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### Transcript of Bhavitha 24.02.2011 EM Maths

&&&&&&&&&W W W . S A K S H I . C O M / V I D Y A / B H A V I T H A.-= .- r.. --.-- : oe a+aaa++Connectives: 1. and 2. or 3. if... then 4. if and only if Compound Statements: 1.Disjunction 2. Conjunction 3. Conditional4. BiconditionalFunction: f:AB, 1. if for every aAthere is b B such that (a/b)fOne-one function (injection): f(x1) = f(x2) x1= x2Arithmetic progression(A.P) difference (d) is equalGeneral form of A.P a, a + d, a + 2d, ....Modulus of 'x', |x| |x| = x if x > 0 or - xif x < 0 or 0 if x = 0|x| = a solution: x=a or x= - aQuadratic equation ax2+ bx+c=0Discriminent = b24ac > 0 Roots are real, unequalSexagesimal system DegreeCentesimal system gradeCircular measure RadianConvex Set: X is convex if the line segment joining any two points P, Q in x is contained in xLinear programming problem L.P.P consists of Minimising/maximising a function f = ax+by, a, bR subject to certain constraints Circum center Concurrence point of perpendicular bisector of the sides of the Triangle.In center concurrence point of angle bisector of the Triangle.Equation of X-axis y = KEquation of Y-axis x = KSlope of X-axis 010thMATHEMATICSBITBANK SPECIAL Practice Bits Important Questions Question Trends Preparation Tips Quick Review10thMATHEMATICSBITBANK SPECIALQUICK RE'VIEW': ,r --.-- a+ ..o aa++2p or not p is example forMATHEMATICS BIT BANKSTATEMENTS, SETSSTATEMENTS1. The terms which connect two statements arecalled ________2. If the switch P is OFF we represent it by________3. The complement law using is ________4. The truth value of (32) (2=3) is _______5. The statement of the form If...... then.......is called an ________6. Acombination of one or more simple state-ments with a connective is called a _______ 7. The symbol for existential quantifier________ (June 2009), (June 2008)8. ~(p q) = ________9. The contrapositive of If a polygen is asquare then it is a rectangle is _________ 10. p, q, r are threee statements then p (q r)= (p q) (q r) is ________ law11. For all or For every is called ________quantifier.12. If p and q are switches. The combination ofp q is called _____________________13. p and q are two statements. The symbolicform of Converse of a conditional is equiv-alent to its inverse is ____________14. The statement which uses the connectiveOR is called a __________________15. The truth value of (4 7 = 20) (47=1)is ___________________16. P is the statement then ~(~(~p)) is _______17. The symbolic form of If x is not odd thenx2is odd ___________________18. p: It is raining, q: The sun is shining .Connect p,q using conjuction is ________19. Denial of a statement is called its ________20. p and q are two statements then example fortautology is ________________21. p(~p) is very simple example of a ______(June 2009)22. ~(pq) __________ (June 2009)23. Pp = p. This is ________ law. (June 2010)24. The symbol of Universal Quantifier is________ (March 2009)25. ~(pq) (~p) (~q) is _________ law.(June 2008)26. p(qr) (pr) (pr) is ______ law.(March 2008)27. The truth value of implication statement : If 3 2 = 5 then 1 0 = 0 is _________(March 2008)28. The last column of truth table contains onlyF it is called _________________29. p or not p is example for ___________30. The inverse of ~p ~q is __________SETS1. If Aand B are disjoint sets, then n(A B) =____________ (June 2009)2. If AB then AB = _______(June 2009)3. The complement of is ____________(March 2009)4. n() = _________ (March 2009)5. If A B then A B = ______(June 2008)6. If AB and BA then ______ (June 2008)7. A A' = ________ (June 2008)8. If AB and n(A) = 5, n(B) = 6 then n(AB)= _______ (March 2008)9. The set builder form of B = {1,8,27,64,125}is ________ (March 2008)10. (A B)' = ________ (March 2010)11. If A = {3,4}, B = {4,5} then n (AB) =_________12. (A B) (AC) = _________13. If Asand B are two sets then A B = _____14. If AB, n(A) = 10 and n(B) = 15 then n(A-B) = _________15. If AB = , n(AB) = 12 then n(AB) =__________16. If A, B, C are three sets A(BC) = ______17. n(AB) = 8, n(AB) = 2, n(B) = 3 thenn(A) = _________18. If A= {x; x 5, x N}, B = {2,3,6,8} thenAB = ________19. If A, B are disjoint sets n(A) = 4, n(AB) =12 then n(B) = _________20. (A B)' = A' B' is ________ law.21. A, B are two sets then x (A B) = _____22. A B and n(A) = 5, n(B) = 6 then n(AB)= _______23. The sets which are having same cardnialnumbers are called __________24. If Ahas n elements then the number of ele-ments in proper sub set is ________25. If A and B are disjoint sets then n(AB) =______________26. If n(A) = 7, n(B) = 5 then the maximumnumber of elements in AB is _________27. If AB = then BA = _____________28. If any law of quality of sets, if we inter-change and and and the resultinglaw also true, this is known as ___________29. A