Solution

Total distance =6010=600 km

New speed =600/4=150 km/hr

Increase in speed =150-60=90 km/hr

Solution

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Speed of the train relative to man =66-6=60 km/hr

Solution

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N = H.C.F of (4665 - 1305), (6905 - 4665) and (6905 - 1305)

N = H.C.F of 3360, 2240 and 5600

N = 1120

Sum of digits in N is = 1 + 1 + 2 + 0 = 4

Solution

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Gullible means being easily persuaded to believe something.

Solution

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Passing cloud means something that lasts only for a short period of time.

Solution

Only Option c) is grammatically correct.

Solution

It is given in the passage ‘PK will be remembered for his famous vocal tonic - those legendary pre-match pep talks he delivered to inspire players to defy odds.’

Solution

Here cursor-> link() moves the cursor to the next node and that was assigned to cursor itself, hence now it is pointing to the next pointer.

Solution

Solution

Perfect Binary Tree: A Binary tree is a Perfect Binary Tree in which all internal nodes have two children and all leaves are at the same level.

A Perfect Binary Tree of height h (where height is the number of nodes on path from root to leaf) has (2^h) – 1 node.

Solution

The asyncio.gather() function is used to concurrently execute multiple coroutines and wait for all of them to complete. It returns a list of results in the same order as the input coroutines. In this case, it ensures that all three fetch_data coroutines run concurrently, making the overall execution more efficient.

Solution

Polymorphism is the ability of objects of different types to be treated as if they were of the same type. In this code, both Dog and Cat inherit from the Animal class. However, they implement the speak() method differently, demonstrating polymorphism. When we call the speak() method on either dog or cat, the appropriate implementation is invoked based on the object's type.

Solution

A closure in Python is a function that remembers and has access to variables from its enclosing scope, even after the outer function has finished executing.

Solution

This dictionary comprehension iterates over each tuple in the data list, unpacking the tuple into x and y. It then creates a key-value pair in the dictionary, where x is the key and y is the value.

Solution

While the with statement simplifies file operations, its primary purpose is to ensure proper resource management, especially in case of exceptions.

Solution

It filters the infinite sequence generated by infinite_sequence() to include only the first 10 even numbers.

Solution

L =(n-1)I+1 where L= no. of leaf nodes, I= Internal Node

41 = (n-1)10+1

41 = 10n - 10+1

10n= 41-1+10

N = 5

Solution

• In a MAX heap the smallest values of the heap will always be present on the last level of heap and time complexity of reaching the last level of heap is O(n).
• We have to search all the elements to reach the smallest element and heap using linear search.
• To traverse all elements using linear search will take O(n) time.

Solution

P: True. All input orderings give the worst case running time. The running time doesn’t depend on the order of the inputs in any significant way

Q: True: Using base 10, each integer has d = logn^5 = 5 logn digits. Each counting sort call takes Θ(n+10) = Θ(n) time, so the running time of Radix sort is Θ(nd) = Θ(nlogn).

Solution

Q: Dijkstra will visit the vertices in the following order: S, C, A, D, F, E, B. Dijkstra will relax the edge from D to E before the edge from F to E, since D is closer to S than F.

Solution

Here, we can get the first item using profit per weight even if we are using a 0/1 knapsack.

→ According to the above Profit/weight ratio, the item-1 has maximum profit. So, pick item-1.

→ Now M=7, Pick item-2 because it has more profit.

→ Now M=5, Now according to profit/weight ratio we can pick item-3 or item-5 but item-5 has more weight, so it exceeds capacity. If we are selecting item-3 means we are wasting 1 slot. So, here, profit/weight ratio fails. So, follow brute force technique in this position. We can pick item-4 because it has weight 5.

→ Now, M=0 and Profit=19. [item1 + item2 + item4]

Note: In exam time, we have enough time, so cross verify once again your procedure and answer.

Solution

There may be many possibilities to reach the same city to cover all other cities but the minimum distance is 10. And the shortest possible route is A-C-E-B-D-A

Solution

A transaction is said to follow Two Phase Locking protocol if Locking and Unlocking can be done in two phases.

1. Growing Phase: New locks on data items may be acquired but none can be released.
2. Shrinking Phase: Existing locks may be released but no new locks can be acquired.

Solution

From the given properties of the columns, only A and B are good for indexing.

