> How do you treat colinearity?

Colinearity can be handled either through variable selection, or dimensionality reduction. The right approach depends on the data. If you're trying to identify the root cause of some phenomenon, L1 regularized models will pick out variables (though they might pick the wrong one). If you just want to prevent colinear variables from taking over your model, dimensionality reduction is the right choice.

> How will you deal with unbalanced data where the ratio of negative and positive is huge?

This is one area where bayesian statistics really shines. The variance of the posterior predictive distribution for a bayesian model is inversely proportional to the amount of data you use for inference.

> How will you decide whether a customer will buy a product today or not given the income of the customer, location where the customer lives,
profession and gender? Define a machine learning algorithm for this.

Random forests are a good answer to this in terms of predictive accuracy. The problem with random forests is that they don't give you any information about how certain your estimates are. A better technique to use would be Gaussian processes (GPs). GPs are a kernel method somewhat similar to SVMs, but they have the marked advantage that they provide a posterior distribution over their estimates, rather than just the maximum likelihood value.

> Is it useful to apply PCA to your data before SVM classification?

The right answer is that it depends on the shape of your data and the specific SVM kernel/hyperparameters you're using. If you have a square matrix and you're doing linear SVM, PCA first will be slower. On the other hand, for a highly asymmetric matrix and nonlinear SVM, PCA done by stochastic approximation of the SVD, followed by SVM will be much faster. From a prediction accuracy standpoint it isn't going to make a large difference in either case since the kernel trick effectively projects your data into a high dimensionality feature space.

> From a long sorted list and a short 4 element sorted list, which algorithm will you use to search the long sorted list for 4 elements.

To answer this properly you need to know if the list has repeated elements. If there are no repeated elements then a binary search on the first element of the 4 item list, then scanning forward from there is the correct answer. If you admit the possibility of (possible massive) repetition of elements then this is no longer the case.

> How will inspect missing data and when are they important for your analysis?

This is yet another case where bayesian analysis shines (can you tell what I specialize in?). With bayesian methods you don't have to impute a value, rather you can treat unknowns as coming from a specific distribution (which can be the exactly distribution of that variable, via empirical bayes). This prevents you from introducing bias in your model.

> Estimate the probability of a disease in a particular city given that the probability of the disease on a national level is low.

This question is kind of bad given that it doesn't put a bound on what data is available to you. In terms of model, this is just a classification problem in disguise