B' = _________30. A, B are subsets of then A B' = _____FUNCTIONS1. If f(A) = B then f : AB is a/an _________function (June 2009)2. Let f : RR be defined by f(x) = 3x+2, thenthe element of the domain of f which has 11 as image is _______________3. Range of a constant function is a _____ set.4. If f : NN is defined by f(x) = x+1, then therange of f is __________ (June 2009)5. If f(x) = xx, then f is a/an ___________function (June 2009), ( March 2008)6. If f(x) = x2 x + 6 then f(4) = ___________(March 2008)7. f(x) = x2+ 4x 12,what are the zeros of f(x)__________ (March 2008)8. f(x) = x3, g(x) = x22 for xR then (gof)(x)= ________ (March 2008)9. f(x) = x2+ 2x K and if f(2) = 8 then k=_________ (June 2007)10. f : AB is an objective and if n(A) = 4 thenn (B) = _________ (June 2007)11. If f(x) = x then the function f is _________(June 2010)12. A function is one - one and on-to then thefunction is _________ (June 2010)13. If f = {(1,2),(2,3),(3,1)} then f1(2) = _____14. If f is Identity function f(5) = ___________15. If f(x1) = f(x2) x1= x2then f is ________function.16. f : AB and f (x) = cxAthen f is ______17. If f : AB such that f (A) B then f is_________18. f = {(1,2), (2,3), (3,4)}, g = {(2,5), (3,6),(4,7)} then fog = __________19. The domain of the function is_______20. f : AB and f(x) = 2x +5 then the inverseof f is ___________21. If f(x) = then _______22. The range of constant function is ________23. If f = {(1,2), (2,3), (3,4), (4,1)} then fof =_________24. If f(x) = ax + b and f (2) = 6 then the rela-tion between a and b is _______25. f(x) = x + 2 and g (x) = 2x1 then f (1) -g(-1) = ________[ ] fo(fof ) (x) = x21x 16 K.Umamaheswara ReddySr. TeacherBeechupallyBITBANK Written byKEY1. Connectivities 2. P13. (p (~p)) f 4. True5. conditional (or) implication 6. Compoundstatement 7. ; 8. ~p q (or) p ~q 9. If apolygon is not a rectangle then it is not asquare. 10. Distributive law. 11. Universal 12.Parallel combination 13. (q p) ~(p q)14. Disjuction 15. True 16. ~p 17. x is notodd x2is odd 18. p q 19. Negation 20.p(~q) 21. contradiction 22. ~p~q 23. idem-potent law 24. 25. De morgans law 26. dis-tributive law 27. True 28. contradiction 29.Tautology 30. p q4 Marks1. Using element wise prove that A (B C)= (A B) (A C)2. Prove that A (B C) = (AB) (A C)3. Let A,B are two subsets of a Universal set show that A B = A B1= B A14. Prove that (A B)1= A1 B12 Marks1. Define implication and write truth table?2. Write the truth table (~P) (P q).3. Write the converse, inverse and contrapa-sitive of the conditional If in a triangleABC, AB > AC then C > B.4. If A B = then show that B A1= B5. Using element wise proof show that A B= AB16. If A,B are any two sets, prove that A1-B1=BA7. Show that A B = , implies A= and B= .1 Mark1. Define Tautology and contradiction?2. Write Truth table for conjunction?3. Prove that (A1)1= A4. Write contrapasitive of a conditional Iftwo triangles are congruent then they aresimilar.5. Show that P (~P) is contradiction.6. If A = {1,2,3}, B={2,3,4} then find AB.7. Write set-builder form of8. Prove that A B Afor any two sets A, B. 9. Prove that ~(~P) = P1 1 1 1 1A 1, , , , ,2 3 4 5 6 = STATEMENTS AND SETS: Important QuestionsKEY1. n(A)+n(B) 2. A 3. 4. 0 5. B 6. A = B 7. 8. 6 9. {x/x = n3, n N, n 5} 10. A' B' 11.4 12. A (B C) 13. (AB)-(AB) (or) (A-B) (B-A) 14. 0 15. 12 16. (A-B)(A-C) 17.7 18. {2,3} 19. 8 20. De Morgans law 21. xAand x B 22. 6 23. equivalent sets 24. 2n-2 25. 0 26. 5 27. B 28. Principle of duality 29.AB 30. A-BpqA B: ,r --.-- a+ ..o aa++3f : AB and B R then f is.. MATHEMATICS BIT BANKPOLYNOMIALS OVERINTEGERS26. If a function is both one-one and on-to thenthe function is _________27. f : AB is a function then B is called _____28. f : AB such that f (A) = B then f is ______29. f : AB and B R then f is ___________30. A constant function f : NN is defined byf (x) = 5 then f (15) = _______31. _____32. The range of the function f = {(a,x), (b,y),(c,z)} is ________33. The inverse of a function will be a functionagain if it is _________34. If f : x log2x then f (16) = __________35. The set builder form of R = {(1,3), (2,4), (3,5)} is ________36. f1(x) = x3, g1(x) = x1 then (fog)1=_________37. What is the zeros of the adjacent function is_________38. Number of elements in {3,5,7,9} {4,6,8}is __________39. A function f : AB is said to be ________function, if for all y B there exists x Asuch that f (x) = y.40. If f(x) = 2x, g(x) = 3x + 2 then (fog) (2) =________41. f(x) = x+1, then 3f(2)2f(3) = ________42. f = {(x,1004)/x N} then f is ________43. The condition to define gof is ________44. Let f : RR, f(x) = 6x+5 then f1(x) = ____45. If f(x) = 2x 3 the value of is ________POLYNOMIALS OVER INTEGERS1. Product of the roots of equation x2(a+b)x = c is ________2. If , are the roots of the equation 2x29x+8 = 0 then + = ________3. The line y = mx+c cuts the y-axi