1. In the set of all straight lines in a plane, the relation R “to be
Perpendicular” is-
(a) Reflexive and transitive
(b) Symmetric and transitive
(c) Symmetric
(d) None of these
Ans: (c) Symmetric
Explanation :
If line L1 is perpendicular to the line L₂ , then L₂ will also be
perpendicular to L1
If (L1, L₂) = R⇒(L₂, L1)€R
Hence, R is symmetric.
2. f: A→B will be an onto function if-
(a) f(A) C B
(b) f(A) = B
(c) f(A) )B
(d) f(A) € B
Ans: (b)-f(A) = B
Explanation :
A function is said to be onto iff Range of function is equal to co-domain of the function
.f: A B is onto iff f(A) = B
3. If f(x1) = f(x₂) ⇒ x1=x₂V, x₂६A, then what type of a function
if f: A – B ?
(a) One-one
(b) Constant
(c) Onto
(d) Many one
Ans: (a) One-one
Explanation:
If, f(x1) = f(x₂)
X1= x₂, then f(x) is one-one.
4. The operation is defined as a * b = 2a + b, then (2 * 5) * 4 is.
(a) 18
(b) 17
(c) 19
(d) 21
Ans: (a) 18
Explanation
We have,
a*b=2a+b
(2*3)*4 = (2×2+3)*4 = 7*4
= 2 × 7+4 = 18
5. Let A = {1,2,3}, which of the following function f: A → A does not have an inverse function?
(a) {(1,1),(2,2), (3,3)}
(b) {(1,2), (2,1), (3,1)}
(c) {(1,3), (3,2), (2,1)}
(d) {(1,2), (2,3), (3,1)}
Ans: (b) {(1,2), (2,1),(3,1)}
Explanation:
Any function will be an invertible function, when function is one-one and onto.
Check option (a)
Check one one :
f = {(1,1),(2,2), (3,3)}
Since each element has unique image, f is one-one. Check onto:
Since for every image, there is a corresponding
Thus f is onto.
Since function is both one-one and onto It will have inverse
f = {(1,1),(2,2), (3,3)}
f’ = {(1,1),(2,2,),(3,3)}
Check option (b)
element,