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In the following question, two statements are given each followed by two conclusions I and II. You have to consider the statements to be true even ifthey seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements. Statements:
(I) Empty set is a subset of any set.
(II) A set is a subset of power set. Conclusion:
(I) Empty set is a power set.
(II) A set is a subset of power set.
Of 30 integers, 12 are in set A , 22 are in set A , 22 are in set B , and 7 are in both set A and B. How many of the integers in NITTHER set A nor set B?
Below are given some specific features in research as Set - I while their descriptive explanations in Set - II. Match the items of Set - I with that of Set - II and choose correct code : Set - I (Features) Set – II           (Descriptive explanations) (a) Empiricism (i) Data collection and analysis procedure from which only one interpretation can be made (b) Precision (ii) Results can be confirmed or revised insubsequent research (c) Parsimonious explanation   (iii) Guided by evidence obtained from systematic research methods (d) Verification   (iv) Reduce complex realities to simple explanation of phenomena (e) Adler (v) Extensive and detailed description including instrument validity and reliability
Given below are sets. Set I mentions some terms from the Preamble to the Constitution of India and Set II gives their explanation. Match the item from Set I with explanation from Set II. Set I (Terms) Set II (Explanation) (a) Socialism (i) State ha no religion, it is neither pro nor against any religion (b) Secularism (ii) a system in which government is elected and managed by the people of the country (c) Democacy (iii) Political idea that all people are equal and resources should be equally shared (d) Republic (iv) a nation state that has an elected government and elected leader   Select correct answer from the following options:
Consider the following statements: 1. The null set is a subset of every set. 2. Every set is a subset of itself. 3. If a set has 10 elements, then its power set will have 1024 elements. Which of the above statements are correct?
Let N be the set of natural numbers. Consider the following sets. P: Set of Rational numbers (positive and negative) Q: Set of functions from {0, 1} to N R: Set of functions from N to {0, 1} S: Set of finite subsets of N. Which of the sets above are countable?
Suppose on performing reduced error pruning, we collapsed a node and observed an improvement in the prediction accuracy on the validation set. Which among the following statements are possible in light of the performance improvement observed? (a) The collapsed node helped overcome the effect of one or more noise affected data points in the training set (b) The validation set had one or more noise affected data points in the region corresponding to the collapsed node (c) The validation set did not have any data points along at least one of the collapsed branches (d) The validation set did have data points adversely affected by the collapsed node
Mark the incorrect proposition:
1. Set-off is a statutory defence to a plaintiff's action, whereas a counterclaim is a cross-action.
2. Set-off and counter-claim arises out of the same transaction.
3. Set-off should not be barred on the date of the suit while counter-claim should not be barred on the date of filing of written statement.
4. Claim for set-off cannot exceed plaintiff's claim, whereas counterclaim can exceed the plaintiffs claim.
5. Both set-off and counter-claim cannot exceed the pecuniary jurisdiction of the court.
The average of a set of 12 numbers, which includes 35, is N. If 35 is removed from the set and 38 is added to the set, then what is the average of the new set of numbers in terms of N ?
The average of a set of 12 numbers, which includes 34, is A. If 34 is removed from the set and 38 is included to the set , what is the average of the new set of numbers in terms of A ?