Q 1 . Define Relation with example. Explain various types of relations with example.

Relation को उदाहरण के साथ परिभाषित करें। विभिन्न प्रकार के relations को उदाहरण देकर समझाइए। Q 2: Let f (x) = 2x+3, g(x) = 3x+4 and h(x) = 4x for x ∈ R.Where R is set of real numbers. Find gof, fo8, foh and goh. Q 3: Using mathematical induction show that Q 4: State and prove Pigeonhole principle with an example.

Pigeonhole सिद्धान्त को लिखें एवं उदाहरण के साथ सिद्ध करें। Q5:What do you mean by Algebraic structures? Explain its different properties.

Algebraic structures से आप क्या समझते है? इसकी विभिन्न properties को समझाइए। Q 6: Differentiate between Homomorphism and Isomorphism Q 7: Differentiate between Rings and fields Q 8: Show that the algebraic structure { (a+b root 2 : a,b∈I }.+ } forms a group. Q 9: Establish the validity of argument using to role of contradiction. Q 10: Show that the following are Tautologies. Q 11: Explain universal and existential quantities with example. Q 12: Define the following. i) Planar graph ii) Multigraph iii) Euler graph Q 13 Determine shortest path between vertices 'a' and 'z' in graph. Q 14: Solve the recurrence relation. a_{n} = a_{ n-1} + 6 a _{n -2} giving initial condition a_{0}= 3 and a_{1}=6.
Q 15: When it can be said that two graph G1 and G2 are isomorphic?
Q 16 : Write short notes on Binomial theorem
Q 17: Write short notes on Multinomial coefficient
Q 18: Write short notes on Lattices
Q 19: Write short notes on Hasse diagrams

Relation को उदाहरण के साथ परिभाषित करें। विभिन्न प्रकार के relations को उदाहरण देकर समझाइए। Q 2: Let f (x) = 2x+3, g(x) = 3x+4 and h(x) = 4x for x ∈ R.Where R is set of real numbers. Find gof, fo8, foh and goh. Q 3: Using mathematical induction show that Q 4: State and prove Pigeonhole principle with an example.

Pigeonhole सिद्धान्त को लिखें एवं उदाहरण के साथ सिद्ध करें। Q5:What do you mean by Algebraic structures? Explain its different properties.

Algebraic structures से आप क्या समझते है? इसकी विभिन्न properties को समझाइए। Q 6: Differentiate between Homomorphism and Isomorphism Q 7: Differentiate between Rings and fields Q 8: Show that the algebraic structure { (a+b root 2 : a,b∈I }.+ } forms a group. Q 9: Establish the validity of argument using to role of contradiction. Q 10: Show that the following are Tautologies. Q 11: Explain universal and existential quantities with example. Q 12: Define the following. i) Planar graph ii) Multigraph iii) Euler graph Q 13 Determine shortest path between vertices 'a' and 'z' in graph. Q 14: Solve the recurrence relation. a

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