning a dice game where the one with lesser number wins.

• The probability of winning depends on the number of sides on the dice.

• If the dice has an odd number of sides, the probability of winning is higher for the second player.

• If the dice has an even number of sides, the probability of winning is equal for both players.

Compute working days using given functions f, g, and h.

• To compute the 3rd working day, apply function g three times to function f.

• To compute the 2nd working day of the previous month, apply function h to function f, then apply function g twice.

• To compute the 4th working day of the next month, apply function g four times to function f.

Linked list algorithms involve operations on linked lists, such as insertion, deletion, and traversal.

• Linked list algorithms are used to manipulate data stored in linked lists.

• Common operations include inserting a new node, deleting a node, and traversing the list.

• Examples of linked list algorithms include reversing a linked list, finding the middle node, and detecting a loop in the list.