Solution

• From the given set of functional dependencies, it can be observed that B is a candidate key of R.
• So all 300 values of B must be unique in R.
• There is no functional dependency given for S.
• To get the maximum number of tuples in output, there can be two possibilities for S.

1) All 200 values of B in S are the same and there is an entry in R that matches with this value. In this case, we get 200 tuples in output.

2) All 200 values of B in S are different and these values are present in R also. In this case also, we get 200 tuples.

Solution

If a functional dependency X->Y holds true where Y is not a subset of X then this dependency is called non trivial Functional dependency

Solution

Data discretization involves converting continuous data into discrete categories, often for classification tasks.

Solution

Each sales transaction can occur in any of the 100 regions, but each entry in the fact table represents a unique transaction-region pair. So the fact table will have:

500,000 * 100 = 50,000,000 entries

Solution

There are 24 hours in a day and 60 minutes per hour. The total number of data points before downsampling is:

24 * 60 = 1440 samples

After downsampling to 1 reading per hour, the number of samples will be:

24 samples

Solution

Solution

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Solution

Since X is uniformly distributed between [0, 1]

Solution

The probability of having 2 defective gearwheels is 0.2613

The probability of having more than 2 defective gearwheels is

1 − (the sum of the probabilities of having 0, 1, and 2 defective gearwheels),

i.e.

1 − (0.0907 + 0.2177 + 0.2613), that is, 0.4303

Solution

Let A = Probability of A hit target = ⅖

Solution

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The above matrix is the resulting matrix. Hence convert the above matrix in equation form to get the values of x, y, z.

From this set, we can automatically observe that the value of the variable y is equal to 0. Now by using this knowledge to substitute it on the second equation to solve for z, and then substitute both y and z values on the first equation to solve for x

Solution

Solution

We must find all solutions to Ax = 0. Reducing the augmented matrix of this system yields

Since the two vectors in this spanning set are not proportional, they are linearly independent. Consequently, a basis for nullspace(A) is {(−9, 7, 1, 0), (−10, 7, 0, 1)}.

Solution

is not considered because there are no real values of a1 and a2.

Therefore, the given function f is one-one.

Solution

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Solution

Given:

∫ cos(x) dx = sin(x) + C

Evaluate the definite integral

Solution

Perceptron always gives a linear decision boundary. However, for the Implementation of the XOR function, we need a non-linear decision boundary.

Solution

For option (d), the gradients will be higher for small values of parameters. Activation functions like signmoid and tanh saturate at large values.

Solution

The SVM effectiveness depends upon how you choose the basic 3 requirements mentioned above in such a way that it maximizes your efficiency and reduces error and overfitting.

Solution

w0=1,w1=1,w2=−1

Explanation:

The perceptron function is:

f(x) = w0 * x0 + w1 * x1 + w2 * b1

where b1 = 1 and the threshold function outputs 1 if f(x) > 0, otherwise 0.

Substituting w0 = 1, w1 = 1, and w2 = -1:

f(x) = 1 * x0 + 1 * x1 - 1 * 1

Let's evaluate for all possible inputs:

Solution

Substituting w0 = 1, w1 = 1, and w2 = 0:

f(x) = 1 * x0 + 1 * x1 + 0 * 1

Evaluate for all inputs:

Solution

False positives are the emails incorrectly classified as spam:

FP = Detected spam emails - True positives = 150 - 50 = 100

False negatives are the actual spam emails that were not detected as spam:

FN = Total spam emails - True positives = 300 - 50 = 250

Precision = True positives (TP) / (True positives (TP) + False positives (FP))

Precision = 50 / (50 + 100) = 50 / 150 = 33.33%

Recall = True positives (TP) / (True positives (TP) + False negatives (FN))

Recall = 50 / (50 + 250) = 50 / 300 = 16.66%

Solution

4*1 + 10*2 +5*3 + 20*4

Solution

Since

h(n)=5 exceeds the actual cost of 3, the heuristic overestimates, violating admissibility and potentially leading A* to a suboptimal path

Solution

A* Search is optimal with a consistent heuristic, as it ensures that each node expansion yields the lowest-cost path possible.

Solution

Solution

Minimax assumes that both players are playing optimally: the maximizer tries to maximize their score, and the minimizer tries to minimize the score.