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The following sentences form a paragraph. These four parts are numbered as P, Q, R and S. They are not given in their proper order. Read the sentences and choose the alternative that arranges them in correct order. P. Inverse problem refers to the scientific problem of estimating the different causes that led to a particular outcome.  Q. This is in contrast to the forward or the direct problem where scientists try to find the outcome that results from a series of causes. R. A scientist observing a photograph, for instance, would be faced with the inverse problem while trying to figure out the various causal factors that combined to form the final photograph. The inverse problem is applied to understand processes in a wide variety of sciences. S. Scientists trying to understand an observation may at times have to work backwards to estimate the causal factors behind it.
In the question given below are two conclusions followed by five statements. You have to choose the correct set of statements that logically satisfies conclusions. Conclusions: I. Some Star are Moon II. Some Sun are not Mars Statements: I. Some Sun are Moon, Some Moon are star and No star is Mars. II. Some Sun are Moon, All Moon are Star and No Star is Mars. III. All Sun are Moon, All Moon are Star and Some Star are Mars. IV. All Sun are Moon, Some Moon are Star and No Star is Mars. V. Some Sun are Moon, Some Moon are Star and No Moon is Mars.
Given below are some statements, followed by some conclusions. Assume the facts in the statements to be true and decide which of the conclusions logically follow(s) from the statements. Statement: Some bags are stickers. Some stickers are stamp. Some stamps are paints. Conclusion: 1. Some bags are stamps. 2. Some stickers are paints. 3. Some paints are stamps. 4. Some paints are stickers.
If for sets A and B there exists an injective function but not bijective function from A to B then?
In each of the following question below are given some statements followed by some conclusions. Taking the given statements to be true even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusion logically follows the given statements. Statements: I. Some knifes are spoons. II. Some forks are knifes. III. No fork is a green. Conclusions: I. Some spoons are forks. II. Some knifes are green. III. Some green are not knifes. IV. Some knifes are not green. 
In each of the following question below are given some statements followed by some conclusions. Taking the given statements to be true even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusion logically follows the given statements. Statements: I. Some men are hardworking. II. No blue is a advocate. III. Some blue are men. Conclusions: I. Some blue are hardworking. II. Some men are advocate. III. Some blue are not hardworking. IV. Some men are not advocate.
In each of the following question below are given some statements followed by some conclusions. Taking the given statements to be true even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusion logically follows the given statements. Statements: I. Some cups are plates. II. All spoons are blue. III. No plates are spoon. Conclusions: I. Some cups are not spoon. II. Some plates are not blue. III. Some cups are not blue. IV. Some blue are not plates.
In the following question below are given some statements followed by some conclusions. Taking the given statements to be true even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusion logically follows the given statements. Statements:   Some cats are dogs. No cat is cow. All cats are bull. Conclusions:  I) Some cows are not dog. II) Some dogs are not cow. III) Some cows are not bull. IV) Some bulls are not cow.
In each of the following question below are given some statements followed by some conclusions. Taking the given statements to be true even if theyseem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. Some cups are plates.
II. All spoons are blue.
III. No plates are spoon.
Conclusions:
I. Some cups are not spoon.
II. Some plates are not blue.
III. Some cups are not blue.
IV. Some blue are not plates.
Which of the following statements is/are true:  If f is a bijective function then f is invertible If f: A → B and g: B → C are invertible functions then g o f is also invertible function. (g o f)-1 = f-1 o g-1