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CBSE 12 Mathematics, Chapter 1 (Relations and functions), Important Questions Unsolved, , , , SECTION -A, , Q.1: If.a*b denotes the larger of ‘a’ and ‘b and if a0 b = (a*b) + 3, then write the, value of (5) o (10), where * and o are binary operations., , Q.2: Let * bea binary operation defined by a* b = 2a + b -3. Find 3* 4., , Q.3: Let * bea binary operation on N given by a + b = HCF (a,b) a,b EN. Write, the value of 22 + 4., , Q.4: If: R > R be defined by f(x) =(3 — x*)/, then find f of (x)., , Q.5: Let A = {1,2,3},B = {4,5,6, 7} and let f = {(1,4), (2, 5), (3, 6)} bea function, from A to B. State whether f is one-one or not., , Q.6: The binary operation *: R x R > R, is defined as a*b = 2a + b. find (2*3)*4., , Q.7: If(R) = {(x, y):x+ 2y = 8} isa relation on N, write the range of R., , Q.8: If f(x) =x+7 and g(x) =x-7,xeR,, find (fog) (7)., , Q.9: If binary operation * on the set of integers Z, is defined by a « b = a + 3b”, then, find the value 2 * 4., , Q. 10: What is the range of the function:, , Ix-11,, , =o, , , , Ema y 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com

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Q.11:; State the reason for the relation R in the set {1, 2, 3} given by R = {(1,2), (2, 1)}, not to be transitive., , Q.12:; Let * be a ‘binary’ operation on N given by a * b = LCM (a,b)Va,beN., , Q.13: Let * bea binary operation, on the set of all non- zero real number, given by, ab, a*xb= = fora beR— {0}., , Find the value of x,given that 2 (x * 5) = 10., , Er eRe iy 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com, , , , SECTION - B, , Q.14: Let f : R > R be defined as f(x) = 10x + 7. Find the function g : R > R such, that g of = fog = Ip., , Q.15: A binary operation * on the set {0, 1, 2,3, 4,5} is defined as, axb={ a+b, if a+b<6, a+b—-6 if a+b>6, , Show that zero is the identify for this operation and each element ‘a’ of the set is, invertible with 6 — a, being the inverse of ‘a’., , Q. 16: (é Is The binary operation *, defined on set N, given by, , b F aa . 7, a*b= a for alla, b € Q,commutative? (ii) is the above binary operation *, associative?, , Q.17: Prove that the relation R in the set, , A= {1,2,3,4,5} given by R = {(a,b):|a — b| is even}, is an equivalence, relation., , Q.18: Let Z be the set of all integers and R be the relation on Z defined as, R= {(a,b):a,b € Zand (a — b) is divisible by 5. } Prove that R is an, equivalence relation., , eRe Hy 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com

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Q.19: Consider the binary operation * on the set {1, 2, 3, 4, 5} defined by, a» b = min{a, b}. Write the operation table of the operation *., , Q.20: Let A =IR - {3} and B = IR - {1}. Consider the function fA — B defined by, , —2, = 5) . show that f is one — one and onto and hence find f~1, , , , fo =(, , x, Q. 21: Let A= {1,2,3,.....,} and R be the relation in A x A defined by, (a,b) R (c,d) ifa +d =b+cfor(a,b),(c,d) inA x A. Prove that R is an, equivalence relation. Also obtain the equivalence class [(2,5)]., , Q. 22: Show that the function f in A = R — {2}, , Defined as f(x) = = is one — one and onto. hence find f—1., , Q.23:; Show that the relation R defined by (a, b) R (c, d) >a +d =b +c on the setNx N, is an equivalence relation., , Q.24; Let f: N > N be defined by, , , , nt+1, , ifnis odd, fm = 2 foralln EN., 2’ if niseven, , Find whether the function f is bijective., , Q.25: Show that the relation S in the set A = {x € Z: 0 < x < 12} given by, S = {(a,b): a,b € Z,|a — b| is divisible by 4} is an equivalence relation. Find, the set of all elements related to 1., , Q.26: Let f : R > R be defined as f(x) = 10x + 7. Find the function g : R > R such, that gof= fog = Ip., , Q.27: A binary operation * on the set {0, 1, 2,3, 4,5} is defined as, _f( atb, if a+b<6, oD al Ve if at+b>6, , Show that zero is the identity for this operation and each element ‘a’ of the set is, invertible with 6 — a, being the inverse of ‘a’., , Ermey 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com

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Er eR ee Hy, , Q.28:, , Q.29:, , Q.30:, , Q.31:, , Cena, , Show that f:N — N, given by,, , x+1, if xisodd, , f= fr “1, Af xis even is both one — one and onto., , Consider the binary operations* : R x R —R defined as, a* b=|a—b| andaob =a for alla, b € R. show that ‘*’ is commutative but not, associative ‘o’ is associative but not commutative., , Consider f: R,. > [4,00)given by f (x) =x? + 4.Show that f is invertible with the, inverse f~' of given by f~* (y) =/y — 4 where R , is the set of all non — negative, real numbers., , If the function f: R > R be given by f(x) = x? + 2 and g: R > R be given by, @= xe, 9) =e ,, , -1, find fog and gof and hence find fog(2)and gof(-3)., , 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com, , EO Raony, , , , eRe Hy, , Q.32:, , Q.33:, , Q.34:, , eRe Uy, , SECTION - C, , Consider f: R > [—5,00) given by f(x) = 9x? + 6x —5., , Show that f is invertible with f-1(y) = ( ~e), , Hence Find, af"), Wy iff) =5,, , Where R., is the set of all non-negative real numbers., , Discuss the commutativity and associativity of binary operation ‘*’ defined on, A= Q-{1}by the rule a * b =a— b+ ab foralla,b € A. Also find the, identity element of * in A and hence find the invertible elements of A., , Let N denote the set of all natural numbers and R be the relation on N x N, defined by (a, b) R (c, d) if ad (b + c) = be (a +d). Show that R is an equivalence, relation., , 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com 4ono.com, , 4ono.com