List of top Mathematics Questions asked in CBSE CLASS XII, CBSE Compartment XII

Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y): x and y have same number of pages} is an equivalence relation.

Find which of the operations given above has identity.

Let * be a binary operation on the set Q of rational numbers as follows: 
(i) a * b=a−b 
(ii) a * b=a²+b²
(iii) a * b=a+ab 
(iv) a * b= (a−b)² 
(v) a * b= \(\frac {ab} {4}\)
(vi) a * b=ab²

Find which of the binary operations are commutative and which are associative. 

Let * be the binary operation on N defined by a * b=H.C.F. of a and b. Is * commutative? Is * associative? Does there exist identity for this binary operation on N?

Is * defined on the set {1,2,3,4,5} by a*b=L.C.M. of a and b a binary operation? Justify your answer.

Let * be the binary operation on N given by a*b=L.C.M. of a and b. Find 
(i) 5*7, 20*16 
(ii) Is * commutative? 
(iii) Is * associative? 
(iv) Find the identity of * in N 
(v) Which elements of N are invertible for the operation *?

Let*′ be the binary operation on the set {1,2,3,4,5} defined by a*′b=H.C.F. of a and b. Is the operation *′ same as the operation * defined in Exercise 4 above? Justify your answer.

Consider a binary operation * on the set {1,2,3,4,5} given by the following multiplication table. 
(i) Compute (2 * 3)*4 and 2 *(3 * 4) 
(ii)Is * commutative? 
(iii)Compute (2 * 3)*(4 * 5).

(Hint: use the following table)

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∨.

Determine whether or not each of the definition of given below gives a binary operation.
In the event that * is not a binary operation, give justification for this.
(i) On Z⁺, define * by a * b = a − b
(ii) On Z⁺, define * by a * b = ab
(iii) On R, define * by a * b = ab²
(iv) On Z⁺, define * by a * b = |a − b|
(v) On Z⁺, define * by a * b = a

Let f : X → Y be an invertible function. Show that the inverse of f^-1 is f, i.e., (f^-1)^-1 = f.

State with reason whether following functions have inverse

 (i) f: {1, 2, 3, 4} → {10} with
 f = {(1, 10), (2, 10), (3, 10), (4, 10)}

 (ii) g: {5, 6, 7, 8} → {1, 2, 3, 4} with
 g = {(5, 4), (6, 3), (7, 4), (8, 2)}

 (iii) h: {2, 3, 4, 5} → {7, 9, 11, 13} with
 h = {(2, 7), (3, 9), (4, 11), (5, 13)}

1. f(x)=IxI and g(x)=I5x-2I
2. f(x)=8x3 and g(x)=x1/3

Let R be the relation in the set N given by R = {(a, b): a = b − 2, b > 6}. Choose the correct answer. (A) (2, 4) ∈ R (B) (3, 8) ∈R (C) (6, 8) ∈R (D) (8, 7) ∈ R

Show that the relation R in R defined as R = {(a, b): a ≤ b}, is reflexive and transitive but not symmetric. 

Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.